cocoroboBlockly/static/tracking.js

/**
 * tracking - A modern approach for Computer Vision on the web.
 * @author Eduardo Lundgren <edu@rdo.io>
 * @version v1.1.3
 * @link http://trackingjs.com
 * @license BSD
 */
(function(window, undefined) {
  window.tracking = window.tracking || {};

  /**
   * Inherit the prototype methods from one constructor into another.
   *
   * Usage:
   * <pre>
   * function ParentClass(a, b) { }
   * ParentClass.prototype.foo = function(a) { }
   *
   * function ChildClass(a, b, c) {
   *   tracking.base(this, a, b);
   * }
   * tracking.inherits(ChildClass, ParentClass);
   *
   * var child = new ChildClass('a', 'b', 'c');
   * child.foo();
   * </pre>
   *
   * @param {Function} childCtor Child class.
   * @param {Function} parentCtor Parent class.
   */
  tracking.inherits = function(childCtor, parentCtor) {
    function TempCtor() {
    }
    TempCtor.prototype = parentCtor.prototype;
    childCtor.superClass_ = parentCtor.prototype;
    childCtor.prototype = new TempCtor();
    childCtor.prototype.constructor = childCtor;

    /**
     * Calls superclass constructor/method.
     *
     * This function is only available if you use tracking.inherits to express
     * inheritance relationships between classes.
     *
     * @param {!object} me Should always be "this".
     * @param {string} methodName The method name to call. Calling superclass
     *     constructor can be done with the special string 'constructor'.
     * @param {...*} var_args The arguments to pass to superclass
     *     method/constructor.
     * @return {*} The return value of the superclass method/constructor.
     */
    childCtor.base = function(me, methodName) {
      var args = Array.prototype.slice.call(arguments, 2);
      return parentCtor.prototype[methodName].apply(me, args);
    };
  };

  /**
   * Captures the user camera when tracking a video element and set its source
   * to the camera stream.
   * @param {HTMLVideoElement} element Canvas element to track.
   * @param {object} opt_options Optional configuration to the tracker.
   */
  tracking.initUserMedia_ = function(element, opt_options) {
    window.navigator.mediaDevices.getUserMedia({
      video: true,
      audio: (opt_options && opt_options.audio) ? true : false,
    }).then(function(stream) {
      element.srcObject = stream;
    }).catch(function(err) {
      throw Error('Cannot capture user camera.');
    });
  };

  /**
   * Tests whether the object is a dom node.
   * @param {object} o Object to be tested.
   * @return {boolean} True if the object is a dom node.
   */
  tracking.isNode = function(o) {
    return o.nodeType || this.isWindow(o);
  };

  /**
   * Tests whether the object is the `window` object.
   * @param {object} o Object to be tested.
   * @return {boolean} True if the object is the `window` object.
   */
  tracking.isWindow = function(o) {
    return !!(o && o.alert && o.document);
  };

  /**
   * Selects a dom node from a CSS3 selector using `document.querySelector`.
   * @param {string} selector
   * @param {object} opt_element The root element for the query. When not
   *     specified `document` is used as root element.
   * @return {HTMLElement} The first dom element that matches to the selector.
   *     If not found, returns `null`.
   */
  tracking.one = function(selector, opt_element) {
    if (this.isNode(selector)) {
      return selector;
    }
    return (opt_element || document).querySelector(selector);
  };

  /**
   * Tracks a canvas, image or video element based on the specified `tracker`
   * instance. This method extract the pixel information of the input element
   * to pass to the `tracker` instance. When tracking a video, the
   * `tracker.track(pixels, width, height)` will be in a
   * `requestAnimationFrame` loop in order to track all video frames.
   *
   * Example:
   * var tracker = new tracking.ColorTracker();
   *
   * tracking.track('#video', tracker);
   * or
   * tracking.track('#video', tracker, { camera: true });
   *
   * tracker.on('track', function(event) {
   *   // console.log(event.data[0].x, event.data[0].y)
   * });
   *
   * @param {HTMLElement} element The element to track, canvas, image or
   *     video.
   * @param {tracking.Tracker} tracker The tracker instance used to track the
   *     element.
   * @param {object} opt_options Optional configuration to the tracker.
   */
  tracking.track = function(element, tracker, opt_options) {
    element = tracking.one(element);
    if (!element) {
      throw new Error('Element not found, try a different element or selector.');
    }
    if (!tracker) {
      throw new Error('Tracker not specified, try `tracking.track(element, new tracking.FaceTracker())`.');
    }

    switch (element.nodeName.toLowerCase()) {
      case 'canvas':
        return this.trackCanvas_(element, tracker, opt_options);
      case 'img':
        return this.trackImg_(element, tracker, opt_options);
      case 'video':
        if (opt_options) {
          if (opt_options.camera) {
            this.initUserMedia_(element, opt_options);
          }
        }
        return this.trackVideo_(element, tracker, opt_options);
      default:
        throw new Error('Element not supported, try in a canvas, img, or video.');
    }
  };

  /**
   * Tracks a canvas element based on the specified `tracker` instance and
   * returns a `TrackerTask` for this track.
   * @param {HTMLCanvasElement} element Canvas element to track.
   * @param {tracking.Tracker} tracker The tracker instance used to track the
   *     element.
   * @param {object} opt_options Optional configuration to the tracker.
   * @return {tracking.TrackerTask}
   * @private
   */
  tracking.trackCanvas_ = function(element, tracker) {
    var self = this;
    var task = new tracking.TrackerTask(tracker);
    task.on('run', function() {
      self.trackCanvasInternal_(element, tracker);
    });
    return task.run();
  };

  /**
   * Tracks a canvas element based on the specified `tracker` instance. This
   * method extract the pixel information of the input element to pass to the
   * `tracker` instance.
   * @param {HTMLCanvasElement} element Canvas element to track.
   * @param {tracking.Tracker} tracker The tracker instance used to track the
   *     element.
   * @param {object} opt_options Optional configuration to the tracker.
   * @private
   */
  tracking.trackCanvasInternal_ = function(element, tracker) {
    var width = element.width;
    var height = element.height;
    var context = element.getContext('2d');
    var imageData = context.getImageData(0, 0, width, height);
    tracker.track(imageData.data, width, height);
  };

  /**
   * Tracks a image element based on the specified `tracker` instance. This
   * method extract the pixel information of the input element to pass to the
   * `tracker` instance.
   * @param {HTMLImageElement} element Canvas element to track.
   * @param {tracking.Tracker} tracker The tracker instance used to track the
   *     element.
   * @param {object} opt_options Optional configuration to the tracker.
   * @private
   */
  tracking.trackImg_ = function(element, tracker) {
    var width = element.width;
    var height = element.height;
    var canvas = document.createElement('canvas');

    canvas.width = width;
    canvas.height = height;

    var task = new tracking.TrackerTask(tracker);
    task.on('run', function() {
      tracking.Canvas.loadImage(canvas, element.src, 0, 0, width, height, function() {
        tracking.trackCanvasInternal_(canvas, tracker);
      });
    });
    return task.run();
  };

  /**
   * Tracks a video element based on the specified `tracker` instance. This
   * method extract the pixel information of the input element to pass to the
   * `tracker` instance. The `tracker.track(pixels, width, height)` will be in
   * a `requestAnimationFrame` loop in order to track all video frames.
   * @param {HTMLVideoElement} element Canvas element to track.
   * @param {tracking.Tracker} tracker The tracker instance used to track the
   *     element.
   * @param {object} opt_options Optional configuration to the tracker.
   * @private
   */
  tracking.trackVideo_ = function(element, tracker) {
    var canvas = document.createElement('canvas');
    var context = canvas.getContext('2d');
    var width;
    var height;

    var resizeCanvas_ = function() {
      width = element.offsetWidth;
      height = element.offsetHeight;
      canvas.width = width;
      canvas.height = height;
    };
    resizeCanvas_();
    element.addEventListener('resize', resizeCanvas_);

    var requestId;
    var requestAnimationFrame_ = function() {
      requestId = window.requestAnimationFrame(function() {
        if (element.readyState === element.HAVE_ENOUGH_DATA) {
          try {
            // Firefox v~30.0 gets confused with the video readyState firing an
            // erroneous HAVE_ENOUGH_DATA just before HAVE_CURRENT_DATA state,
            // hence keep trying to read it until resolved.
            context.drawImage(element, 0, 0, width, height);
          } catch (err) {}
          tracking.trackCanvasInternal_(canvas, tracker);
        }
        requestAnimationFrame_();
      });
    };

    var task = new tracking.TrackerTask(tracker);
    task.on('stop', function() {
      window.cancelAnimationFrame(requestId);
    });
    task.on('run', function() {
      requestAnimationFrame_();
    });
    return task.run();
  };

  // Browser polyfills
  //===================

  if (!window.URL) {
    window.URL = window.URL || window.webkitURL || window.msURL || window.oURL;
  }

  if (!navigator.getUserMedia) {
    navigator.getUserMedia = navigator.getUserMedia || navigator.webkitGetUserMedia ||
    navigator.mozGetUserMedia || navigator.msGetUserMedia;
  }
}(window));

(function() {
  /**
   * EventEmitter utility.
   * @constructor
   */
  tracking.EventEmitter = function() {};

  /**
   * Holds event listeners scoped by event type.
   * @type {object}
   * @private
   */
  tracking.EventEmitter.prototype.events_ = null;

  /**
   * Adds a listener to the end of the listeners array for the specified event.
   * @param {string} event
   * @param {function} listener
   * @return {object} Returns emitter, so calls can be chained.
   */
  tracking.EventEmitter.prototype.addListener = function(event, listener) {
    if (typeof listener !== 'function') {
      throw new TypeError('Listener must be a function');
    }
    if (!this.events_) {
      this.events_ = {};
    }

    this.emit('newListener', event, listener);

    if (!this.events_[event]) {
      this.events_[event] = [];
    }

    this.events_[event].push(listener);

    return this;
  };

  /**
   * Returns an array of listeners for the specified event.
   * @param {string} event
   * @return {array} Array of listeners.
   */
  tracking.EventEmitter.prototype.listeners = function(event) {
    return this.events_ && this.events_[event];
  };

  /**
   * Execute each of the listeners in order with the supplied arguments.
   * @param {string} event
   * @param {*} opt_args [arg1], [arg2], [...]
   * @return {boolean} Returns true if event had listeners, false otherwise.
   */
  tracking.EventEmitter.prototype.emit = function(event) {
    var listeners = this.listeners(event);
    if (listeners) {
      var args = Array.prototype.slice.call(arguments, 1);
      for (var i = 0; i < listeners.length; i++) {
        if (listeners[i]) {
          listeners[i].apply(this, args);
        }
      }
      return true;
    }
    return false;
  };

  /**
   * Adds a listener to the end of the listeners array for the specified event.
   * @param {string} event
   * @param {function} listener
   * @return {object} Returns emitter, so calls can be chained.
   */
  tracking.EventEmitter.prototype.on = tracking.EventEmitter.prototype.addListener;

  /**
   * Adds a one time listener for the event. This listener is invoked only the
   * next time the event is fired, after which it is removed.
   * @param {string} event
   * @param {function} listener
   * @return {object} Returns emitter, so calls can be chained.
   */
  tracking.EventEmitter.prototype.once = function(event, listener) {
    var self = this;
    self.on(event, function handlerInternal() {
      self.removeListener(event, handlerInternal);
      listener.apply(this, arguments);
    });
  };

  /**
   * Removes all listeners, or those of the specified event. It's not a good
   * idea to remove listeners that were added elsewhere in the code,
   * especially when it's on an emitter that you didn't create.
   * @param {string} event
   * @return {object} Returns emitter, so calls can be chained.
   */
  tracking.EventEmitter.prototype.removeAllListeners = function(opt_event) {
    if (!this.events_) {
      return this;
    }
    if (opt_event) {
      delete this.events_[opt_event];
    } else {
      delete this.events_;
    }
    return this;
  };

  /**
   * Remove a listener from the listener array for the specified event.
   * Caution: changes array indices in the listener array behind the listener.
   * @param {string} event
   * @param {function} listener
   * @return {object} Returns emitter, so calls can be chained.
   */
  tracking.EventEmitter.prototype.removeListener = function(event, listener) {
    if (typeof listener !== 'function') {
      throw new TypeError('Listener must be a function');
    }
    if (!this.events_) {
      return this;
    }

    var listeners = this.listeners(event);
    if (Array.isArray(listeners)) {
      var i = listeners.indexOf(listener);
      if (i < 0) {
        return this;
      }
      listeners.splice(i, 1);
    }

    return this;
  };

  /**
   * By default EventEmitters will print a warning if more than 10 listeners
   * are added for a particular event. This is a useful default which helps
   * finding memory leaks. Obviously not all Emitters should be limited to 10.
   * This function allows that to be increased. Set to zero for unlimited.
   * @param {number} n The maximum number of listeners.
   */
  tracking.EventEmitter.prototype.setMaxListeners = function() {
    throw new Error('Not implemented');
  };

}());

(function() {
  /**
   * Canvas utility.
   * @static
   * @constructor
   */
  tracking.Canvas = {};

  /**
   * Loads an image source into the canvas.
   * @param {HTMLCanvasElement} canvas The canvas dom element.
   * @param {string} src The image source.
   * @param {number} x The canvas horizontal coordinate to load the image.
   * @param {number} y The canvas vertical coordinate to load the image.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {function} opt_callback Callback that fires when the image is loaded
   *     into the canvas.
   * @static
   */
  tracking.Canvas.loadImage = function(canvas, src, x, y, width, height, opt_callback) {
    var instance = this;
    var img = new window.Image();
    img.crossOrigin = '*';
    img.onload = function() {
      var context = canvas.getContext('2d');
      canvas.width = width;
      canvas.height = height;
      context.drawImage(img, x, y, width, height);
      if (opt_callback) {
        opt_callback.call(instance);
      }
      img = null;
    };
    img.src = src;
  };
}());

(function() {
  /**
   * DisjointSet utility with path compression. Some applications involve
   * grouping n distinct objects into a collection of disjoint sets. Two
   * important operations are then finding which set a given object belongs to
   * and uniting the two sets. A disjoint set data structure maintains a
   * collection S={ S1 , S2 ,..., Sk } of disjoint dynamic sets. Each set is
   * identified by a representative, which usually is a member in the set.
   * @static
   * @constructor
   */
  tracking.DisjointSet = function(length) {
    if (length === undefined) {
      throw new Error('DisjointSet length not specified.');
    }
    this.length = length;
    this.parent = new Uint32Array(length);
    for (var i = 0; i < length; i++) {
      this.parent[i] = i;
    }
  };

  /**
   * Holds the length of the internal set.
   * @type {number}
   */
  tracking.DisjointSet.prototype.length = null;

  /**
   * Holds the set containing the representative values.
   * @type {Array.<number>}
   */
  tracking.DisjointSet.prototype.parent = null;

  /**
   * Finds a pointer to the representative of the set containing i.
   * @param {number} i
   * @return {number} The representative set of i.
   */
  tracking.DisjointSet.prototype.find = function(i) {
    if (this.parent[i] === i) {
      return i;
    } else {
      return (this.parent[i] = this.find(this.parent[i]));
    }
  };

  /**
   * Unites two dynamic sets containing objects i and j, say Si and Sj, into
   * a new set that Si ∪ Sj, assuming that Si ∩ Sj = ∅;
   * @param {number} i
   * @param {number} j
   */
  tracking.DisjointSet.prototype.union = function(i, j) {
    var iRepresentative = this.find(i);
    var jRepresentative = this.find(j);
    this.parent[iRepresentative] = jRepresentative;
  };

}());

(function() {
  /**
   * Image utility.
   * @static
   * @constructor
   */
  tracking.Image = {};

  /**
   * Computes gaussian blur. Adapted from
   * https://github.com/kig/canvasfilters.
   * @param {pixels} pixels The pixels in a linear [r,g,b,a,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {number} diameter Gaussian blur diameter, must be greater than 1.
   * @return {array} The edge pixels in a linear [r,g,b,a,...] array.
   */
  tracking.Image.blur = function(pixels, width, height, diameter) {
    diameter = Math.abs(diameter);
    if (diameter <= 1) {
      throw new Error('Diameter should be greater than 1.');
    }
    var radius = diameter / 2;
    var len = Math.ceil(diameter) + (1 - (Math.ceil(diameter) % 2));
    var weights = new Float32Array(len);
    var rho = (radius + 0.5) / 3;
    var rhoSq = rho * rho;
    var gaussianFactor = 1 / Math.sqrt(2 * Math.PI * rhoSq);
    var rhoFactor = -1 / (2 * rho * rho);
    var wsum = 0;
    var middle = Math.floor(len / 2);
    for (var i = 0; i < len; i++) {
      var x = i - middle;
      var gx = gaussianFactor * Math.exp(x * x * rhoFactor);
      weights[i] = gx;
      wsum += gx;
    }
    for (var j = 0; j < weights.length; j++) {
      weights[j] /= wsum;
    }
    return this.separableConvolve(pixels, width, height, weights, weights, false);
  };

  /**
   * Computes the integral image for summed, squared, rotated and sobel pixels.
   * @param {array} pixels The pixels in a linear [r,g,b,a,...] array to loop
   *     through.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {array} opt_integralImage Empty array of size `width * height` to
   *     be filled with the integral image values. If not specified compute sum
   *     values will be skipped.
   * @param {array} opt_integralImageSquare Empty array of size `width *
   *     height` to be filled with the integral image squared values. If not
   *     specified compute squared values will be skipped.
   * @param {array} opt_tiltedIntegralImage Empty array of size `width *
   *     height` to be filled with the rotated integral image values. If not
   *     specified compute sum values will be skipped.
   * @param {array} opt_integralImageSobel Empty array of size `width *
   *     height` to be filled with the integral image of sobel values. If not
   *     specified compute sobel filtering will be skipped.
   * @static
   */
  tracking.Image.computeIntegralImage = function(pixels, width, height, opt_integralImage, opt_integralImageSquare, opt_tiltedIntegralImage, opt_integralImageSobel) {
    if (arguments.length < 4) {
      throw new Error('You should specify at least one output array in the order: sum, square, tilted, sobel.');
    }
    var pixelsSobel;
    if (opt_integralImageSobel) {
      pixelsSobel = tracking.Image.sobel(pixels, width, height);
    }
    for (var i = 0; i < height; i++) {
      for (var j = 0; j < width; j++) {
        var w = i * width * 4 + j * 4;
        var pixel = ~~(pixels[w] * 0.299 + pixels[w + 1] * 0.587 + pixels[w + 2] * 0.114);
        if (opt_integralImage) {
          this.computePixelValueSAT_(opt_integralImage, width, i, j, pixel);
        }
        if (opt_integralImageSquare) {
          this.computePixelValueSAT_(opt_integralImageSquare, width, i, j, pixel * pixel);
        }
        if (opt_tiltedIntegralImage) {
          var w1 = w - width * 4;
          var pixelAbove = ~~(pixels[w1] * 0.299 + pixels[w1 + 1] * 0.587 + pixels[w1 + 2] * 0.114);
          this.computePixelValueRSAT_(opt_tiltedIntegralImage, width, i, j, pixel, pixelAbove || 0);
        }
        if (opt_integralImageSobel) {
          this.computePixelValueSAT_(opt_integralImageSobel, width, i, j, pixelsSobel[w]);
        }
      }
    }
  };

  /**
   * Helper method to compute the rotated summed area table (RSAT) by the
   * formula:
   *
   * RSAT(x, y) = RSAT(x-1, y-1) + RSAT(x+1, y-1) - RSAT(x, y-2) + I(x, y) + I(x, y-1)
   *
   * @param {number} width The image width.
   * @param {array} RSAT Empty array of size `width * height` to be filled with
   *     the integral image values. If not specified compute sum values will be
   *     skipped.
   * @param {number} i Vertical position of the pixel to be evaluated.
   * @param {number} j Horizontal position of the pixel to be evaluated.
   * @param {number} pixel Pixel value to be added to the integral image.
   * @static
   * @private
   */
  tracking.Image.computePixelValueRSAT_ = function(RSAT, width, i, j, pixel, pixelAbove) {
    var w = i * width + j;
    RSAT[w] = (RSAT[w - width - 1] || 0) + (RSAT[w - width + 1] || 0) - (RSAT[w - width - width] || 0) + pixel + pixelAbove;
  };

  /**
   * Helper method to compute the summed area table (SAT) by the formula:
   *
   * SAT(x, y) = SAT(x, y-1) + SAT(x-1, y) + I(x, y) - SAT(x-1, y-1)
   *
   * @param {number} width The image width.
   * @param {array} SAT Empty array of size `width * height` to be filled with
   *     the integral image values. If not specified compute sum values will be
   *     skipped.
   * @param {number} i Vertical position of the pixel to be evaluated.
   * @param {number} j Horizontal position of the pixel to be evaluated.
   * @param {number} pixel Pixel value to be added to the integral image.
   * @static
   * @private
   */
  tracking.Image.computePixelValueSAT_ = function(SAT, width, i, j, pixel) {
    var w = i * width + j;
    SAT[w] = (SAT[w - width] || 0) + (SAT[w - 1] || 0) + pixel - (SAT[w - width - 1] || 0);
  };

  /**
   * Converts a color from a colorspace based on an RGB color model to a
   * grayscale representation of its luminance. The coefficients represent the
   * measured intensity perception of typical trichromat humans, in
   * particular, human vision is most sensitive to green and least sensitive
   * to blue.
   * @param {pixels} pixels The pixels in a linear [r,g,b,a,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {boolean} fillRGBA If the result should fill all RGBA values with the gray scale
   *  values, instead of returning a single value per pixel.
   * @param {Uint8ClampedArray} The grayscale pixels in a linear array ([p,p,p,a,...] if fillRGBA
   *  is true and [p1, p2, p3, ...] if fillRGBA is false).
   * @static
   */
  tracking.Image.grayscale = function(pixels, width, height, fillRGBA) {
    var gray = new Uint8ClampedArray(fillRGBA ? pixels.length : pixels.length >> 2);
    var p = 0;
    var w = 0;
    for (var i = 0; i < height; i++) {
      for (var j = 0; j < width; j++) {
        var value = pixels[w] * 0.299 + pixels[w + 1] * 0.587 + pixels[w + 2] * 0.114;
        gray[p++] = value;

        if (fillRGBA) {
          gray[p++] = value;
          gray[p++] = value;
          gray[p++] = pixels[w + 3];
        }

        w += 4;
      }
    }
    return gray;
  };

  /**
   * Fast horizontal separable convolution. A point spread function (PSF) is
   * said to be separable if it can be broken into two one-dimensional
   * signals: a vertical and a horizontal projection. The convolution is
   * performed by sliding the kernel over the image, generally starting at the
   * top left corner, so as to move the kernel through all the positions where
   * the kernel fits entirely within the boundaries of the image. Adapted from
   * https://github.com/kig/canvasfilters.
   * @param {pixels} pixels The pixels in a linear [r,g,b,a,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {array} weightsVector The weighting vector, e.g [-1,0,1].
   * @param {number} opaque
   * @return {array} The convoluted pixels in a linear [r,g,b,a,...] array.
   */
  tracking.Image.horizontalConvolve = function(pixels, width, height, weightsVector, opaque) {
    var side = weightsVector.length;
    var halfSide = Math.floor(side / 2);
    var output = new Float32Array(width * height * 4);
    var alphaFac = opaque ? 1 : 0;

    for (var y = 0; y < height; y++) {
      for (var x = 0; x < width; x++) {
        var sy = y;
        var sx = x;
        var offset = (y * width + x) * 4;
        var r = 0;
        var g = 0;
        var b = 0;
        var a = 0;
        for (var cx = 0; cx < side; cx++) {
          var scy = sy;
          var scx = Math.min(width - 1, Math.max(0, sx + cx - halfSide));
          var poffset = (scy * width + scx) * 4;
          var wt = weightsVector[cx];
          r += pixels[poffset] * wt;
          g += pixels[poffset + 1] * wt;
          b += pixels[poffset + 2] * wt;
          a += pixels[poffset + 3] * wt;
        }
        output[offset] = r;
        output[offset + 1] = g;
        output[offset + 2] = b;
        output[offset + 3] = a + alphaFac * (255 - a);
      }
    }
    return output;
  };

  /**
   * Fast vertical separable convolution. A point spread function (PSF) is
   * said to be separable if it can be broken into two one-dimensional
   * signals: a vertical and a horizontal projection. The convolution is
   * performed by sliding the kernel over the image, generally starting at the
   * top left corner, so as to move the kernel through all the positions where
   * the kernel fits entirely within the boundaries of the image. Adapted from
   * https://github.com/kig/canvasfilters.
   * @param {pixels} pixels The pixels in a linear [r,g,b,a,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {array} weightsVector The weighting vector, e.g [-1,0,1].
   * @param {number} opaque
   * @return {array} The convoluted pixels in a linear [r,g,b,a,...] array.
   */
  tracking.Image.verticalConvolve = function(pixels, width, height, weightsVector, opaque) {
    var side = weightsVector.length;
    var halfSide = Math.floor(side / 2);
    var output = new Float32Array(width * height * 4);
    var alphaFac = opaque ? 1 : 0;

    for (var y = 0; y < height; y++) {
      for (var x = 0; x < width; x++) {
        var sy = y;
        var sx = x;
        var offset = (y * width + x) * 4;
        var r = 0;
        var g = 0;
        var b = 0;
        var a = 0;
        for (var cy = 0; cy < side; cy++) {
          var scy = Math.min(height - 1, Math.max(0, sy + cy - halfSide));
          var scx = sx;
          var poffset = (scy * width + scx) * 4;
          var wt = weightsVector[cy];
          r += pixels[poffset] * wt;
          g += pixels[poffset + 1] * wt;
          b += pixels[poffset + 2] * wt;
          a += pixels[poffset + 3] * wt;
        }
        output[offset] = r;
        output[offset + 1] = g;
        output[offset + 2] = b;
        output[offset + 3] = a + alphaFac * (255 - a);
      }
    }
    return output;
  };

  /**
   * Fast separable convolution. A point spread function (PSF) is said to be
   * separable if it can be broken into two one-dimensional signals: a
   * vertical and a horizontal projection. The convolution is performed by
   * sliding the kernel over the image, generally starting at the top left
   * corner, so as to move the kernel through all the positions where the
   * kernel fits entirely within the boundaries of the image. Adapted from
   * https://github.com/kig/canvasfilters.
   * @param {pixels} pixels The pixels in a linear [r,g,b,a,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {array} horizWeights The horizontal weighting vector, e.g [-1,0,1].
   * @param {array} vertWeights The vertical vector, e.g [-1,0,1].
   * @param {number} opaque
   * @return {array} The convoluted pixels in a linear [r,g,b,a,...] array.
   */
  tracking.Image.separableConvolve = function(pixels, width, height, horizWeights, vertWeights, opaque) {
    var vertical = this.verticalConvolve(pixels, width, height, vertWeights, opaque);
    return this.horizontalConvolve(vertical, width, height, horizWeights, opaque);
  };

  /**
   * Compute image edges using Sobel operator. Computes the vertical and
   * horizontal gradients of the image and combines the computed images to
   * find edges in the image. The way we implement the Sobel filter here is by
   * first grayscaling the image, then taking the horizontal and vertical
   * gradients and finally combining the gradient images to make up the final
   * image. Adapted from https://github.com/kig/canvasfilters.
   * @param {pixels} pixels The pixels in a linear [r,g,b,a,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @return {array} The edge pixels in a linear [r,g,b,a,...] array.
   */
  tracking.Image.sobel = function(pixels, width, height) {
    pixels = this.grayscale(pixels, width, height, true);
    var output = new Float32Array(width * height * 4);
    var sobelSignVector = new Float32Array([-1, 0, 1]);
    var sobelScaleVector = new Float32Array([1, 2, 1]);
    var vertical = this.separableConvolve(pixels, width, height, sobelSignVector, sobelScaleVector);
    var horizontal = this.separableConvolve(pixels, width, height, sobelScaleVector, sobelSignVector);

    for (var i = 0; i < output.length; i += 4) {
      var v = vertical[i];
      var h = horizontal[i];
      var p = Math.sqrt(h * h + v * v);
      output[i] = p;
      output[i + 1] = p;
      output[i + 2] = p;
      output[i + 3] = 255;
    }

    return output;
  };

  /**
   * Equalizes the histogram of a grayscale image, normalizing the
   * brightness and increasing the contrast of the image.
   * @param {pixels} pixels The grayscale pixels in a linear array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @return {array} The equalized grayscale pixels in a linear array.
   */
  tracking.Image.equalizeHist = function(pixels, width, height){
    var equalized = new Uint8ClampedArray(pixels.length);

    var histogram = new Array(256);
    for(var i=0; i < 256; i++) histogram[i] = 0;

    for(var i=0; i < pixels.length; i++){
      equalized[i] = pixels[i];
      histogram[pixels[i]]++;
    }

    var prev = histogram[0];
    for(var i=0; i < 256; i++){
      histogram[i] += prev;
      prev = histogram[i];
    }

    var norm = 255 / pixels.length;
    for(var i=0; i < pixels.length; i++)
      equalized[i] = (histogram[pixels[i]] * norm + 0.5) | 0;

    return equalized;
  }

}());

(function() {
  /**
   * ViolaJones utility.
   * @static
   * @constructor
   */
  tracking.ViolaJones = {};

  /**
   * Holds the minimum area of intersection that defines when a rectangle is
   * from the same group. Often when a face is matched multiple rectangles are
   * classified as possible rectangles to represent the face, when they
   * intersects they are grouped as one face.
   * @type {number}
   * @default 0.5
   * @static
   */
  tracking.ViolaJones.REGIONS_OVERLAP = 0.5;

  /**
   * Holds the HAAR cascade classifiers converted from OpenCV training.
   * @type {array}
   * @static
   */
  tracking.ViolaJones.classifiers = {};

  /**
   * Detects through the HAAR cascade data rectangles matches.
   * @param {pixels} pixels The pixels in a linear [r,g,b,a,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {number} initialScale The initial scale to start the block
   *     scaling.
   * @param {number} scaleFactor The scale factor to scale the feature block.
   * @param {number} stepSize The block step size.
   * @param {number} edgesDensity Percentage density edges inside the
   *     classifier block. Value from [0.0, 1.0], defaults to 0.2. If specified
   *     edge detection will be applied to the image to prune dead areas of the
   *     image, this can improve significantly performance.
   * @param {number} data The HAAR cascade data.
   * @return {array} Found rectangles.
   * @static
   */
  tracking.ViolaJones.detect = function(pixels, width, height, initialScale, scaleFactor, stepSize, edgesDensity, data) {
    var total = 0;
    var rects = [];
    var integralImage = new Int32Array(width * height);
    var integralImageSquare = new Int32Array(width * height);
    var tiltedIntegralImage = new Int32Array(width * height);

    var integralImageSobel;
    if (edgesDensity > 0) {
      integralImageSobel = new Int32Array(width * height);
    }

    tracking.Image.computeIntegralImage(pixels, width, height, integralImage, integralImageSquare, tiltedIntegralImage, integralImageSobel);

    var minWidth = data[0];
    var minHeight = data[1];
    var scale = initialScale * scaleFactor;
    var blockWidth = (scale * minWidth) | 0;
    var blockHeight = (scale * minHeight) | 0;

    while (blockWidth < width && blockHeight < height) {
      var step = (scale * stepSize + 0.5) | 0;
      for (var i = 0; i < (height - blockHeight); i += step) {
        for (var j = 0; j < (width - blockWidth); j += step) {

          if (edgesDensity > 0) {
            if (this.isTriviallyExcluded(edgesDensity, integralImageSobel, i, j, width, blockWidth, blockHeight)) {
              continue;
            }
          }

          if (this.evalStages_(data, integralImage, integralImageSquare, tiltedIntegralImage, i, j, width, blockWidth, blockHeight, scale)) {
            rects[total++] = {
              width: blockWidth,
              height: blockHeight,
              x: j,
              y: i
            };
          }
        }
      }

      scale *= scaleFactor;
      blockWidth = (scale * minWidth) | 0;
      blockHeight = (scale * minHeight) | 0;
    }
    return this.mergeRectangles_(rects);
  };

  /**
   * Fast check to test whether the edges density inside the block is greater
   * than a threshold, if true it tests the stages. This can improve
   * significantly performance.
   * @param {number} edgesDensity Percentage density edges inside the
   *     classifier block.
   * @param {array} integralImageSobel The integral image of a sobel image.
   * @param {number} i Vertical position of the pixel to be evaluated.
   * @param {number} j Horizontal position of the pixel to be evaluated.
   * @param {number} width The image width.
   * @return {boolean} True whether the block at position i,j can be skipped,
   *     false otherwise.
   * @static
   * @protected
   */
  tracking.ViolaJones.isTriviallyExcluded = function(edgesDensity, integralImageSobel, i, j, width, blockWidth, blockHeight) {
    var wbA = i * width + j;
    var wbB = wbA + blockWidth;
    var wbD = wbA + blockHeight * width;
    var wbC = wbD + blockWidth;
    var blockEdgesDensity = (integralImageSobel[wbA] - integralImageSobel[wbB] - integralImageSobel[wbD] + integralImageSobel[wbC]) / (blockWidth * blockHeight * 255);
    if (blockEdgesDensity < edgesDensity) {
      return true;
    }
    return false;
  };

  /**
   * Evaluates if the block size on i,j position is a valid HAAR cascade
   * stage.
   * @param {number} data The HAAR cascade data.
   * @param {number} i Vertical position of the pixel to be evaluated.
   * @param {number} j Horizontal position of the pixel to be evaluated.
   * @param {number} width The image width.
   * @param {number} blockSize The block size.
   * @param {number} scale The scale factor of the block size and its original
   *     size.
   * @param {number} inverseArea The inverse area of the block size.
   * @return {boolean} Whether the region passes all the stage tests.
   * @private
   * @static
   */
  tracking.ViolaJones.evalStages_ = function(data, integralImage, integralImageSquare, tiltedIntegralImage, i, j, width, blockWidth, blockHeight, scale) {
    var inverseArea = 1.0 / (blockWidth * blockHeight);
    var wbA = i * width + j;
    var wbB = wbA + blockWidth;
    var wbD = wbA + blockHeight * width;
    var wbC = wbD + blockWidth;
    var mean = (integralImage[wbA] - integralImage[wbB] - integralImage[wbD] + integralImage[wbC]) * inverseArea;
    var variance = (integralImageSquare[wbA] - integralImageSquare[wbB] - integralImageSquare[wbD] + integralImageSquare[wbC]) * inverseArea - mean * mean;

    var standardDeviation = 1;
    if (variance > 0) {
      standardDeviation = Math.sqrt(variance);
    }

    var length = data.length;

    for (var w = 2; w < length; ) {
      var stageSum = 0;
      var stageThreshold = data[w++];
      var nodeLength = data[w++];

      while (nodeLength--) {
        var rectsSum = 0;
        var tilted = data[w++];
        var rectsLength = data[w++];

        for (var r = 0; r < rectsLength; r++) {
          var rectLeft = (j + data[w++] * scale + 0.5) | 0;
          var rectTop = (i + data[w++] * scale + 0.5) | 0;
          var rectWidth = (data[w++] * scale + 0.5) | 0;
          var rectHeight = (data[w++] * scale + 0.5) | 0;
          var rectWeight = data[w++];

          var w1;
          var w2;
          var w3;
          var w4;
          if (tilted) {
            // RectSum(r) = RSAT(x-h+w, y+w+h-1) + RSAT(x, y-1) - RSAT(x-h, y+h-1) - RSAT(x+w, y+w-1)
            w1 = (rectLeft - rectHeight + rectWidth) + (rectTop + rectWidth + rectHeight - 1) * width;
            w2 = rectLeft + (rectTop - 1) * width;
            w3 = (rectLeft - rectHeight) + (rectTop + rectHeight - 1) * width;
            w4 = (rectLeft + rectWidth) + (rectTop + rectWidth - 1) * width;
            rectsSum += (tiltedIntegralImage[w1] + tiltedIntegralImage[w2] - tiltedIntegralImage[w3] - tiltedIntegralImage[w4]) * rectWeight;
          } else {
            // RectSum(r) = SAT(x-1, y-1) + SAT(x+w-1, y+h-1) - SAT(x-1, y+h-1) - SAT(x+w-1, y-1)
            w1 = rectTop * width + rectLeft;
            w2 = w1 + rectWidth;
            w3 = w1 + rectHeight * width;
            w4 = w3 + rectWidth;
            rectsSum += (integralImage[w1] - integralImage[w2] - integralImage[w3] + integralImage[w4]) * rectWeight;
            // TODO: Review the code below to analyze performance when using it instead.
            // w1 = (rectLeft - 1) + (rectTop - 1) * width;
            // w2 = (rectLeft + rectWidth - 1) + (rectTop + rectHeight - 1) * width;
            // w3 = (rectLeft - 1) + (rectTop + rectHeight - 1) * width;
            // w4 = (rectLeft + rectWidth - 1) + (rectTop - 1) * width;
            // rectsSum += (integralImage[w1] + integralImage[w2] - integralImage[w3] - integralImage[w4]) * rectWeight;
          }
        }

        var nodeThreshold = data[w++];
        var nodeLeft = data[w++];
        var nodeRight = data[w++];

        if (rectsSum * inverseArea < nodeThreshold * standardDeviation) {
          stageSum += nodeLeft;
        } else {
          stageSum += nodeRight;
        }
      }

      if (stageSum < stageThreshold) {
        return false;
      }
    }
    return true;
  };

  /**
   * Postprocess the detected sub-windows in order to combine overlapping
   * detections into a single detection.
   * @param {array} rects
   * @return {array}
   * @private
   * @static
   */
  tracking.ViolaJones.mergeRectangles_ = function(rects) {
    var disjointSet = new tracking.DisjointSet(rects.length);

    for (var i = 0; i < rects.length; i++) {
      var r1 = rects[i];
      for (var j = 0; j < rects.length; j++) {
        var r2 = rects[j];
        if (tracking.Math.intersectRect(r1.x, r1.y, r1.x + r1.width, r1.y + r1.height, r2.x, r2.y, r2.x + r2.width, r2.y + r2.height)) {
          var x1 = Math.max(r1.x, r2.x);
          var y1 = Math.max(r1.y, r2.y);
          var x2 = Math.min(r1.x + r1.width, r2.x + r2.width);
          var y2 = Math.min(r1.y + r1.height, r2.y + r2.height);
          var overlap = (x1 - x2) * (y1 - y2);
          var area1 = (r1.width * r1.height);
          var area2 = (r2.width * r2.height);

          if ((overlap / (area1 * (area1 / area2)) >= this.REGIONS_OVERLAP) &&
            (overlap / (area2 * (area1 / area2)) >= this.REGIONS_OVERLAP)) {
            disjointSet.union(i, j);
          }
        }
      }
    }

    var map = {};
    for (var k = 0; k < disjointSet.length; k++) {
      var rep = disjointSet.find(k);
      if (!map[rep]) {
        map[rep] = {
          total: 1,
          width: rects[k].width,
          height: rects[k].height,
          x: rects[k].x,
          y: rects[k].y
        };
        continue;
      }
      map[rep].total++;
      map[rep].width += rects[k].width;
      map[rep].height += rects[k].height;
      map[rep].x += rects[k].x;
      map[rep].y += rects[k].y;
    }

    var result = [];
    Object.keys(map).forEach(function(key) {
      var rect = map[key];
      result.push({
        total: rect.total,
        width: (rect.width / rect.total + 0.5) | 0,
        height: (rect.height / rect.total + 0.5) | 0,
        x: (rect.x / rect.total + 0.5) | 0,
        y: (rect.y / rect.total + 0.5) | 0
      });
    });

    return result;
  };

}());

(function() {
  /**
   * Brief intends for "Binary Robust Independent Elementary Features".This
   * method generates a binary string for each keypoint found by an extractor
   * method.
   * @static
   * @constructor
   */
  tracking.Brief = {};

  /**
   * The set of binary tests is defined by the nd (x,y)-location pairs
   * uniquely chosen during the initialization. Values could vary between N =
   * 128,256,512. N=128 yield good compromises between speed, storage
   * efficiency, and recognition rate.
   * @type {number}
   */
  tracking.Brief.N = 512;

  /**
   * Caches coordinates values of (x,y)-location pairs uniquely chosen during
   * the initialization.
   * @type {Object.<number, Int32Array>}
   * @private
   * @static
   */
  tracking.Brief.randomImageOffsets_ = {};

  /**
   * Caches delta values of (x,y)-location pairs uniquely chosen during
   * the initialization.
   * @type {Int32Array}
   * @private
   * @static
   */
  tracking.Brief.randomWindowOffsets_ = null;

  /**
   * Generates a binary string for each found keypoints extracted using an
   * extractor method.
   * @param {array} The grayscale pixels in a linear [p1,p2,...] array.
   * @param {number} width The image width.
   * @param {array} keypoints
   * @return {Int32Array} Returns an array where for each four sequence int
   *     values represent the descriptor binary string (128 bits) necessary
   *     to describe the corner, e.g. [0,0,0,0, 0,0,0,0, ...].
   * @static
   */
  tracking.Brief.getDescriptors = function(pixels, width, keypoints) {
    // Optimizing divide by 32 operation using binary shift
    // (this.N >> 5) === this.N/32.
    var descriptors = new Int32Array((keypoints.length >> 1) * (this.N >> 5));
    var descriptorWord = 0;
    var offsets = this.getRandomOffsets_(width);
    var position = 0;

    for (var i = 0; i < keypoints.length; i += 2) {
      var w = width * keypoints[i + 1] + keypoints[i];

      var offsetsPosition = 0;
      for (var j = 0, n = this.N; j < n; j++) {
        if (pixels[offsets[offsetsPosition++] + w] < pixels[offsets[offsetsPosition++] + w]) {
          // The bit in the position `j % 32` of descriptorWord should be set to 1. We do
          // this by making an OR operation with a binary number that only has the bit
          // in that position set to 1. That binary number is obtained by shifting 1 left by
          // `j % 32` (which is the same as `j & 31` left) positions.
          descriptorWord |= 1 << (j & 31);
        }

        // If the next j is a multiple of 32, we will need to use a new descriptor word to hold
        // the next results.
        if (!((j + 1) & 31)) {
          descriptors[position++] = descriptorWord;
          descriptorWord = 0;
        }
      }
    }

    return descriptors;
  };

  /**
   * Matches sets of features {mi} and {m′j} extracted from two images taken
   * from similar, and often successive, viewpoints. A classical procedure
   * runs as follows. For each point {mi} in the first image, search in a
   * region of the second image around location {mi} for point {m′j}. The
   * search is based on the similarity of the local image windows, also known
   * as kernel windows, centered on the points, which strongly characterizes
   * the points when the images are sufficiently close. Once each keypoint is
   * described with its binary string, they need to be compared with the
   * closest matching point. Distance metric is critical to the performance of
   * in- trusion detection systems. Thus using binary strings reduces the size
   * of the descriptor and provides an interesting data structure that is fast
   * to operate whose similarity can be measured by the Hamming distance.
   * @param {array} keypoints1
   * @param {array} descriptors1
   * @param {array} keypoints2
   * @param {array} descriptors2
   * @return {Int32Array} Returns an array where the index is the corner1
   *     index coordinate, and the value is the corresponding match index of
   *     corner2, e.g. keypoints1=[x0,y0,x1,y1,...] and
   *     keypoints2=[x'0,y'0,x'1,y'1,...], if x0 matches x'1 and x1 matches x'0,
   *     the return array would be [3,0].
   * @static
   */
  tracking.Brief.match = function(keypoints1, descriptors1, keypoints2, descriptors2) {
    var len1 = keypoints1.length >> 1;
    var len2 = keypoints2.length >> 1;
    var matches = new Array(len1);

    for (var i = 0; i < len1; i++) {
      var min = Infinity;
      var minj = 0;
      for (var j = 0; j < len2; j++) {
        var dist = 0;
        // Optimizing divide by 32 operation using binary shift
        // (this.N >> 5) === this.N/32.
        for (var k = 0, n = this.N >> 5; k < n; k++) {
          dist += tracking.Math.hammingWeight(descriptors1[i * n + k] ^ descriptors2[j * n + k]);
        }
        if (dist < min) {
          min = dist;
          minj = j;
        }
      }
      matches[i] = {
        index1: i,
        index2: minj,
        keypoint1: [keypoints1[2 * i], keypoints1[2 * i + 1]],
        keypoint2: [keypoints2[2 * minj], keypoints2[2 * minj + 1]],
        confidence: 1 - min / this.N
      };
    }

    return matches;
  };

  /**
   * Removes matches outliers by testing matches on both directions.
   * @param {array} keypoints1
   * @param {array} descriptors1
   * @param {array} keypoints2
   * @param {array} descriptors2
   * @return {Int32Array} Returns an array where the index is the corner1
   *     index coordinate, and the value is the corresponding match index of
   *     corner2, e.g. keypoints1=[x0,y0,x1,y1,...] and
   *     keypoints2=[x'0,y'0,x'1,y'1,...], if x0 matches x'1 and x1 matches x'0,
   *     the return array would be [3,0].
   * @static
   */
  tracking.Brief.reciprocalMatch = function(keypoints1, descriptors1, keypoints2, descriptors2) {
    var matches = [];
    if (keypoints1.length === 0 || keypoints2.length === 0) {
      return matches;
    }

    var matches1 = tracking.Brief.match(keypoints1, descriptors1, keypoints2, descriptors2);
    var matches2 = tracking.Brief.match(keypoints2, descriptors2, keypoints1, descriptors1);
    for (var i = 0; i < matches1.length; i++) {
      if (matches2[matches1[i].index2].index2 === i) {
        matches.push(matches1[i]);
      }
    }
    return matches;
  };

  /**
   * Gets the coordinates values of (x,y)-location pairs uniquely chosen
   * during the initialization.
   * @return {array} Array with the random offset values.
   * @private
   */
  tracking.Brief.getRandomOffsets_ = function(width) {
    if (!this.randomWindowOffsets_) {
      var windowPosition = 0;
      var windowOffsets = new Int32Array(4 * this.N);
      for (var i = 0; i < this.N; i++) {
        windowOffsets[windowPosition++] = Math.round(tracking.Math.uniformRandom(-15, 16));
        windowOffsets[windowPosition++] = Math.round(tracking.Math.uniformRandom(-15, 16));
        windowOffsets[windowPosition++] = Math.round(tracking.Math.uniformRandom(-15, 16));
        windowOffsets[windowPosition++] = Math.round(tracking.Math.uniformRandom(-15, 16));
      }
      this.randomWindowOffsets_ = windowOffsets;
    }

    if (!this.randomImageOffsets_[width]) {
      var imagePosition = 0;
      var imageOffsets = new Int32Array(2 * this.N);
      for (var j = 0; j < this.N; j++) {
        imageOffsets[imagePosition++] = this.randomWindowOffsets_[4 * j] * width + this.randomWindowOffsets_[4 * j + 1];
        imageOffsets[imagePosition++] = this.randomWindowOffsets_[4 * j + 2] * width + this.randomWindowOffsets_[4 * j + 3];
      }
      this.randomImageOffsets_[width] = imageOffsets;
    }

    return this.randomImageOffsets_[width];
  };
}());

(function() {
  /**
   * FAST intends for "Features from Accelerated Segment Test". This method
   * performs a point segment test corner detection. The segment test
   * criterion operates by considering a circle of sixteen pixels around the
   * corner candidate p. The detector classifies p as a corner if there exists
   * a set of n contiguous pixelsin the circle which are all brighter than the
   * intensity of the candidate pixel Ip plus a threshold t, or all darker
   * than Ip − t.
   *
   *       15 00 01
   *    14          02
   * 13                03
   * 12       []       04
   * 11                05
   *    10          06
   *       09 08 07
   *
   * For more reference:
   * http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.60.3991&rep=rep1&type=pdf
   * @static
   * @constructor
   */
  tracking.Fast = {};

  /**
   * Holds the threshold to determine whether the tested pixel is brighter or
   * darker than the corner candidate p.
   * @type {number}
   * @default 40
   * @static
   */
  tracking.Fast.THRESHOLD = 40;

  /**
   * Caches coordinates values of the circle surrounding the pixel candidate p.
   * @type {Object.<number, Int32Array>}
   * @private
   * @static
   */
  tracking.Fast.circles_ = {};

  /**
   * Finds corners coordinates on the graysacaled image.
   * @param {array} The grayscale pixels in a linear [p1,p2,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {number} threshold to determine whether the tested pixel is brighter or
   *     darker than the corner candidate p. Default value is 40.
   * @return {array} Array containing the coordinates of all found corners,
   *     e.g. [x0,y0,x1,y1,...], where P(x0,y0) represents a corner coordinate.
   * @static
   */
  tracking.Fast.findCorners = function(pixels, width, height, opt_threshold) {
    var circleOffsets = this.getCircleOffsets_(width);
    var circlePixels = new Int32Array(16);
    var corners = [];

    if (opt_threshold === undefined) {
      opt_threshold = this.THRESHOLD;
    }

    // When looping through the image pixels, skips the first three lines from
    // the image boundaries to constrain the surrounding circle inside the image
    // area.
    for (var i = 3; i < height - 3; i++) {
      for (var j = 3; j < width - 3; j++) {
        var w = i * width + j;
        var p = pixels[w];

        // Loops the circle offsets to read the pixel value for the sixteen
        // surrounding pixels.
        for (var k = 0; k < 16; k++) {
          circlePixels[k] = pixels[w + circleOffsets[k]];
        }

        if (this.isCorner(p, circlePixels, opt_threshold)) {
          // The pixel p is classified as a corner, as optimization increment j
          // by the circle radius 3 to skip the neighbor pixels inside the
          // surrounding circle. This can be removed without compromising the
          // result.
          corners.push(j, i);
          j += 3;
        }
      }
    }

    return corners;
  };

  /**
   * Checks if the circle pixel is brighter than the candidate pixel p by
   * a threshold.
   * @param {number} circlePixel The circle pixel value.
   * @param {number} p The value of the candidate pixel p.
   * @param {number} threshold
   * @return {Boolean}
   * @static
   */
  tracking.Fast.isBrighter = function(circlePixel, p, threshold) {
    return circlePixel - p > threshold;
  };

  /**
   * Checks if the circle pixel is within the corner of the candidate pixel p
   * by a threshold.
   * @param {number} p The value of the candidate pixel p.
   * @param {number} circlePixel The circle pixel value.
   * @param {number} threshold
   * @return {Boolean}
   * @static
   */
  tracking.Fast.isCorner = function(p, circlePixels, threshold) {
    if (this.isTriviallyExcluded(circlePixels, p, threshold)) {
      return false;
    }

    for (var x = 0; x < 16; x++) {
      var darker = true;
      var brighter = true;

      for (var y = 0; y < 9; y++) {
        var circlePixel = circlePixels[(x + y) & 15];

        if (!this.isBrighter(p, circlePixel, threshold)) {
          brighter = false;
          if (darker === false) {
            break;
          }
        }

        if (!this.isDarker(p, circlePixel, threshold)) {
          darker = false;
          if (brighter === false) {
            break;
          }
        }
      }

      if (brighter || darker) {
        return true;
      }
    }

    return false;
  };

  /**
   * Checks if the circle pixel is darker than the candidate pixel p by
   * a threshold.
   * @param {number} circlePixel The circle pixel value.
   * @param {number} p The value of the candidate pixel p.
   * @param {number} threshold
   * @return {Boolean}
   * @static
   */
  tracking.Fast.isDarker = function(circlePixel, p, threshold) {
    return p - circlePixel > threshold;
  };

  /**
   * Fast check to test if the candidate pixel is a trivially excluded value.
   * In order to be a corner, the candidate pixel value should be darker or
   * brighter than 9-12 surrounding pixels, when at least three of the top,
   * bottom, left and right pixels are brighter or darker it can be
   * automatically excluded improving the performance.
   * @param {number} circlePixel The circle pixel value.
   * @param {number} p The value of the candidate pixel p.
   * @param {number} threshold
   * @return {Boolean}
   * @static
   * @protected
   */
  tracking.Fast.isTriviallyExcluded = function(circlePixels, p, threshold) {
    var count = 0;
    var circleBottom = circlePixels[8];
    var circleLeft = circlePixels[12];
    var circleRight = circlePixels[4];
    var circleTop = circlePixels[0];

    if (this.isBrighter(circleTop, p, threshold)) {
      count++;
    }
    if (this.isBrighter(circleRight, p, threshold)) {
      count++;
    }
    if (this.isBrighter(circleBottom, p, threshold)) {
      count++;
    }
    if (this.isBrighter(circleLeft, p, threshold)) {
      count++;
    }

    if (count < 3) {
      count = 0;
      if (this.isDarker(circleTop, p, threshold)) {
        count++;
      }
      if (this.isDarker(circleRight, p, threshold)) {
        count++;
      }
      if (this.isDarker(circleBottom, p, threshold)) {
        count++;
      }
      if (this.isDarker(circleLeft, p, threshold)) {
        count++;
      }
      if (count < 3) {
        return true;
      }
    }

    return false;
  };

  /**
   * Gets the sixteen offset values of the circle surrounding pixel.
   * @param {number} width The image width.
   * @return {array} Array with the sixteen offset values of the circle
   *     surrounding pixel.
   * @private
   */
  tracking.Fast.getCircleOffsets_ = function(width) {
    if (this.circles_[width]) {
      return this.circles_[width];
    }

    var circle = new Int32Array(16);

    circle[0] = -width - width - width;
    circle[1] = circle[0] + 1;
    circle[2] = circle[1] + width + 1;
    circle[3] = circle[2] + width + 1;
    circle[4] = circle[3] + width;
    circle[5] = circle[4] + width;
    circle[6] = circle[5] + width - 1;
    circle[7] = circle[6] + width - 1;
    circle[8] = circle[7] - 1;
    circle[9] = circle[8] - 1;
    circle[10] = circle[9] - width - 1;
    circle[11] = circle[10] - width - 1;
    circle[12] = circle[11] - width;
    circle[13] = circle[12] - width;
    circle[14] = circle[13] - width + 1;
    circle[15] = circle[14] - width + 1;

    this.circles_[width] = circle;
    return circle;
  };
}());

(function() {
  /**
   * Math utility.
   * @static
   * @constructor
   */
  tracking.Math = {};

  /**
   * Euclidean distance between two points P(x0, y0) and P(x1, y1).
   * @param {number} x0 Horizontal coordinate of P0.
   * @param {number} y0 Vertical coordinate of P0.
   * @param {number} x1 Horizontal coordinate of P1.
   * @param {number} y1 Vertical coordinate of P1.
   * @return {number} The euclidean distance.
   */
  tracking.Math.distance = function(x0, y0, x1, y1) {
    var dx = x1 - x0;
    var dy = y1 - y0;

    return Math.sqrt(dx * dx + dy * dy);
  };

  /**
   * Calculates the Hamming weight of a string, which is the number of symbols that are
   * different from the zero-symbol of the alphabet used. It is thus
   * equivalent to the Hamming distance from the all-zero string of the same
   * length. For the most typical case, a string of bits, this is the number
   * of 1's in the string.
   *
   * Example:
   *
   * <pre>
   *  Binary string     Hamming weight
   *   11101                 4
   *   11101010              5
   * </pre>
   *
   * @param {number} i Number that holds the binary string to extract the hamming weight.
   * @return {number} The hamming weight.
   */
  tracking.Math.hammingWeight = function(i) {
    i = i - ((i >> 1) & 0x55555555);
    i = (i & 0x33333333) + ((i >> 2) & 0x33333333);

    return ((i + (i >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
  };

  /**
   * Generates a random number between [a, b] interval.
   * @param {number} a
   * @param {number} b
   * @return {number}
   */
  tracking.Math.uniformRandom = function(a, b) {
    return a + Math.random() * (b - a);
  };

  /**
   * Tests if a rectangle intersects with another.
   *
   *  <pre>
   *  x0y0 --------       x2y2 --------
   *      |       |           |       |
   *      -------- x1y1       -------- x3y3
   * </pre>
   *
   * @param {number} x0 Horizontal coordinate of P0.
   * @param {number} y0 Vertical coordinate of P0.
   * @param {number} x1 Horizontal coordinate of P1.
   * @param {number} y1 Vertical coordinate of P1.
   * @param {number} x2 Horizontal coordinate of P2.
   * @param {number} y2 Vertical coordinate of P2.
   * @param {number} x3 Horizontal coordinate of P3.
   * @param {number} y3 Vertical coordinate of P3.
   * @return {boolean}
   */
  tracking.Math.intersectRect = function(x0, y0, x1, y1, x2, y2, x3, y3) {
    return !(x2 > x1 || x3 < x0 || y2 > y1 || y3 < y0);
  };

}());

(function() {
  /**
   * Matrix utility.
   * @static
   * @constructor
   */
  tracking.Matrix = {};

  /**
   * Loops the array organized as major-row order and executes `fn` callback
   * for each iteration. The `fn` callback receives the following parameters:
   * `(r,g,b,a,index,i,j)`, where `r,g,b,a` represents the pixel color with
   * alpha channel, `index` represents the position in the major-row order
   * array and `i,j` the respective indexes positions in two dimensions.
   * @param {array} pixels The pixels in a linear [r,g,b,a,...] array to loop
   *     through.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {function} fn The callback function for each pixel.
   * @param {number} opt_jump Optional jump for the iteration, by default it
   *     is 1, hence loops all the pixels of the array.
   * @static
   */
  tracking.Matrix.forEach = function(pixels, width, height, fn, opt_jump) {
    opt_jump = opt_jump || 1;
    for (var i = 0; i < height; i += opt_jump) {
      for (var j = 0; j < width; j += opt_jump) {
        var w = i * width * 4 + j * 4;
        fn.call(this, pixels[w], pixels[w + 1], pixels[w + 2], pixels[w + 3], w, i, j);
      }
    }
  };

  /**
   * Calculates the per-element subtraction of two NxM matrices and returns a 
   * new NxM matrix as the result.
   * @param {matrix} a The first matrix.
   * @param {matrix} a The second matrix.
   * @static
   */
  tracking.Matrix.sub = function(a, b){
    var res = tracking.Matrix.clone(a);
    for(var i=0; i < res.length; i++){
      for(var j=0; j < res[i].length; j++){
        res[i][j] -= b[i][j]; 
      }
    }
    return res;
  }

  /**
   * Calculates the per-element sum of two NxM matrices and returns a new NxM
   * NxM matrix as the result.
   * @param {matrix} a The first matrix.
   * @param {matrix} a The second matrix.
   * @static
   */
  tracking.Matrix.add = function(a, b){
    var res = tracking.Matrix.clone(a);
    for(var i=0; i < res.length; i++){
      for(var j=0; j < res[i].length; j++){
        res[i][j] += b[i][j]; 
      }
    }
    return res;
  }

  /**
   * Clones a matrix (or part of it) and returns a new matrix as the result.
   * @param {matrix} src The matrix to be cloned.
   * @param {number} width The second matrix.
   * @static
   */
  tracking.Matrix.clone = function(src, width, height){
    width = width || src[0].length;
    height = height || src.length;
    var temp = new Array(height);
    var i = height;
    while(i--){
      temp[i] = new Array(width);
      var j = width;
      while(j--) temp[i][j] = src[i][j];
    } 
    return temp;
  }

  /**
   * Multiply a matrix by a scalar and returns a new matrix as the result.
   * @param {number} scalar The scalar to multiply the matrix by.
   * @param {matrix} src The matrix to be multiplied.
   * @static
   */
  tracking.Matrix.mulScalar = function(scalar, src){
    var res = tracking.Matrix.clone(src);
    for(var i=0; i < src.length; i++){
      for(var j=0; j < src[i].length; j++){
        res[i][j] *= scalar;
      }
    }
    return res;
  }

  /**
   * Transpose a matrix and returns a new matrix as the result.
   * @param {matrix} src The matrix to be transposed.
   * @static
   */
  tracking.Matrix.transpose = function(src){
    var transpose = new Array(src[0].length);
    for(var i=0; i < src[0].length; i++){
      transpose[i] = new Array(src.length);
      for(var j=0; j < src.length; j++){
        transpose[i][j] = src[j][i];
      }
    }
    return transpose;
  }

  /**
   * Multiply an MxN matrix with an NxP matrix and returns a new MxP matrix
   * as the result.
   * @param {matrix} a The first matrix.
   * @param {matrix} b The second matrix.
   * @static
   */
  tracking.Matrix.mul = function(a, b) {
    var res = new Array(a.length);
    for (var i = 0; i < a.length; i++) {
      res[i] = new Array(b[0].length);
      for (var j = 0; j < b[0].length; j++) {
        res[i][j] = 0;            
        for (var k = 0; k < a[0].length; k++) {
          res[i][j] += a[i][k] * b[k][j];
        }
      }
    }
    return res;
  }

  /**
   * Calculates the absolute norm of a matrix.
   * @param {matrix} src The matrix which norm will be calculated.
   * @static
   */
  tracking.Matrix.norm = function(src){
    var res = 0;
    for(var i=0; i < src.length; i++){
      for(var j=0; j < src[i].length; j++){
        res += src[i][j]*src[i][j];
      }
    }
    return Math.sqrt(res);
  }

  /**
   * Calculates and returns the covariance matrix of a set of vectors as well
   * as the mean of the matrix.
   * @param {matrix} src The matrix which covariance matrix will be calculated.
   * @static
   */
  tracking.Matrix.calcCovarMatrix = function(src){

    var mean = new Array(src.length);
    for(var i=0; i < src.length; i++){
      mean[i] = [0.0];
      for(var j=0; j < src[i].length; j++){
        mean[i][0] += src[i][j]/src[i].length;
      }
    }

    var deltaFull = tracking.Matrix.clone(mean);
    for(var i=0; i < deltaFull.length; i++){
      for(var j=0; j < src[0].length - 1; j++){
        deltaFull[i].push(deltaFull[i][0]);
      }
    }

    var a = tracking.Matrix.sub(src, deltaFull);
    var b = tracking.Matrix.transpose(a);
    var covar = tracking.Matrix.mul(b,a); 
    return [covar, mean];

  }

}());
(function() {
  /**
   * EPnp utility.
   * @static
   * @constructor
   */
  tracking.EPnP = {};

  tracking.EPnP.solve = function(objectPoints, imagePoints, cameraMatrix) {};
}());

(function() {
  /**
   * Tracker utility.
   * @constructor
   * @extends {tracking.EventEmitter}
   */
  tracking.Tracker = function() {
    tracking.Tracker.base(this, 'constructor');
  };

  tracking.inherits(tracking.Tracker, tracking.EventEmitter);

  /**
   * Tracks the pixels on the array. This method is called for each video
   * frame in order to emit `track` event.
   * @param {Uint8ClampedArray} pixels The pixels data to track.
   * @param {number} width The pixels canvas width.
   * @param {number} height The pixels canvas height.
   */
  tracking.Tracker.prototype.track = function() {};
}());

(function() {
  /**
   * TrackerTask utility.
   * @constructor
   * @extends {tracking.EventEmitter}
   */
  tracking.TrackerTask = function(tracker) {
    tracking.TrackerTask.base(this, 'constructor');

    if (!tracker) {
      throw new Error('Tracker instance not specified.');
    }

    this.setTracker(tracker);
  };

  tracking.inherits(tracking.TrackerTask, tracking.EventEmitter);

  /**
   * Holds the tracker instance managed by this task.
   * @type {tracking.Tracker}
   * @private
   */
  tracking.TrackerTask.prototype.tracker_ = null;

  /**
   * Holds if the tracker task is in running.
   * @type {boolean}
   * @private
   */
  tracking.TrackerTask.prototype.running_ = false;

  /**
   * Gets the tracker instance managed by this task.
   * @return {tracking.Tracker}
   */
  tracking.TrackerTask.prototype.getTracker = function() {
    return this.tracker_;
  };

  /**
   * Returns true if the tracker task is in running, false otherwise.
   * @return {boolean}
   * @private
   */
  tracking.TrackerTask.prototype.inRunning = function() {
    return this.running_;
  };

  /**
   * Sets if the tracker task is in running.
   * @param {boolean} running
   * @private
   */
  tracking.TrackerTask.prototype.setRunning = function(running) {
    this.running_ = running;
  };

  /**
   * Sets the tracker instance managed by this task.
   * @return {tracking.Tracker}
   */
  tracking.TrackerTask.prototype.setTracker = function(tracker) {
    this.tracker_ = tracker;
  };

  /**
   * Emits a `run` event on the tracker task for the implementers to run any
   * child action, e.g. `requestAnimationFrame`.
   * @return {object} Returns itself, so calls can be chained.
   */
  tracking.TrackerTask.prototype.run = function() {
    var self = this;

    if (this.inRunning()) {
      return;
    }

    this.setRunning(true);
    this.reemitTrackEvent_ = function(event) {
      self.emit('track', event);
    };
    this.tracker_.on('track', this.reemitTrackEvent_);
    this.emit('run');
    return this;
  };

  /**
   * Emits a `stop` event on the tracker task for the implementers to stop any
   * child action being done, e.g. `requestAnimationFrame`.
   * @return {object} Returns itself, so calls can be chained.
   */
  tracking.TrackerTask.prototype.stop = function() {
    if (!this.inRunning()) {
      return;
    }

    this.setRunning(false);
    this.emit('stop');
    this.tracker_.removeListener('track', this.reemitTrackEvent_);
    return this;
  };
}());

(function() {
  /**
   * ColorTracker utility to track colored blobs in a frame using color
   * difference evaluation.
   * @constructor
   * @param {string|Array.<string>} opt_colors Optional colors to track.
   * @extends {tracking.Tracker}
   */
  tracking.ColorTracker = function(opt_colors) {
    tracking.ColorTracker.base(this, 'constructor');

    if (typeof opt_colors === 'string') {
      opt_colors = [opt_colors];
    }

    if (opt_colors) {
      opt_colors.forEach(function(color) {
        if (!tracking.ColorTracker.getColor(color)) {
          throw new Error('Color not valid, try `new tracking.ColorTracker("magenta")`.');
        }
      });
      this.setColors(opt_colors);
    }
  };

  tracking.inherits(tracking.ColorTracker, tracking.Tracker);

  /**
   * Holds the known colors.
   * @type {Object.<string, function>}
   * @private
   * @static
   */
  tracking.ColorTracker.knownColors_ = {};

  /**
   * Caches coordinates values of the neighbours surrounding a pixel.
   * @type {Object.<number, Int32Array>}
   * @private
   * @static
   */
  tracking.ColorTracker.neighbours_ = {};

  /**
   * Registers a color as known color.
   * @param {string} name The color name.
   * @param {function} fn The color function to test if the passed (r,g,b) is
   *     the desired color.
   * @static
   */
  tracking.ColorTracker.registerColor = function(name, fn) {
    tracking.ColorTracker.knownColors_[name] = fn;
  };

  /**
   * Gets the known color function that is able to test whether an (r,g,b) is
   * the desired color.
   * @param {string} name The color name.
   * @return {function} The known color test function.
   * @static
   */
  tracking.ColorTracker.getColor = function(name) {
    return tracking.ColorTracker.knownColors_[name];
  };

  /**
   * Holds the colors to be tracked by the `ColorTracker` instance.
   * @default ['magenta']
   * @type {Array.<string>}
   */
  tracking.ColorTracker.prototype.colors = ['magenta'];

  /**
   * Holds the minimum dimension to classify a rectangle.
   * @default 20
   * @type {number}
   */
  tracking.ColorTracker.prototype.minDimension = 20;

  /**
   * Holds the maximum dimension to classify a rectangle.
   * @default Infinity
   * @type {number}
   */
  tracking.ColorTracker.prototype.maxDimension = Infinity;


  /**
   * Holds the minimum group size to be classified as a rectangle.
   * @default 30
   * @type {number}
   */
  tracking.ColorTracker.prototype.minGroupSize = 30;

  /**
   * Calculates the central coordinate from the cloud points. The cloud points
   * are all points that matches the desired color.
   * @param {Array.<number>} cloud Major row order array containing all the
   *     points from the desired color, e.g. [x1, y1, c2, y2, ...].
   * @param {number} total Total numbers of pixels of the desired color.
   * @return {object} Object containing the x, y and estimated z coordinate of
   *     the blog extracted from the cloud points.
   * @private
   */
  tracking.ColorTracker.prototype.calculateDimensions_ = function(cloud, total) {
    var maxx = -1;
    var maxy = -1;
    var minx = Infinity;
    var miny = Infinity;

    for (var c = 0; c < total; c += 2) {
      var x = cloud[c];
      var y = cloud[c + 1];

      if (x < minx) {
        minx = x;
      }
      if (x > maxx) {
        maxx = x;
      }
      if (y < miny) {
        miny = y;
      }
      if (y > maxy) {
        maxy = y;
      }
    }

    return {
      width: maxx - minx,
      height: maxy - miny,
      x: minx,
      y: miny
    };
  };

  /**
   * Gets the colors being tracked by the `ColorTracker` instance.
   * @return {Array.<string>}
   */
  tracking.ColorTracker.prototype.getColors = function() {
    return this.colors;
  };

  /**
   * Gets the minimum dimension to classify a rectangle.
   * @return {number}
   */
  tracking.ColorTracker.prototype.getMinDimension = function() {
    return this.minDimension;
  };

  /**
   * Gets the maximum dimension to classify a rectangle.
   * @return {number}
   */
  tracking.ColorTracker.prototype.getMaxDimension = function() {
    return this.maxDimension;
  };

  /**
   * Gets the minimum group size to be classified as a rectangle.
   * @return {number}
   */
  tracking.ColorTracker.prototype.getMinGroupSize = function() {
    return this.minGroupSize;
  };

  /**
   * Gets the eight offset values of the neighbours surrounding a pixel.
   * @param {number} width The image width.
   * @return {array} Array with the eight offset values of the neighbours
   *     surrounding a pixel.
   * @private
   */
  tracking.ColorTracker.prototype.getNeighboursForWidth_ = function(width) {
    if (tracking.ColorTracker.neighbours_[width]) {
      return tracking.ColorTracker.neighbours_[width];
    }

    var neighbours = new Int32Array(8);

    neighbours[0] = -width * 4;
    neighbours[1] = -width * 4 + 4;
    neighbours[2] = 4;
    neighbours[3] = width * 4 + 4;
    neighbours[4] = width * 4;
    neighbours[5] = width * 4 - 4;
    neighbours[6] = -4;
    neighbours[7] = -width * 4 - 4;

    tracking.ColorTracker.neighbours_[width] = neighbours;

    return neighbours;
  };

  /**
   * Unites groups whose bounding box intersect with each other.
   * @param {Array.<Object>} rects
   * @private
   */
  tracking.ColorTracker.prototype.mergeRectangles_ = function(rects) {
    var intersects;
    var results = [];
    var minDimension = this.getMinDimension();
    var maxDimension = this.getMaxDimension();

    for (var r = 0; r < rects.length; r++) {
      var r1 = rects[r];
      intersects = true;
      for (var s = r + 1; s < rects.length; s++) {
        var r2 = rects[s];
        if (tracking.Math.intersectRect(r1.x, r1.y, r1.x + r1.width, r1.y + r1.height, r2.x, r2.y, r2.x + r2.width, r2.y + r2.height)) {
          intersects = false;
          var x1 = Math.min(r1.x, r2.x);
          var y1 = Math.min(r1.y, r2.y);
          var x2 = Math.max(r1.x + r1.width, r2.x + r2.width);
          var y2 = Math.max(r1.y + r1.height, r2.y + r2.height);
          r2.height = y2 - y1;
          r2.width = x2 - x1;
          r2.x = x1;
          r2.y = y1;
          break;
        }
      }

      if (intersects) {
        if (r1.width >= minDimension && r1.height >= minDimension) {
          if (r1.width <= maxDimension && r1.height <= maxDimension) {
            results.push(r1);
          }
        }
      }
    }

    return results;
  };

  /**
   * Sets the colors to be tracked by the `ColorTracker` instance.
   * @param {Array.<string>} colors
   */
  tracking.ColorTracker.prototype.setColors = function(colors) {
    this.colors = colors;
  };

  /**
   * Sets the minimum dimension to classify a rectangle.
   * @param {number} minDimension
   */
  tracking.ColorTracker.prototype.setMinDimension = function(minDimension) {
    this.minDimension = minDimension;
  };

  /**
   * Sets the maximum dimension to classify a rectangle.
   * @param {number} maxDimension
   */
  tracking.ColorTracker.prototype.setMaxDimension = function(maxDimension) {
    this.maxDimension = maxDimension;
  };

  /**
   * Sets the minimum group size to be classified as a rectangle.
   * @param {number} minGroupSize
   */
  tracking.ColorTracker.prototype.setMinGroupSize = function(minGroupSize) {
    this.minGroupSize = minGroupSize;
  };

  /**
   * Tracks the `Video` frames. This method is called for each video frame in
   * order to emit `track` event.
   * @param {Uint8ClampedArray} pixels The pixels data to track.
   * @param {number} width The pixels canvas width.
   * @param {number} height The pixels canvas height.
   */
  tracking.ColorTracker.prototype.track = function(pixels, width, height) {
    var self = this;
    var colors = this.getColors();

    if (!colors) {
      throw new Error('Colors not specified, try `new tracking.ColorTracker("magenta")`.');
    }

    var results = [];

    colors.forEach(function(color) {
      results = results.concat(self.trackColor_(pixels, width, height, color));
    });

    this.emit('track', {
      data: results
    });
  };

  /**
   * Find the given color in the given matrix of pixels using Flood fill
   * algorithm to determines the area connected to a given node in a
   * multi-dimensional array.
   * @param {Uint8ClampedArray} pixels The pixels data to track.
   * @param {number} width The pixels canvas width.
   * @param {number} height The pixels canvas height.
   * @param {string} color The color to be found
   * @private
   */
  tracking.ColorTracker.prototype.trackColor_ = function(pixels, width, height, color) {
    var colorFn = tracking.ColorTracker.knownColors_[color];
    var currGroup = new Int32Array(pixels.length >> 2);
    var currGroupSize;
    var currI;
    var currJ;
    var currW;
    var marked = new Int8Array(pixels.length);
    var minGroupSize = this.getMinGroupSize();
    var neighboursW = this.getNeighboursForWidth_(width);
    var queue = new Int32Array(pixels.length);
    var queuePosition;
    var results = [];
    var w = -4;

    if (!colorFn) {
      return results;
    }

    for (var i = 0; i < height; i++) {
      for (var j = 0; j < width; j++) {
        w += 4;

        if (marked[w]) {
          continue;
        }

        currGroupSize = 0;

        queuePosition = -1;
        queue[++queuePosition] = w;
        queue[++queuePosition] = i;
        queue[++queuePosition] = j;

        marked[w] = 1;

        while (queuePosition >= 0) {
          currJ = queue[queuePosition--];
          currI = queue[queuePosition--];
          currW = queue[queuePosition--];

          if (colorFn(pixels[currW], pixels[currW + 1], pixels[currW + 2], pixels[currW + 3], currW, currI, currJ)) {
            currGroup[currGroupSize++] = currJ;
            currGroup[currGroupSize++] = currI;

            for (var k = 0; k < neighboursW.length; k++) {
              var otherW = currW + neighboursW[k];
              var otherI = currI + neighboursI[k];
              var otherJ = currJ + neighboursJ[k];
              if (!marked[otherW] && otherI >= 0 && otherI < height && otherJ >= 0 && otherJ < width) {
                queue[++queuePosition] = otherW;
                queue[++queuePosition] = otherI;
                queue[++queuePosition] = otherJ;

                marked[otherW] = 1;
              }
            }
          }
        }

        if (currGroupSize >= minGroupSize) {
          var data = this.calculateDimensions_(currGroup, currGroupSize);
          if (data) {
            data.color = color;
            results.push(data);
          }
        }
      }
    }

    return this.mergeRectangles_(results);
  };

  // Default colors
  //===================

  tracking.ColorTracker.registerColor('cyan', function(r, g, b) {
    var thresholdGreen = 50,
      thresholdBlue = 70,
      dx = r - 0,
      dy = g - 255,
      dz = b - 255;

    if ((g - r) >= thresholdGreen && (b - r) >= thresholdBlue) {
      return true;
    }
    return dx * dx + dy * dy + dz * dz < 6400;
  });

  tracking.ColorTracker.registerColor('magenta', function(r, g, b) {
    var threshold = 50,
      dx = r - 255,
      dy = g - 0,
      dz = b - 255;

    if ((r - g) >= threshold && (b - g) >= threshold) {
      return true;
    }
    return dx * dx + dy * dy + dz * dz < 19600;
  });

  tracking.ColorTracker.registerColor('yellow', function(r, g, b) {
    var threshold = 50,
      dx = r - 255,
      dy = g - 255,
      dz = b - 0;

    if ((r - b) >= threshold && (g - b) >= threshold) {
      return true;
    }
    return dx * dx + dy * dy + dz * dz < 10000;
  });


  // Caching neighbour i/j offset values.
  //=====================================
  var neighboursI = new Int32Array([-1, -1, 0, 1, 1, 1, 0, -1]);
  var neighboursJ = new Int32Array([0, 1, 1, 1, 0, -1, -1, -1]);
}());

(function() {
  /**
   * ObjectTracker utility.
   * @constructor
   * @param {string|Array.<string|Array.<number>>} opt_classifiers Optional
   *     object classifiers to track.
   * @extends {tracking.Tracker}
   */
  tracking.ObjectTracker = function(opt_classifiers) {
    tracking.ObjectTracker.base(this, 'constructor');

    if (opt_classifiers) {
      if (!Array.isArray(opt_classifiers)) {
        opt_classifiers = [opt_classifiers];
      }

      if (Array.isArray(opt_classifiers)) {
        opt_classifiers.forEach(function(classifier, i) {
          if (typeof classifier === 'string') {
            opt_classifiers[i] = tracking.ViolaJones.classifiers[classifier];
          }
          if (!opt_classifiers[i]) {
            throw new Error('Object classifier not valid, try `new tracking.ObjectTracker("face")`.');
          }
        });
      }
    }

    this.setClassifiers(opt_classifiers);
  };

  tracking.inherits(tracking.ObjectTracker, tracking.Tracker);

  /**
   * Specifies the edges density of a block in order to decide whether to skip
   * it or not.
   * @default 0.2
   * @type {number}
   */
  tracking.ObjectTracker.prototype.edgesDensity = 0.2;

  /**
   * Specifies the initial scale to start the feature block scaling.
   * @default 1.0
   * @type {number}
   */
  tracking.ObjectTracker.prototype.initialScale = 1.0;

  /**
   * Specifies the scale factor to scale the feature block.
   * @default 1.25
   * @type {number}
   */
  tracking.ObjectTracker.prototype.scaleFactor = 1.25;

  /**
   * Specifies the block step size.
   * @default 1.5
   * @type {number}
   */
  tracking.ObjectTracker.prototype.stepSize = 1.5;

  /**
   * Gets the tracker HAAR classifiers.
   * @return {TypedArray.<number>}
   */
  tracking.ObjectTracker.prototype.getClassifiers = function() {
    return this.classifiers;
  };

  /**
   * Gets the edges density value.
   * @return {number}
   */
  tracking.ObjectTracker.prototype.getEdgesDensity = function() {
    return this.edgesDensity;
  };

  /**
   * Gets the initial scale to start the feature block scaling.
   * @return {number}
   */
  tracking.ObjectTracker.prototype.getInitialScale = function() {
    return this.initialScale;
  };

  /**
   * Gets the scale factor to scale the feature block.
   * @return {number}
   */
  tracking.ObjectTracker.prototype.getScaleFactor = function() {
    return this.scaleFactor;
  };

  /**
   * Gets the block step size.
   * @return {number}
   */
  tracking.ObjectTracker.prototype.getStepSize = function() {
    return this.stepSize;
  };

  /**
   * Tracks the `Video` frames. This method is called for each video frame in
   * order to emit `track` event.
   * @param {Uint8ClampedArray} pixels The pixels data to track.
   * @param {number} width The pixels canvas width.
   * @param {number} height The pixels canvas height.
   */
  tracking.ObjectTracker.prototype.track = function(pixels, width, height) {
    var self = this;
    var classifiers = this.getClassifiers();

    if (!classifiers) {
      throw new Error('Object classifier not specified, try `new tracking.ObjectTracker("face")`.');
    }

    var results = [];

    classifiers.forEach(function(classifier) {
      results = results.concat(tracking.ViolaJones.detect(pixels, width, height, self.getInitialScale(), self.getScaleFactor(), self.getStepSize(), self.getEdgesDensity(), classifier));
    });

    this.emit('track', {
      data: results
    });
  };

  /**
   * Sets the tracker HAAR classifiers.
   * @param {TypedArray.<number>} classifiers
   */
  tracking.ObjectTracker.prototype.setClassifiers = function(classifiers) {
    this.classifiers = classifiers;
  };

  /**
   * Sets the edges density.
   * @param {number} edgesDensity
   */
  tracking.ObjectTracker.prototype.setEdgesDensity = function(edgesDensity) {
    this.edgesDensity = edgesDensity;
  };

  /**
   * Sets the initial scale to start the block scaling.
   * @param {number} initialScale
   */
  tracking.ObjectTracker.prototype.setInitialScale = function(initialScale) {
    this.initialScale = initialScale;
  };

  /**
   * Sets the scale factor to scale the feature block.
   * @param {number} scaleFactor
   */
  tracking.ObjectTracker.prototype.setScaleFactor = function(scaleFactor) {
    this.scaleFactor = scaleFactor;
  };

  /**
   * Sets the block step size.
   * @param {number} stepSize
   */
  tracking.ObjectTracker.prototype.setStepSize = function(stepSize) {
    this.stepSize = stepSize;
  };

}());

(function() {


  tracking.LandmarksTracker = function() {
    tracking.LandmarksTracker.base(this, 'constructor');
  }

  tracking.inherits(tracking.LandmarksTracker, tracking.ObjectTracker);

  tracking.LandmarksTracker.prototype.track = function(pixels, width, height) {
	 
    var image = {
      'data': pixels,
      'width': width,
      'height': height
    };

    var classifier = tracking.ViolaJones.classifiers['face'];

    var faces = tracking.ViolaJones.detect(pixels, width, height, 
      this.getInitialScale(), this.getScaleFactor(), this.getStepSize(), 
      this.getEdgesDensity(), classifier);

    var landmarks = tracking.LBF.align(pixels, width, height, faces);

    this.emit('track', {
      'data': {
        'faces' : faces,
        'landmarks' : landmarks
      }
    });

  }

}());

(function() {

  tracking.LBF = {};

  /**
   * LBF Regressor utility.
   * @constructor
   */
  tracking.LBF.Regressor = function(maxNumStages){
    this.maxNumStages = maxNumStages;

    this.rfs = new Array(maxNumStages);
    this.models = new Array(maxNumStages);
    for(var i=0; i < maxNumStages; i++){
      this.rfs[i] = new tracking.LBF.RandomForest(i);
      this.models[i] = tracking.LBF.RegressorData[i].models;
    }

    this.meanShape = tracking.LBF.LandmarksData;
  }

  /**
   * Predicts the position of the landmarks based on the bounding box of the face.
   * @param {pixels} pixels The grayscale pixels in a linear array.
   * @param {number} width Width of the image.
   * @param {number} height Height of the image.
   * @param {object} boudingBox Bounding box of the face to be aligned.
   * @return {matrix} A matrix with each landmark position in a row [x,y].
   */
  tracking.LBF.Regressor.prototype.predict = function(pixels, width, height, boundingBox) {

    var images = [];
    var currentShapes = [];
    var boundingBoxes = [];

    var meanShapeClone = tracking.Matrix.clone(this.meanShape);

    images.push({
      'data': pixels,
      'width': width,
      'height': height
    });
    boundingBoxes.push(boundingBox);

    currentShapes.push(tracking.LBF.projectShapeToBoundingBox_(meanShapeClone, boundingBox));

    for(var stage = 0; stage < this.maxNumStages; stage++){
      var binaryFeatures = tracking.LBF.Regressor.deriveBinaryFeat(this.rfs[stage], images, currentShapes, boundingBoxes, meanShapeClone);
      this.applyGlobalPrediction(binaryFeatures, this.models[stage], currentShapes, boundingBoxes);
    }

    return currentShapes[0];
  };

  /**
   * Multiplies the binary features of the landmarks with the regression matrix
   * to obtain the displacement for each landmark. Then applies this displacement
   * into the landmarks shape.
   * @param {object} binaryFeatures The binary features for the landmarks.
   * @param {object} models The regressor models.
   * @param {matrix} currentShapes The landmarks shapes.
   * @param {array} boudingBoxes The bounding boxes of the faces.
   */
  tracking.LBF.Regressor.prototype.applyGlobalPrediction = function(binaryFeatures, models, currentShapes, 
    boundingBoxes){

    var residual = currentShapes[0].length * 2;

    var rotation = [];
    var deltashape = new Array(residual/2);
    for(var i=0; i < residual/2; i++){
      deltashape[i] = [0.0, 0.0];
    }

    for(var i=0; i < currentShapes.length; i++){
      for(var j=0; j < residual; j++){
        var tmp = 0;
        for(var lx=0, idx=0; (idx = binaryFeatures[i][lx].index) != -1; lx++){
          if(idx <= models[j].nr_feature){
            tmp += models[j].data[(idx - 1)] * binaryFeatures[i][lx].value;
          }
        }
        if(j < residual/2){
          deltashape[j][0] = tmp;
        }else{
          deltashape[j - residual/2][1] = tmp;
        }
      }

      var res = tracking.LBF.similarityTransform_(tracking.LBF.unprojectShapeToBoundingBox_(currentShapes[i], boundingBoxes[i]), this.meanShape);
      var rotation = tracking.Matrix.transpose(res[0]);

      var s = tracking.LBF.unprojectShapeToBoundingBox_(currentShapes[i], boundingBoxes[i]);
      s = tracking.Matrix.add(s, deltashape);

      currentShapes[i] = tracking.LBF.projectShapeToBoundingBox_(s, boundingBoxes[i]);

    }
  };

  /**
   * Derives the binary features from the image for each landmark. 
   * @param {object} forest The random forest to search for the best binary feature match.
   * @param {array} images The images with pixels in a grayscale linear array.
   * @param {array} currentShapes The current landmarks shape.
   * @param {array} boudingBoxes The bounding boxes of the faces.
   * @param {matrix} meanShape The mean shape of the current landmarks set.
   * @return {array} The binary features extracted from the image and matched with the
   *     training data.
   * @static
   */
  tracking.LBF.Regressor.deriveBinaryFeat = function(forest, images, currentShapes, boundingBoxes, meanShape){

    var binaryFeatures = new Array(images.length);
    for(var i=0; i < images.length; i++){
      var t = forest.maxNumTrees * forest.landmarkNum + 1;
      binaryFeatures[i] = new Array(t);
      for(var j=0; j < t; j++){
        binaryFeatures[i][j] = {};
      }
    }

    var leafnodesPerTree = 1 << (forest.maxDepth - 1);

    for(var i=0; i < images.length; i++){

      var projectedShape = tracking.LBF.unprojectShapeToBoundingBox_(currentShapes[i], boundingBoxes[i]);
      var transform = tracking.LBF.similarityTransform_(projectedShape, meanShape);
      
      for(var j=0; j < forest.landmarkNum; j++){
        for(var k=0; k < forest.maxNumTrees; k++){

          var binaryCode = tracking.LBF.Regressor.getCodeFromTree(forest.rfs[j][k], images[i], 
                              currentShapes[i], boundingBoxes[i], transform[0], transform[1]);

          var index = j*forest.maxNumTrees + k;
          binaryFeatures[i][index].index = leafnodesPerTree * index + binaryCode;
          binaryFeatures[i][index].value = 1;

        }
      }
      binaryFeatures[i][forest.landmarkNum * forest.maxNumTrees].index = -1;
      binaryFeatures[i][forest.landmarkNum * forest.maxNumTrees].value = -1;
    }
    return binaryFeatures;

  }

  /**
   * Gets the binary code for a specific tree in a random forest. For each landmark,
   * the position from two pre-defined points are recovered from the training data
   * and then the intensity of the pixels corresponding to these points is extracted 
   * from the image and used to traverse the trees in the random forest. At the end,
   * the ending nodes will be represented by 1, and the remaining nodes by 0.
   * 
   * +--------------------------- Random Forest -----------------------------+ 
   * | Ø = Ending leaf                                                       |
   * |                                                                       |
   * |       O             O             O             O             O       |
   * |     /   \         /   \         /   \         /   \         /   \     |
   * |    O     O       O     O       O     O       O     O       O     O    |
   * |   / \   / \     / \   / \     / \   / \     / \   / \     / \   / \   |
   * |  Ø   O O   O   O   O Ø   O   O   Ø O   O   O   O Ø   O   O   O O   Ø  |
   * |  1   0 0   0   0   0 1   0   0   1 0   0   0   0 1   0   0   0 0   1  |
   * +-----------------------------------------------------------------------+
   * Final binary code for this landmark: 10000010010000100001
   *
   * @param {object} forest The tree to be analyzed.
   * @param {array} image The image with pixels in a grayscale linear array.
   * @param {matrix} shape The current landmarks shape.
   * @param {object} boudingBoxes The bounding box of the face.
   * @param {matrix} rotation The rotation matrix used to transform the projected landmarks
   *     into the mean shape.
   * @param {number} scale The scale factor used to transform the projected landmarks
   *     into the mean shape.
   * @return {number} The binary code extracted from the tree.
   * @static
   */
  tracking.LBF.Regressor.getCodeFromTree = function(tree, image, shape, boundingBox, rotation, scale){
    var current = 0;
    var bincode = 0;

    while(true){
      
      var x1 = Math.cos(tree.nodes[current].feats[0]) * tree.nodes[current].feats[2] * tree.maxRadioRadius * boundingBox.width;
      var y1 = Math.sin(tree.nodes[current].feats[0]) * tree.nodes[current].feats[2] * tree.maxRadioRadius * boundingBox.height;
      var x2 = Math.cos(tree.nodes[current].feats[1]) * tree.nodes[current].feats[3] * tree.maxRadioRadius * boundingBox.width;
      var y2 = Math.sin(tree.nodes[current].feats[1]) * tree.nodes[current].feats[3] * tree.maxRadioRadius * boundingBox.height;

      var project_x1 = rotation[0][0] * x1 + rotation[0][1] * y1;
      var project_y1 = rotation[1][0] * x1 + rotation[1][1] * y1;

      var real_x1 = Math.floor(project_x1 + shape[tree.landmarkID][0]);
      var real_y1 = Math.floor(project_y1 + shape[tree.landmarkID][1]);
      real_x1 = Math.max(0.0, Math.min(real_x1, image.height - 1.0));
      real_y1 = Math.max(0.0, Math.min(real_y1, image.width - 1.0));

      var project_x2 = rotation[0][0] * x2 + rotation[0][1] * y2;
      var project_y2 = rotation[1][0] * x2 + rotation[1][1] * y2;

      var real_x2 = Math.floor(project_x2 + shape[tree.landmarkID][0]);
      var real_y2 = Math.floor(project_y2 + shape[tree.landmarkID][1]);
      real_x2 = Math.max(0.0, Math.min(real_x2, image.height - 1.0));
      real_y2 = Math.max(0.0, Math.min(real_y2, image.width - 1.0));
      var pdf = Math.floor(image.data[real_y1*image.width + real_x1]) - 
          Math.floor(image.data[real_y2 * image.width +real_x2]);

      if(pdf < tree.nodes[current].thresh){
        current = tree.nodes[current].cnodes[0];
      }else{
        current = tree.nodes[current].cnodes[1];
      }

      if (tree.nodes[current].is_leafnode == 1) {
        bincode = 1;
        for (var i=0; i < tree.leafnodes.length; i++) {
          if (tree.leafnodes[i] == current) {
            return bincode;
          }
          bincode++;
        }
        return bincode;
      }

    }

    return bincode;
  }

}());
(function() {
  /**
   * Face Alignment via Regressing Local Binary Features (LBF)
   * This approach has two components: a set of local binary features and
   * a locality principle for learning those features.
   * The locality principle is used to guide the learning of a set of highly
   * discriminative local binary features for each landmark independently.
   * The obtained local binary features are used to learn a linear regression
   * that later will be used to guide the landmarks in the alignment phase.
   * 
   * @authors: VoxarLabs Team (http://cin.ufpe.br/~voxarlabs)
   *           Lucas Figueiredo <lsf@cin.ufpe.br>, Thiago Menezes <tmc2@cin.ufpe.br>,
   *           Thiago Domingues <tald@cin.ufpe.br>, Rafael Roberto <rar3@cin.ufpe.br>,
   *           Thulio Araujo <tlsa@cin.ufpe.br>, Joao Victor <jvfl@cin.ufpe.br>,
   *           Tomer Simis <tls@cin.ufpe.br>)
   */
  
  /**
   * Holds the maximum number of stages that will be used in the alignment algorithm.
   * Each stage contains a different set of random forests and retrieves the binary
   * code from a more "specialized" (i.e. smaller) region around the landmarks.
   * @type {number}
   * @static
   */
  tracking.LBF.maxNumStages = 4;

  /**
   * Holds the regressor that will be responsible for extracting the local features from 
   * the image and guide the landmarks using the training data.
   * @type {object}
   * @protected
   * @static
   */
  tracking.LBF.regressor_ = null; 
  
  /**
   * Generates a set of landmarks for a set of faces
   * @param {pixels} pixels The pixels in a linear [r,g,b,a,...] array.
   * @param {number} width The image width.
   * @param {number} height The image height.
   * @param {array} faces The list of faces detected in the image
   * @return {array} The aligned landmarks, each set of landmarks corresponding
   *     to a specific face.
   * @static
   */
  tracking.LBF.align = function(pixels, width, height, faces){

    if(tracking.LBF.regressor_ == null){
      tracking.LBF.regressor_ = new tracking.LBF.Regressor(
        tracking.LBF.maxNumStages
      );
    }

    pixels = tracking.Image.grayscale(pixels, width, height, false);

    pixels = tracking.Image.equalizeHist(pixels, width, height);

    var shapes = new Array(faces.length);

    for(var i in faces){

      faces[i].height = faces[i].width;

      var boundingBox = {};
      boundingBox.startX = faces[i].x;
      boundingBox.startY = faces[i].y;
      boundingBox.width = faces[i].width;
      boundingBox.height = faces[i].height;

      shapes[i] = tracking.LBF.regressor_.predict(pixels, width, height, boundingBox);
    }

    return shapes;
  }

  /**
   * Unprojects the landmarks shape from the bounding box.
   * @param {matrix} shape The landmarks shape.
   * @param {matrix} boudingBox The bounding box.
   * @return {matrix} The landmarks shape projected into the bounding box.
   * @static
   * @protected
   */
  tracking.LBF.unprojectShapeToBoundingBox_ = function(shape, boundingBox){
    var temp = new Array(shape.length);
    for(var i=0; i < shape.length; i++){
      temp[i] = [
        (shape[i][0] - boundingBox.startX) / boundingBox.width,
        (shape[i][1] - boundingBox.startY) / boundingBox.height
      ];
    }
    return temp;
  }

  /**
   * Projects the landmarks shape into the bounding box. The landmarks shape has
   * normalized coordinates, so it is necessary to map these coordinates into
   * the bounding box coordinates.
   * @param {matrix} shape The landmarks shape.
   * @param {matrix} boudingBox The bounding box.
   * @return {matrix} The landmarks shape.
   * @static
   * @protected
   */
  tracking.LBF.projectShapeToBoundingBox_ = function(shape, boundingBox){
    var temp = new Array(shape.length);
    for(var i=0; i < shape.length; i++){
      temp[i] = [
        shape[i][0] * boundingBox.width + boundingBox.startX,
        shape[i][1] * boundingBox.height + boundingBox.startY
      ];
    }
    return temp;
  }

  /**
   * Calculates the rotation and scale necessary to transform shape1 into shape2.
   * @param {matrix} shape1 The shape to be transformed.
   * @param {matrix} shape2 The shape to be transformed in.
   * @return {[matrix, scalar]} The rotation matrix and scale that applied to shape1
   *     results in shape2.
   * @static
   * @protected
   */
  tracking.LBF.similarityTransform_ = function(shape1, shape2){

    var center1 = [0,0];
    var center2 = [0,0];
    for (var i = 0; i < shape1.length; i++) {
      center1[0] += shape1[i][0];
      center1[1] += shape1[i][1];
      center2[0] += shape2[i][0];
      center2[1] += shape2[i][1];
    }
    center1[0] /= shape1.length;
    center1[1] /= shape1.length;
    center2[0] /= shape2.length;
    center2[1] /= shape2.length;

    var temp1 = tracking.Matrix.clone(shape1);
    var temp2 = tracking.Matrix.clone(shape2);
    for(var i=0; i < shape1.length; i++){
      temp1[i][0] -= center1[0];
      temp1[i][1] -= center1[1];
      temp2[i][0] -= center2[0];
      temp2[i][1] -= center2[1];
    }

    var covariance1, covariance2;
    var mean1, mean2;

    var t = tracking.Matrix.calcCovarMatrix(temp1);
    covariance1 = t[0];
    mean1 = t[1];

    t = tracking.Matrix.calcCovarMatrix(temp2);
    covariance2 = t[0];
    mean2 = t[1];

    var s1 = Math.sqrt(tracking.Matrix.norm(covariance1));
    var s2 = Math.sqrt(tracking.Matrix.norm(covariance2));

    var scale = s1/s2;
    temp1 = tracking.Matrix.mulScalar(1.0/s1, temp1);
    temp2 = tracking.Matrix.mulScalar(1.0/s2, temp2);

    var num = 0, den = 0;
    for (var i = 0; i < shape1.length; i++) {
      num = num + temp1[i][1] * temp2[i][0] - temp1[i][0] * temp2[i][1];
      den = den + temp1[i][0] * temp2[i][0] + temp1[i][1] * temp2[i][1];
    }

    var norm = Math.sqrt(num*num + den*den);
    var sin_theta = num/norm;
    var cos_theta = den/norm;
    var rotation = [
      [cos_theta, -sin_theta],
      [sin_theta, cos_theta]
    ];

    return [rotation, scale];
  }

  /**
   * LBF Random Forest data structure.
   * @static
   * @constructor
   */
  tracking.LBF.RandomForest = function(forestIndex){
    this.maxNumTrees = tracking.LBF.RegressorData[forestIndex].max_numtrees;
    this.landmarkNum = tracking.LBF.RegressorData[forestIndex].num_landmark;
    this.maxDepth = tracking.LBF.RegressorData[forestIndex].max_depth;
    this.stages = tracking.LBF.RegressorData[forestIndex].stages; 

    this.rfs = new Array(this.landmarkNum);
    for(var i=0; i < this.landmarkNum; i++){
      this.rfs[i] = new Array(this.maxNumTrees);
      for(var j=0; j < this.maxNumTrees; j++){
        this.rfs[i][j] = new tracking.LBF.Tree(forestIndex, i, j);
      }
    }
  }

  /**
   * LBF Tree data structure.
   * @static
   * @constructor
   */
  tracking.LBF.Tree = function(forestIndex, landmarkIndex, treeIndex){
    var data = tracking.LBF.RegressorData[forestIndex].landmarks[landmarkIndex][treeIndex];
    this.maxDepth = data.max_depth;
    this.maxNumNodes = data.max_numnodes;
    this.nodes = data.nodes;
    this.landmarkID = data.landmark_id;
    this.numLeafnodes = data.num_leafnodes;
    this.numNodes = data.num_nodes;
    this.maxNumFeats = data.max_numfeats;
    this.maxRadioRadius = data.max_radio_radius;
    this.leafnodes = data.id_leafnodes;
  }

}());