diff --git a/modules/core/src/dxt.cpp b/modules/core/src/dxt.cpp
index 033bf45120..90eb392f58 100644
--- a/modules/core/src/dxt.cpp
+++ b/modules/core/src/dxt.cpp
@@ -1070,11 +1070,12 @@ RealDFT( const T* src, T* dst, int n, int nf, int* factors, const int* itab,
         }
     }
 
-    if( complex_output && (n & 1) == 0 )
+    if (complex_output && ((n & 1) == 0 || n == 1))
     {
         dst[-1] = dst[0];
         dst[0] = 0;
-        dst[n] = 0;
+        if (n > 1)
+            dst[n] = 0;
     }
 }
 
@@ -1473,6 +1474,47 @@ typedef IppStatus (CV_STDCALL* IppDFTGetSizeFunc)(int, int, IppHintAlgorithm, in
 typedef IppStatus (CV_STDCALL* IppDFTInitFunc)(int, int, IppHintAlgorithm, void*, uchar*);
 #endif
 
+namespace cv
+{
+static void complementComplexOutput(Mat& dst, int len, int dft_dims)
+{
+    int i, n = dst.cols;
+    size_t elem_size = dst.elemSize1();
+    if (elem_size == sizeof(float))
+    {
+        float* p0 = dst.ptr<float>();
+        size_t dstep = dst.step / sizeof(p0[0]);
+        for (i = 0; i < len; i++)
+        {
+            float* p = p0 + dstep*i;
+            float* q = dft_dims == 1 || i == 0 || i * 2 == len ? p : p0 + dstep*(len - i);
+
+            for (int j = 1; j < (n + 1) / 2; j++)
+            {
+                p[(n - j) * 2] = q[j * 2];
+                p[(n - j) * 2 + 1] = -q[j * 2 + 1];
+            }
+        }
+    }
+    else
+    {
+        double* p0 = dst.ptr<double>();
+        size_t dstep = dst.step / sizeof(p0[0]);
+        for (i = 0; i < len; i++)
+        {
+            double* p = p0 + dstep*i;
+            double* q = dft_dims == 1 || i == 0 || i * 2 == len ? p : p0 + dstep*(len - i);
+
+            for (int j = 1; j < (n + 1) / 2; j++)
+            {
+                p[(n - j) * 2] = q[j * 2];
+                p[(n - j) * 2 + 1] = -q[j * 2 + 1];
+            }
+        }
+    }
+}
+}
+
 void cv::dft( InputArray _src0, OutputArray _dst, int flags, int nonzero_rows )
 {
     static DFTFunc dft_tbl[6] =
@@ -1688,8 +1730,12 @@ void cv::dft( InputArray _src0, OutputArray _dst, int flags, int nonzero_rows )
                 memset( dptr0, 0, dst_full_len );
             }
 
-            if( stage != 1 )
+            if (stage != 1)
+            {
+                if (!inv && real_transform && dst.channels() == 2)
+                    complementComplexOutput(dst, nonzero_rows, 1);
                 break;
+            }
             src = dst;
         }
         else
@@ -1831,41 +1877,7 @@ void cv::dft( InputArray _src0, OutputArray _dst, int flags, int nonzero_rows )
             if( stage != 0 )
             {
                 if( !inv && real_transform && dst.channels() == 2 && len > 1 )
-                {
-                    int n = dst.cols;
-                    if( elem_size == (int)sizeof(float) )
-                    {
-                        float* p0 = (float*)dst.data;
-                        size_t dstep = dst.step/sizeof(p0[0]);
-                        for( i = 0; i < len; i++ )
-                        {
-                            float* p = p0 + dstep*i;
-                            float* q = i == 0 || i*2 == len ? p : p0 + dstep*(len-i);
-
-                            for( int j = 1; j < (n+1)/2; j++ )
-                            {
-                                p[(n-j)*2] = q[j*2];
-                                p[(n-j)*2+1] = -q[j*2+1];
-                            }
-                        }
-                    }
-                    else
-                    {
-                        double* p0 = (double*)dst.data;
-                        size_t dstep = dst.step/sizeof(p0[0]);
-                        for( i = 0; i < len; i++ )
-                        {
-                            double* p = p0 + dstep*i;
-                            double* q = i == 0 || i*2 == len ? p : p0 + dstep*(len-i);
-
-                            for( int j = 1; j < (n+1)/2; j++ )
-                            {
-                                p[(n-j)*2] = q[j*2];
-                                p[(n-j)*2+1] = -q[j*2+1];
-                            }
-                        }
-                    }
-                }
+                    complementComplexOutput(dst, len, 2);
                 break;
             }
             src = dst;
diff --git a/modules/core/src/lapack.cpp b/modules/core/src/lapack.cpp
index 7ee84a6d45..3084a5354b 100644
--- a/modules/core/src/lapack.cpp
+++ b/modules/core/src/lapack.cpp
@@ -688,7 +688,7 @@ JacobiSVDImpl_(_Tp* At, size_t astep, _Tp* _W, _Tp* Vt, size_t vstep,
                         At[i*astep + k] = t;
                         asum += std::abs(t);
                     }
-                    asum = asum ? 1/asum : 0;
+                    asum = asum > eps * 100 ? 1 / asum : 0;
                     for( k = 0; k < m; k++ )
                         At[i*astep + k] *= asum;
                 }
@@ -1560,18 +1560,18 @@ static void _SVDcompute( InputArray _aarr, OutputArray _w,
         JacobiSVD(temp_a.ptr<double>(), temp_u.step, temp_w.ptr<double>(),
               temp_v.ptr<double>(), temp_v.step, m, n, compute_uv ? urows : 0);
     }
-    temp_w.copyTo(_w);
+    if(_w.needed()) temp_w.copyTo(_w);
     if( compute_uv )
     {
         if( !at )
         {
-            transpose(temp_u, _u);
-            temp_v.copyTo(_vt);
+            if(_u.needed()) transpose(temp_u, _u);
+            if(_vt.needed()) temp_v.copyTo(_vt);
         }
         else
         {
-            transpose(temp_v, _u);
-            temp_u.copyTo(_vt);
+            if(_u.needed()) transpose(temp_v, _u);
+            if(_vt.needed()) temp_u.copyTo(_vt);
         }
     }
 }
diff --git a/modules/core/src/matmul.cpp b/modules/core/src/matmul.cpp
index d537b7dced..4be9c4daa3 100644
--- a/modules/core/src/matmul.cpp
+++ b/modules/core/src/matmul.cpp
@@ -1013,7 +1013,7 @@ void cv::gemm( InputArray matA, InputArray matB, double alpha,
     GEMMBlockMulFunc blockMulFunc;
     GEMMStoreFunc storeFunc;
     Mat *matD = &D, tmat;
-    int tmat_size = 0;
+    size_t tmat_size = 0;
     const uchar* Cdata = C.data;
     size_t Cstep = C.data ? (size_t)C.step : 0;
     AutoBuffer<uchar> buf;
@@ -1046,7 +1046,7 @@ void cv::gemm( InputArray matA, InputArray matB, double alpha,
 
     if( D.data == A.data || D.data == B.data )
     {
-        tmat_size = d_size.width*d_size.height*CV_ELEM_SIZE(type);
+        tmat_size = (size_t)d_size.width*d_size.height*CV_ELEM_SIZE(type);
         // Allocate tmat later, once the size of buf is known
         matD = &tmat;
     }
@@ -1137,7 +1137,7 @@ void cv::gemm( InputArray matA, InputArray matB, double alpha,
         int is_b_t = flags & GEMM_2_T;
         int elem_size = CV_ELEM_SIZE(type);
         int dk0_1, dk0_2;
-        int a_buf_size = 0, b_buf_size, d_buf_size;
+        size_t a_buf_size = 0, b_buf_size, d_buf_size;
         uchar* a_buf = 0;
         uchar* b_buf = 0;
         uchar* d_buf = 0;
@@ -1178,8 +1178,8 @@ void cv::gemm( InputArray matA, InputArray matB, double alpha,
             dn0 = block_size / dk0;
 
         dk0_1 = (dn0+dn0/8+2) & -2;
-        b_buf_size = (dk0+dk0/8+1)*dk0_1*elem_size;
-        d_buf_size = (dk0+dk0/8+1)*dk0_1*work_elem_size;
+        b_buf_size = (size_t)(dk0+dk0/8+1)*dk0_1*elem_size;
+        d_buf_size = (size_t)(dk0+dk0/8+1)*dk0_1*work_elem_size;
 
         if( is_a_t )
         {
diff --git a/modules/core/src/stat.cpp b/modules/core/src/stat.cpp
index 3c24f02541..e88d175108 100644
--- a/modules/core/src/stat.cpp
+++ b/modules/core/src/stat.cpp
@@ -2587,6 +2587,11 @@ 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);
diff --git a/modules/core/test/test_arithm.cpp b/modules/core/test/test_arithm.cpp
index ac88615955..57adb89210 100644
--- a/modules/core/test/test_arithm.cpp
+++ b/modules/core/test/test_arithm.cpp
@@ -1810,3 +1810,13 @@ TEST(MinMaxLoc, Mat_IntMax_Without_Mask)
     ASSERT_EQ(Point(0, 0), minLoc);
     ASSERT_EQ(Point(0, 0), maxLoc);
 }
+
+
+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());
+}
\ No newline at end of file
diff --git a/modules/core/test/test_dxt.cpp b/modules/core/test/test_dxt.cpp
index 1c0c7b00bf..33ddb02660 100644
--- a/modules/core/test/test_dxt.cpp
+++ b/modules/core/test/test_dxt.cpp
@@ -866,3 +866,24 @@ protected:
 };
 
 TEST(Core_DFT, complex_output) { Core_DFTComplexOutputTest test; test.safe_run(); }
+
+TEST(Core_DFT, complex_output2)
+{
+    for (int i = 0; i < 100; i++)
+    {
+        int type = theRNG().uniform(0, 2) ? CV_64F : CV_32F;
+        int m = theRNG().uniform(1, 10);
+        int n = theRNG().uniform(1, 10);
+        Mat x(m, n, type), out;
+        randu(x, -1., 1.);
+        dft(x, out, DFT_ROWS | DFT_COMPLEX_OUTPUT);
+        double nrm = norm(out, NORM_INF);
+        double thresh = n*m * 2;
+        if (nrm > thresh)
+        {
+            cout << "x: " << x << endl;
+            cout << "out: " << out << endl;
+            ASSERT_LT(nrm, thresh);
+        }
+    }
+}
diff --git a/modules/core/test/test_mat.cpp b/modules/core/test/test_mat.cpp
index f854abed7e..0d35e60780 100644
--- a/modules/core/test/test_mat.cpp
+++ b/modules/core/test/test_mat.cpp
@@ -919,6 +919,39 @@ TEST(Core_Mat, copyNx1ToVector)
     ASSERT_PRED_FORMAT2(cvtest::MatComparator(0, 0), ref_dst16, cv::Mat_<ushort>(dst16));
 }
 
+TEST(Core_InputArray, empty)
+{
+    vector<vector<Point> > data;
+    ASSERT_TRUE(_InputArray(data).empty());
+}
+
+
+TEST(Core_CopyMask, bug1918)
+{
+    Mat_<unsigned char> tmpSrc(100, 100);
+    tmpSrc = 124;
+    Mat_<unsigned char> tmpMask(100, 100);
+    tmpMask = 255;
+    Mat_<unsigned char> tmpDst(100, 100);
+    tmpDst = 2;
+    tmpSrc.copyTo(tmpDst, tmpMask);
+    ASSERT_EQ(sum(tmpDst)[0], 124 * 100 * 100);
+}
+
+TEST(Core_SVD, orthogonality)
+{
+    for (int i = 0; i < 2; i++)
+    {
+        int type = i == 0 ? CV_32F : CV_64F;
+        Mat mat_D(2, 2, type);
+        mat_D.setTo(88.);
+        Mat mat_U, mat_W;
+        SVD::compute(mat_D, mat_W, mat_U, noArray(), SVD::FULL_UV);
+        mat_U *= mat_U.t();
+        ASSERT_LT(norm(mat_U, Mat::eye(2, 2, type), NORM_INF), 1e-5);
+    }
+}
+
 TEST(Core_Mat, multiDim)
 {
     int d[]={3,3,3};