added test for ticket #1719 and added a note about contour self-intersections to the docs

modules/imgproc/doc/structural_analysis_and_shape_descriptors.rst

@@ -30,6 +30,14 @@ The function computes moments, up to the 3rd order, of a vector shape or a raste
                 double m02, double m30, double m21, double m12, double m03 );
         Moments( const CvMoments& moments );
         operator CvMoments() const;
+        
+        // spatial moments
+        double  m00, m10, m01, m20, m11, m02, m30, m21, m12, m03;
+        // central moments
+        double  mu20, mu11, mu02, mu30, mu21, mu12, mu03;
+        // central normalized moments
+        double  nu20, nu11, nu02, nu30, nu21, nu12, nu03;
+    }
 
 In case of a raster image, the spatial moments :math:`\texttt{Moments::m}_{ji}` are computed as:
 
@@ -66,6 +74,10 @@ The normalized central moments
 
 The moments of a contour are defined in the same way but computed using the Green's formula (see http://en.wikipedia.org/wiki/Green_theorem). So, due to a limited raster resolution, the moments computed for a contour are slightly different from the moments computed for the same rasterized contour.
 
+.. note::
+
+     Since the contour moments are computed using Green formula, you may get seemingly odd results for contours with self-intersections, e.g. a zero area (``m00``) for butterfly-shaped contours.
+
 .. seealso::
 
     :ocv:func:`contourArea`,
@@ -342,6 +354,7 @@ The function computes a contour area. Similarly to
 :ocv:func:`moments` , the area is computed using the Green formula. Thus, the returned area and the number of non-zero pixels, if you draw the contour using
 :ocv:func:`drawContours` or
 :ocv:func:`fillPoly` , can be different.
+Also, the function will most certainly give a wrong results for contours with self-intersections.
 
 Example: ::
 

modules/imgproc/test/test_moments.cpp

@@ -391,3 +391,33 @@ void CV_HuMomentsTest::prepare_to_validation( int /*test_case_idx*/ )
 
 TEST(Imgproc_Moments, accuracy) { CV_MomentsTest test; test.safe_run(); }
 TEST(Imgproc_HuMoments, accuracy) { CV_HuMomentsTest test; test.safe_run(); }
+
+class CV_SmallContourMomentTest : public cvtest::BaseTest
+{
+public:
+    CV_SmallContourMomentTest() {}
+    ~CV_SmallContourMomentTest() {}   
+protected:
+    void run(int)
+    {
+        try
+        {
+            vector<Point> points;
+            points.push_back(Point(50, 56));
+            points.push_back(Point(53, 53));
+            points.push_back(Point(46, 54));
+            points.push_back(Point(49, 51));
+            
+            Moments m = moments(points, false);
+            double area = contourArea(points);
+            
+            CV_Assert( m.m00 == 0 && m.m01 == 0 && m.m10 == 0 && area == 0 );
+        }
+        catch(...)
+        {
+            ts->set_failed_test_info(cvtest::TS::FAIL_MISMATCH);
+        }
+    }
+};
+
+TEST(Imgproc_ContourMoment, small) { CV_SmallContourMomentTest test; test.safe_run(); }