Fix angle discretization in Hough transforms

In some situations the last value was missing from the discrete theta
values. Now, the last value is chosen such that it is close to the
user-provided maximum theta, while the distance to pi remains always
at least theta_step/2. This should avoid duplicate detections.

A better way would probably be to use max_theta as is and adjust the
resolution (theta_step) instead, such that the discretization would
always be uniform (in a circular sense) when full angle range is used.

modules/imgproc/include/opencv2/imgproc.hpp

@@ -2024,23 +2024,24 @@ transform.
 
 @param image 8-bit, single-channel binary source image. The image may be modified by the function.
 @param lines Output vector of lines. Each line is represented by a 2 or 3 element vector
-\f$(\rho, \theta)\f$ or \f$(\rho, \theta, \textrm{votes})\f$ . \f$\rho\f$ is the distance from the coordinate origin \f$(0,0)\f$ (top-left corner of
+\f$(\rho, \theta)\f$ or \f$(\rho, \theta, \textrm{votes})\f$, where \f$\rho\f$ is the distance from
-the image). \f$\theta\f$ is the line rotation angle in radians (
+the coordinate origin \f$(0,0)\f$ (top-left corner of the image), \f$\theta\f$ is the line rotation
-\f$0 \sim \textrm{vertical line}, \pi/2 \sim \textrm{horizontal line}\f$ ).
+angle in radians ( \f$0 \sim \textrm{vertical line}, \pi/2 \sim \textrm{horizontal line}\f$ ), and
 \f$\textrm{votes}\f$ is the value of accumulator.
 @param rho Distance resolution of the accumulator in pixels.
 @param theta Angle resolution of the accumulator in radians.
-@param threshold Accumulator threshold parameter. Only those lines are returned that get enough
+@param threshold %Accumulator threshold parameter. Only those lines are returned that get enough
 votes ( \f$>\texttt{threshold}\f$ ).
-@param srn For the multi-scale Hough transform, it is a divisor for the distance resolution rho .
+@param srn For the multi-scale Hough transform, it is a divisor for the distance resolution rho.
 The coarse accumulator distance resolution is rho and the accurate accumulator resolution is
-rho/srn . If both srn=0 and stn=0 , the classical Hough transform is used. Otherwise, both these
+rho/srn. If both srn=0 and stn=0, the classical Hough transform is used. Otherwise, both these
 parameters should be positive.
 @param stn For the multi-scale Hough transform, it is a divisor for the distance resolution theta.
 @param min_theta For standard and multi-scale Hough transform, minimum angle to check for lines.
 Must fall between 0 and max_theta.
-@param max_theta For standard and multi-scale Hough transform, maximum angle to check for lines.
+@param max_theta For standard and multi-scale Hough transform, an upper bound for the angle.
-Must fall between min_theta and CV_PI.
+Must fall between min_theta and CV_PI. The actual maximum angle in the accumulator may be slightly
+less than max_theta, depending on the parameters min_theta and theta.
  */
 CV_EXPORTS_W void HoughLines( InputArray image, OutputArray lines,
                               double rho, double theta, int threshold,
@@ -2068,7 +2069,7 @@ And this is the output of the above program in case of the probabilistic Hough t
 line segment.
 @param rho Distance resolution of the accumulator in pixels.
 @param theta Angle resolution of the accumulator in radians.
-@param threshold Accumulator threshold parameter. Only those lines are returned that get enough
+@param threshold %Accumulator threshold parameter. Only those lines are returned that get enough
 votes ( \f$>\texttt{threshold}\f$ ).
 @param minLineLength Minimum line length. Line segments shorter than that are rejected.
 @param maxLineGap Maximum allowed gap between points on the same line to link them.
@@ -2087,13 +2088,14 @@ The function finds lines in a set of points using a modification of the Hough tr
 @param lines Output vector of found lines. Each vector is encoded as a vector<Vec3d> \f$(votes, rho, theta)\f$.
 The larger the value of 'votes', the higher the reliability of the Hough line.
 @param lines_max Max count of Hough lines.
-@param threshold Accumulator threshold parameter. Only those lines are returned that get enough
+@param threshold %Accumulator threshold parameter. Only those lines are returned that get enough
 votes ( \f$>\texttt{threshold}\f$ ).
 @param min_rho Minimum value for \f$\rho\f$ for the accumulator (Note: \f$\rho\f$ can be negative. The absolute value \f$|\rho|\f$ is the distance of a line to the origin.).
 @param max_rho Maximum value for \f$\rho\f$ for the accumulator.
 @param rho_step Distance resolution of the accumulator.
 @param min_theta Minimum angle value of the accumulator in radians.
-@param max_theta Maximum angle value of the accumulator in radians.
+@param max_theta Upper bound for the angle value of the accumulator in radians. The actual maximum
+angle may be slightly less than max_theta, depending on the parameters min_theta and theta_step.
 @param theta_step Angle resolution of the accumulator in radians.
  */
 CV_EXPORTS_W void HoughLinesPointSet( InputArray point, OutputArray lines, int lines_max, int threshold,

modules/imgproc/src/hough.cpp

@@ -68,6 +68,18 @@ struct hough_cmp_gt
     const int* aux;
 };
 
+static inline int
+computeNumangle( double min_theta, double max_theta, double theta_step )
+{
+    int numangle = cvFloor((max_theta - min_theta) / theta_step) + 1;
+    // If the distance between the first angle and the last angle is
+    // approximately equal to pi, then the last angle will be removed
+    // in order to prevent a line to be detected twice.
+    if ( numangle > 1 && fabs(CV_PI - (numangle-1)*theta_step) < theta_step/2 )
+        --numangle;
+    return numangle;
+}
+
 static void
 createTrigTable( int numangle, double min_theta, double theta_step,
                  float irho, float *tabSin, float *tabCos )
@@ -130,7 +142,7 @@ HoughLinesStandard( InputArray src, OutputArray lines, int type,
 
     CV_CheckGE(max_theta, min_theta, "max_theta must be greater than min_theta");
 
-    int numangle = cvRound((max_theta - min_theta) / theta);
+    int numangle = computeNumangle(min_theta, max_theta, theta);
     int numrho = cvRound(((max_rho - min_rho) + 1) / rho);
 
 #if defined HAVE_IPP && IPP_VERSION_X100 >= 810 && !IPP_DISABLE_HOUGH
@@ -475,7 +487,7 @@ HoughLinesProbabilistic( Mat& image,
     int width = image.cols;
     int height = image.rows;
 
-    int numangle = cvRound(CV_PI / theta);
+    int numangle = computeNumangle(0.0, CV_PI, theta);
     int numrho = cvRound(((width + height) * 2 + 1) / rho);
 
 #if defined HAVE_IPP && IPP_VERSION_X100 >= 810 && !IPP_DISABLE_HOUGH
@@ -792,7 +804,7 @@ static bool ocl_HoughLines(InputArray _src, OutputArray _lines, double rho, doub
     }
 
     UMat src = _src.getUMat();
-    int numangle = cvRound((max_theta - min_theta) / theta);
+    int numangle = computeNumangle(min_theta, max_theta, theta);
     int numrho = cvRound(((src.cols + src.rows) * 2 + 1) / rho);
 
     UMat pointsList;
@@ -846,7 +858,7 @@ static bool ocl_HoughLinesP(InputArray _src, OutputArray _lines, double rho, dou
     }
 
     UMat src = _src.getUMat();
-    int numangle = cvRound(CV_PI / theta);
+    int numangle = computeNumangle(0.0, CV_PI, theta);
     int numrho = cvRound(((src.cols + src.rows) * 2 + 1) / rho);
 
     UMat pointsList;
@@ -956,7 +968,7 @@ void HoughLinesPointSet( InputArray _point, OutputArray _lines, int lines_max, i
     int i;
     float irho = 1 / (float)rho_step;
     float irho_min = ((float)min_rho * irho);
-    int numangle = cvRound((max_theta - min_theta) / theta_step);
+    int numangle = computeNumangle(min_theta, max_theta, theta_step);
     int numrho = cvRound((max_rho - min_rho + 1) / rho_step);
 
     Mat _accum = Mat::zeros( (numangle+2), (numrho+2), CV_32SC1 );

modules/imgproc/test/test_houghlines.cpp

@@ -329,6 +329,17 @@ TEST(HoughLinesPointSet, regression_21029)
     EXPECT_TRUE(lines.empty());
 }
 
+TEST(HoughLines, regression_21983)
+{
+    Mat img(200, 200, CV_8UC1, Scalar(0));
+    line(img, Point(0, 100), Point(100, 100), Scalar(255));
+    std::vector<Vec2f> lines;
+    HoughLines(img, lines, 1, CV_PI/180, 90, 0, 0, 0.001, 1.58);
+    ASSERT_EQ(lines.size(), 1U);
+    EXPECT_EQ(lines[0][0], 100);
+    EXPECT_NEAR(lines[0][1], 1.57179642, 1e-4);
+}
+
 INSTANTIATE_TEST_CASE_P( ImgProc, StandartHoughLinesTest, testing::Combine(testing::Values( "shared/pic5.png", "../stitching/a1.png" ),
                                                                            testing::Values( 1, 10 ),
                                                                            testing::Values( 0.05, 0.1 ),