Итак, я пытаюсь реализовать грубое преобразование, эта версия является 1-мерной (для всех димов уменьшена до 1 дим оптимизации), основанной на второстепенных свойствах. В приложении мой код, с образцом изображения ... ввод и вывод.

Очевидный вопрос: что я делаю не так? Я трижды проверил мою логику и код, и это хорошо смотрится и с моими параметрами. Но, очевидно, мне чего-то не хватает.

Обратите внимание, что красные пиксели должны быть центрами эллипсов, в то время как синие пиксели являются краями, которые нужно удалить (принадлежат эллипсу, который соответствует математическим уравнениям).

Кроме того, я не заинтересован в использовании openCV / matlab / ocatve / etc .. (ничего против них). Большое спасибо!

var fs = require("fs"),
    Canvas = require("canvas"),
    Image = Canvas.Image;


var LEAST_REQUIRED_DISTANCE = 40, // LEAST required distance between 2 points , lets say smallest ellipse minor
    LEAST_REQUIRED_ELLIPSES = 6, // number of found ellipse
    arr_accum = [],
    arr_edges = [],
    edges_canvas,
    xy,
    x1y1,
    x2y2,
    x0,
    y0,
    a,
    alpha,
    d,
    b,
    max_votes,
    cos_tau,
    sin_tau_sqr,
    f,
    new_x0,
    new_y0,
    any_minor_dist,
    max_minor,
    i,
    found_minor_in_accum,
    arr_edges_len,
    hough_file = 'sample_me2.jpg',


edges_canvas = drawImgToCanvasSync(hough_file); // make sure everything is black and white!


arr_edges    = getEdgesArr(edges_canvas);

arr_edges_len = arr_edges.length;

var hough_canvas_img_data = edges_canvas.getContext('2d').getImageData(0, 0, edges_canvas.width,edges_canvas.height);

for(x1y1 = 0; x1y1 < arr_edges_len ; x1y1++){

  if (arr_edges[x1y1].x === -1) { continue; }

  for(x2y2 = 0 ; x2y2 < arr_edges_len; x2y2++){

    if ((arr_edges[x2y2].x === -1) ||
        (arr_edges[x2y2].x === arr_edges[x1y1].x && arr_edges[x2y2].y === arr_edges[x1y1].y)) { continue; }

    if (distance(arr_edges[x1y1],arr_edges[x2y2]) > LEAST_REQUIRED_DISTANCE){

      x0    = (arr_edges[x1y1].x + arr_edges[x2y2].x) / 2;
      y0    = (arr_edges[x1y1].y + arr_edges[x2y2].y) / 2;
      a     = Math.sqrt((arr_edges[x1y1].x - arr_edges[x2y2].x) * (arr_edges[x1y1].x - arr_edges[x2y2].x) + (arr_edges[x1y1].y - arr_edges[x2y2].y) * (arr_edges[x1y1].y - arr_edges[x2y2].y)) / 2;
      alpha = Math.atan((arr_edges[x2y2].y - arr_edges[x1y1].y) / (arr_edges[x2y2].x - arr_edges[x1y1].x));

      for(xy = 0 ; xy < arr_edges_len; xy++){

        if ((arr_edges[xy].x === -1) || 
            (arr_edges[xy].x === arr_edges[x2y2].x && arr_edges[xy].y === arr_edges[x2y2].y) ||
            (arr_edges[xy].x === arr_edges[x1y1].x && arr_edges[xy].y === arr_edges[x1y1].y)) { continue; }

        d = distance({x: x0, y: y0},arr_edges[xy]);

        if (d > LEAST_REQUIRED_DISTANCE){
          f           = distance(arr_edges[xy],arr_edges[x2y2]); // focus
          cos_tau     = (a * a + d * d - f * f) / (2 * a * d);
          sin_tau_sqr = (1 - cos_tau * cos_tau);//Math.sqrt(1 - cos_tau * cos_tau); // getting sin out of cos
          b           = (a * a * d * d * sin_tau_sqr ) / (a * a - d * d * cos_tau * cos_tau);
          b           = Math.sqrt(b);
          b           = parseInt(b.toFixed(0));
          d           = parseInt(d.toFixed(0));

          if (b > 0){
            found_minor_in_accum = arr_accum.hasOwnProperty(b);

            if (!found_minor_in_accum){
              arr_accum[b] = {f: f, cos_tau: cos_tau, sin_tau_sqr: sin_tau_sqr, b: b, d: d, xy: xy, xy_point: JSON.stringify(arr_edges[xy]), x0: x0, y0: y0, accum: 0};
            }
            else{
              arr_accum[b].accum++;
            }
          }// b
        }// if2 - LEAST_REQUIRED_DISTANCE
      }// for xy

      max_votes = getMaxMinor(arr_accum);

      // ONE ellipse has been detected
      if (max_votes != null &&
          (max_votes.max_votes > LEAST_REQUIRED_ELLIPSES)){

        // output ellipse details
        new_x0 = parseInt(arr_accum[max_votes.index].x0.toFixed(0)),
        new_y0 = parseInt(arr_accum[max_votes.index].y0.toFixed(0));

        setPixel(hough_canvas_img_data,new_x0,new_y0,255,0,0,255); // Red centers

        // remove the pixels on the detected ellipse from edge pixel array
        for (i=0; i < arr_edges.length; i++){
          any_minor_dist = distance({x:new_x0, y: new_y0}, arr_edges[i]);
          any_minor_dist = parseInt(any_minor_dist.toFixed(0));
          max_minor      = b;//Math.max(b,arr_accum[max_votes.index].d); // between the max and the min

          // coloring in blue the edges we don't need
          if (any_minor_dist <= max_minor){
            setPixel(hough_canvas_img_data,arr_edges[i].x,arr_edges[i].y,0,0,255,255);
            arr_edges[i] = {x: -1, y: -1};

          }// if

        }// for


      }// if - LEAST_REQUIRED_ELLIPSES

      // clear accumulated array
      arr_accum = [];

    }// if1 - LEAST_REQUIRED_DISTANCE

  }// for x2y2
}// for xy

edges_canvas.getContext('2d').putImageData(hough_canvas_img_data, 0, 0);

writeCanvasToFile(edges_canvas, __dirname + '/hough.jpg', function() {
});



function getMaxMinor(accum_in){
  var max_votes = -1,
      max_votes_idx,
      i,
      accum_len = accum_in.length;

  for(i in accum_in){

    if (accum_in[i].accum > max_votes){
      max_votes     = accum_in[i].accum;
      max_votes_idx = i;
    } // if
  }


  if (max_votes > 0){
    return {max_votes: max_votes, index: max_votes_idx};
  }
  return null;
}

function distance(point_a,point_b){
  return Math.sqrt((point_a.x - point_b.x) * (point_a.x - point_b.x) + (point_a.y - point_b.y) * (point_a.y - point_b.y));
}
function getEdgesArr(canvas_in){

  var x,
      y,
      width = canvas_in.width,
      height = canvas_in.height,
      pixel,
      edges = [],
      ctx = canvas_in.getContext('2d'),
      img_data = ctx.getImageData(0, 0, width, height);


  for(x = 0; x < width; x++){
    for(y = 0; y < height; y++){

      pixel = getPixel(img_data, x,y);


      if (pixel.r !== 0 && 
          pixel.g !== 0 &&
          pixel.b !== 0 ){
        edges.push({x: x, y: y});
      }

    } // for
  }// for 

  return edges
} // getEdgesArr

function drawImgToCanvasSync(file) {
  var data = fs.readFileSync(file)
  var canvas = dataToCanvas(data);
  return canvas;
}
function dataToCanvas(imagedata) {
  img = new Canvas.Image();
  img.src = new Buffer(imagedata, 'binary');

  var canvas = new Canvas(img.width, img.height);
  var ctx = canvas.getContext('2d');
  ctx.patternQuality = "best";

  ctx.drawImage(img, 0, 0, img.width, img.height,
    0, 0, img.width, img.height);
  return canvas;
}
function writeCanvasToFile(canvas, file, callback) {
  var out = fs.createWriteStream(file)
  var stream = canvas.createPNGStream();

  stream.on('data', function(chunk) {
    out.write(chunk);
  });

  stream.on('end', function() {
    callback();
  });
}


function setPixel(imageData, x, y, r, g, b, a) {
    index = (x + y * imageData.width) * 4;
    imageData.data[index+0] = r;
    imageData.data[index+1] = g;
    imageData.data[index+2] = b;
    imageData.data[index+3] = a;
}
function getPixel(imageData, x, y) {
    index = (x + y * imageData.width) * 4;

    return {
      r: imageData.data[index+0],
      g: imageData.data[index+1],
      b: imageData.data[index+2],
      a: imageData.data[index+3]
    }
}