diff --git a/modules/core/src/arithm.cpp b/modules/core/src/arithm.cpp
index 5ea596ffc6..e3ded859b6 100644
--- a/modules/core/src/arithm.cpp
+++ b/modules/core/src/arithm.cpp
@@ -1233,7 +1233,7 @@ void cv::compare(InputArray _src1, InputArray _src2, OutputArray _dst, int op)
     CV_Assert( op == CMP_LT || op == CMP_LE || op == CMP_EQ ||
                op == CMP_NE || op == CMP_GE || op == CMP_GT );
 
-    if(_src1.empty() && _src2.empty())
+    if(_src1.empty() || _src2.empty())
     {
         _dst.release();
         return;
diff --git a/modules/core/src/copy.cpp b/modules/core/src/copy.cpp
index b8a52f2f5a..8775bff4aa 100644
--- a/modules/core/src/copy.cpp
+++ b/modules/core/src/copy.cpp
@@ -411,6 +411,8 @@ Mat& Mat::operator = (const Scalar& s)
 {
     CV_INSTRUMENT_REGION()
 
+    if (empty()) return *this;
+
     const Mat* arrays[] = { this };
     uchar* dptr;
     NAryMatIterator it(arrays, &dptr, 1);
diff --git a/modules/core/src/rand.cpp b/modules/core/src/rand.cpp
index 7b7f8ed9b6..a456c72633 100644
--- a/modules/core/src/rand.cpp
+++ b/modules/core/src/rand.cpp
@@ -511,6 +511,8 @@ static RandnScaleFunc randnScaleTab[] =
 void RNG::fill( InputOutputArray _mat, int disttype,
                 InputArray _param1arg, InputArray _param2arg, bool saturateRange )
 {
+    if (_mat.empty())
+        return;
     Mat mat = _mat.getMat(), _param1 = _param1arg.getMat(), _param2 = _param2arg.getMat();
     int depth = mat.depth(), cn = mat.channels();
     AutoBuffer<double> _parambuf;
diff --git a/modules/core/test/test_rand.cpp b/modules/core/test/test_rand.cpp
index 82bb6104a9..8677aa0c31 100644
--- a/modules/core/test/test_rand.cpp
+++ b/modules/core/test/test_rand.cpp
@@ -168,11 +168,12 @@ void Core_RandTest::run( int )
         {
             tested_rng = saved_rng;
             int sz = 0, dsz = 0, slice;
-            for( slice = 0; slice < maxSlice; slice++, sz += dsz )
+            for( slice = 0; slice < maxSlice && sz < SZ; slice++, sz += dsz )
             {
-                dsz = slice+1 < maxSlice ? (int)(cvtest::randInt(rng) % (SZ - sz + 1)) : SZ - sz;
+                dsz = slice+1 < maxSlice ? (int)(cvtest::randInt(rng) % (SZ - sz) + 1) : SZ - sz;
                 Mat aslice = arr[k].colRange(sz, sz + dsz);
                 tested_rng.fill(aslice, dist_type, A, B);
+                printf("%d - %d\n", sz, sz + dsz);
             }
         }
 
diff --git a/modules/imgproc/test/test_grabcut.cpp b/modules/imgproc/test/test_grabcut.cpp
index eae8b3e482..7bf6555a0c 100644
--- a/modules/imgproc/test/test_grabcut.cpp
+++ b/modules/imgproc/test/test_grabcut.cpp
@@ -89,7 +89,6 @@ void CV_GrabcutTest::run( int /* start_from */)
     Mat exp_bgdModel, exp_fgdModel;
 
     Mat mask;
-    mask = Scalar(0);
     Mat bgdModel, fgdModel;
     grabCut( img, mask, rect, bgdModel, fgdModel, 0, GC_INIT_WITH_RECT );
     bgdModel.copyTo(exp_bgdModel);