Merge pull request #16561 from vpisarev:better_hough_circles

* improved version of HoughCircles (HOUGH_GRADIENT_ALT method)

* trying to fix build problems on Windows

* fixed typo

* * fixed warnings on Windows
* make use of param2. make it minCos2 (minimal value of squared cosine between the gradient at the pixel edge and the vector connecting it with circle center). with minCos2=0.85 we can detect some more eyes :)

* * added description of HOUGH_GRADIENT_ALT
* cleaned up the implementation; added comments, replaced built-in numeic constants with symbolic constants
* rewrote circle_popcount() to use built-in popcount() if possible
* modified some of HoughCircles tests to use method parameter instead of the built-in loop

* fixed warnings on Windows

modules/imgproc/include/opencv2/imgproc.hpp

@@ -473,7 +473,8 @@ enum HoughModes {
     /** multi-scale variant of the classical Hough transform. The lines are encoded the same way as
     HOUGH_STANDARD. */
     HOUGH_MULTI_SCALE   = 2,
-    HOUGH_GRADIENT      = 3 //!< basically *21HT*, described in @cite Yuen90
+    HOUGH_GRADIENT      = 3, //!< basically *21HT*, described in @cite Yuen90
+    HOUGH_GRADIENT_ALT  = 4, //!< variation of HOUGH_GRADIENT to get better accuracy
 };
 
 //! Variants of Line Segment %Detector
@@ -2096,28 +2097,37 @@ Example: :
 
 @note Usually the function detects the centers of circles well. However, it may fail to find correct
 radii. You can assist to the function by specifying the radius range ( minRadius and maxRadius ) if
-you know it. Or, you may set maxRadius to a negative number to return centers only without radius
-search, and find the correct radius using an additional procedure.
+you know it. Or, in the case of #HOUGH_GRADIENT method you may set maxRadius to a negative number
+to return centers only without radius search, and find the correct radius using an additional procedure.
+
+It also helps to smooth image a bit unless it's already soft. For example,
+GaussianBlur() with 7x7 kernel and 1.5x1.5 sigma or similar blurring may help.
 
 @param image 8-bit, single-channel, grayscale input image.
 @param circles Output vector of found circles. Each vector is encoded as  3 or 4 element
 floating-point vector \f$(x, y, radius)\f$ or \f$(x, y, radius, votes)\f$ .
-@param method Detection method, see #HoughModes. Currently, the only implemented method is #HOUGH_GRADIENT
+@param method Detection method, see #HoughModes. The available methods are #HOUGH_GRADIENT and #HOUGH_GRADIENT_ALT.
 @param dp Inverse ratio of the accumulator resolution to the image resolution. For example, if
 dp=1 , the accumulator has the same resolution as the input image. If dp=2 , the accumulator has
-half as big width and height.
+half as big width and height. For #HOUGH_GRADIENT_ALT the recommended value is dp=1.5,
+unless some small very circles need to be detected.
 @param minDist Minimum distance between the centers of the detected circles. If the parameter is
 too small, multiple neighbor circles may be falsely detected in addition to a true one. If it is
 too large, some circles may be missed.
-@param param1 First method-specific parameter. In case of #HOUGH_GRADIENT , it is the higher
-threshold of the two passed to the Canny edge detector (the lower one is twice smaller).
-@param param2 Second method-specific parameter. In case of #HOUGH_GRADIENT , it is the
+@param param1 First method-specific parameter. In case of #HOUGH_GRADIENT and #HOUGH_GRADIENT_ALT,
+it is the higher threshold of the two passed to the Canny edge detector (the lower one is twice smaller).
+Note that #HOUGH_GRADIENT_ALT uses #Scharr algorithm to compute image derivatives, so the threshold value
+shough normally be higher, such as 300 or normally exposed and contrasty images.
+@param param2 Second method-specific parameter. In case of #HOUGH_GRADIENT, it is the
 accumulator threshold for the circle centers at the detection stage. The smaller it is, the more
 false circles may be detected. Circles, corresponding to the larger accumulator values, will be
-returned first.
+returned first. In the case of #HOUGH_GRADIENT_ALT algorithm, this is the circle "perfectness" measure.
+The closer it to 1, the better shaped circles algorithm selects. In most cases 0.9 should be fine.
+If you want get better detection of small circles, you may decrease it to 0.85, 0.8 or even less.
+But then also try to limit the search range [minRadius, maxRadius] to avoid many false circles.
 @param minRadius Minimum circle radius.
-@param maxRadius Maximum circle radius. If <= 0, uses the maximum image dimension. If < 0, returns
-centers without finding the radius.
+@param maxRadius Maximum circle radius. If <= 0, uses the maximum image dimension. If < 0, #HOUGH_GRADIENT returns
+centers without finding the radius. #HOUGH_GRADIENT_ALT always computes circle radiuses.
 
 @sa fitEllipse, minEnclosingCircle
  */