fixed http://code.opencv.org/issues/3828, added test. thanks to berak for the patch

modules/core/src/stat.cpp

@@ -3826,6 +3826,11 @@ void cv::findNonZero( InputArray _src, OutputArray _idx )
     Mat src = _src.getMat();
     CV_Assert( src.type() == CV_8UC1 );
     int n = countNonZero(src);
+    if( n == 0 )
+    {
+        _idx.release();
+        return;
+    }
     if( _idx.kind() == _InputArray::MAT && !_idx.getMatRef().isContinuous() )
         _idx.release();
     _idx.create(n, 1, CV_32SC2);

modules/core/test/test_arithm.cpp

@@ -1791,3 +1791,13 @@ INSTANTIATE_TEST_CASE_P(Arithm, SubtractOutputMatNotEmpty, testing::Combine(
     testing::Values(perf::MatType(CV_8UC1), CV_8UC3, CV_8UC4, CV_16SC1, CV_16SC3),
     testing::Values(-1, CV_16S, CV_32S, CV_32F),
     testing::Bool()));
+
+
+TEST(Core_FindNonZero, singular)
+{
+    Mat img(10, 10, CV_8U, Scalar::all(0));
+    vector<Point> pts, pts2(10);
+    findNonZero(img, pts);
+    findNonZero(img, pts2);
+    ASSERT_TRUE(pts.empty() && pts2.empty());
+}