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Common stones are colourless,looks dull,gray... it's expected they have low Saturation in HSV. Shadow is dark than... low brightness.

I've made my attempt around above points using MORPH_CLOSE to improve dark areas. This is the result, below is description and code.

Steps:

1. Scale down the image because it's too big...
2. Use Gaussian Blur to reduce variation a bit
3. Convert to HSV
4. Use MORPH_CLOSE on Saturation channel (use a structure half than wanted stone)
5. Normalize the histogram to get more stable threshold
6. Threshold dark saturation to select stones and shadows

The mask includes shadows. If this it's a problem you could try to remove shadows using the brightness channels... (shadows are dark)

1. Use MORPH_CLOSE on brightness Channel (use same a structure as above)
2. Normalize the histogram to get more stable threshold
3. Threshold dark brightness to select just shadows

Get binary mask for the stone and process it with contour or blobs

1. Make logical (stones+shadows) AND (NOT shadows) you should obtain just stones
2. Find contours and process them

This is the code. Get BrightnessAndContrastAuto here.

#define CL_BLU      cv::Scalar(255, 0,      0   )
#define CL_GREEN    cv::Scalar(0,   255,    0   )
#define CL_RED      cv::Scalar(0,   0,      255 )
#define CL_WHITE    cv::Scalar(255, 255,    255 )
const string winName="Stones";
Mat src,dst;
int minSizeMM,thStone,thShadow,removeShadow;
float pix2mm;

//helper function
void MorphClose(const Mat &imgIn,Mat &imgOut,int minThickess=2);
//get the source [here](http://answers.opencv.org/question/75510/how-to-make-auto-adjustmentsbrightness-and-contrast-for-image-android-opencv-image-correction/)
void BrightnessAndContrastAuto(const cv::Mat &src, cv::Mat &dst, float clipHistPercent=0);

// ON TRACK BAR FUNCTION
void onStonesTb(int, void*)
{
  Mat blur,bwStones,bwShadow;
  vector<vector<Point> > contours;
  char buf[80];

  cv::GaussianBlur(src,blur,Size(),2,2);

  // convert to HSV
  Mat src_hsv,brightness,saturation;
  vector<Mat> hsv_planes;
  cvtColor(blur, src_hsv, COLOR_BGR2HSV);
  split(src_hsv, hsv_planes);
  saturation = hsv_planes[1];
  brightness = hsv_planes[2];

  int minSizePx = cvRound(minSizeMM/pix2mm);
  int closerSize = minSizePx /2.0;

  //SELECT STONES (INCLUDING SHADOW)
  MorphClose(saturation,saturation,closerSize);
  BrightnessAndContrastAuto(saturation,saturation,1);
  threshold(saturation,bwStones,thStone,255,THRESH_BINARY_INV); //Get 0..thStone
  //show the selection
  findContours(bwStones, contours, CV_RETR_LIST, CV_CHAIN_APPROX_SIMPLE);
  for (int i = 0; i < contours.size(); i++)
    cv::drawContours(saturation,contours,i,CL_WHITE,2);
  imshow("Threshold Stones+Shadow on Saturation",saturation);

  if(removeShadow)
  {
    //SELECT DARK AREAS (MAYBE SHADOWS)
    MorphClose(brightness,brightness,closerSize);
    BrightnessAndContrastAuto(brightness,brightness,1);
    threshold(brightness,bwShadow,thShadow,255,THRESH_BINARY); //Get thShadow..255
    //show the selection
    contours.clear();
    findContours(bwShadow, contours, CV_RETR_CCOMP, CV_CHAIN_APPROX_SIMPLE);
    for (int i = 0; i < contours.size(); i++)
      cv::drawContours(brightness,contours,i,CL_WHITE,2);
    imshow("Threshold Shadow on Brightness",brightness);

    //remove shadows from stones
    cv::bitwise_and(bwStones,bwShadow,bwStones);
  }

  //show the result
  src.copyTo(dst);
  findContours(bwStones, contours, CV_RETR_EXTERNAL, CV_CHAIN_APPROX_SIMPLE);
  Point2f centroid;
  for (int i = 0; i < contours.size(); i++)
  {

    //draw the contour
    polylines(dst, contours[i], true, CL_GREEN,2);
    //get the bounding rect
    cv::Rect rect = cv::boundingRect(contours[i]);
    //ignore small objects
    if ( max(rect.width,rect.width) < minSizePx)
      continue;

    //calculate moments
    cv::Moments M = cv::moments(contours[i], false);
    //reject if area is 0
    double area = M.m00;
    if (area <= 0)
      continue;

    // OK! THE STONE HAS BEEN SELECTED 
    cv::rectangle(dst,rect,CL_RED,2);
    //get and draw the center
    centroid.x = cvRound(M.m10 / M.m00);
    centroid.y = cvRound(M.m01 / M.m00);
    cv::circle(dst,centroid,3,CL_RED,1);
    sprintf(buf,"%.0fx%.0fmm",rect.width*pix2mm,rect.height*pix2mm);
    cv::putText(dst,buf,rect.tl(),CV_FONT_HERSHEY_PLAIN,1.2,CL_BLU,1,CV_AA);
  }
  imshow(winName,dst);
}

void Main_Stones()
{
  Mat orig = imread(_IMG_PATH_"stones.jpg");
  int knowDistancePX = 170;
  int knowDistanceMM = 150;
  pix2mm = (float)knowDistancePX / knowDistanceMM;

  //Scale down your because it's big... let's say to 50%
  float scale = 0.5;
  resize(orig,src,Size(),scale,scale);
  pix2mm = pix2mm / scale;

  //set defaults
  minSizeMM=40;  // width in millimetre
  thStone=100;    // max saturation for stones
  thShadow=128;   // max brightness for shadow
  removeShadow=1; // try to remove shadows (1=Yes 0=No)

  imshow(winName,src);
  createTrackbar("Size(mm)", winName, &minSizeMM,100, onStonesTb, 0);
  createTrackbar("thStone", winName, &thStone, 255, onStonesTb, 0);
  createTrackbar("thShadow", winName, &thShadow, 255, onStonesTb, 0);
  createTrackbar("remove Shadow", winName, &removeShadow, 1, onStonesTb, 0);
  onStonesTb(0,0);
  waitKey(0);
}

void MorphClose(const Mat &imgIn,Mat &imgOut,int minThickess)
{
  int size = minThickess / 2;
  Point anchor = Point(size, size);
  Mat element = getStructuringElement(MORPH_ELLIPSE, Size(2 * size + 1, 2 * size + 1), anchor);
  morphologyEx(imgIn, imgOut, MORPH_CLOSE, element, anchor);
}