diff --git a/modules/core/src/matrix.cpp b/modules/core/src/matrix.cpp
index 517ee9dacb..8e32b0fbee 100644
--- a/modules/core/src/matrix.cpp
+++ b/modules/core/src/matrix.cpp
@@ -2691,16 +2691,18 @@ double cv::kmeans( InputArray _data, int K,
                    int flags, OutputArray _centers )
 {
     const int SPP_TRIALS = 3;
-    Mat data = _data.getMat();
-    bool isrow = data.rows == 1 && data.channels() > 1;
-    int N = !isrow ? data.rows : data.cols;
-    int dims = (!isrow ? data.cols : 1)*data.channels();
-    int type = data.depth();
+    Mat data0 = _data.getMat();
+    bool isrow = data0.rows == 1 && data0.channels() > 1;
+    int N = !isrow ? data0.rows : data0.cols;
+    int dims = (!isrow ? data0.cols : 1)*data0.channels();
+    int type = data0.depth();
 
     attempts = std::max(attempts, 1);
-    CV_Assert( data.dims <= 2 && type == CV_32F && K > 0 );
+    CV_Assert( data0.dims <= 2 && type == CV_32F && K > 0 );
     CV_Assert( N >= K );
 
+    Mat data(N, dims, CV_32F, data0.data, isrow ? dims * sizeof(float) : static_cast<size_t>(data0.step));
+
     _bestLabels.create(N, 1, CV_32S, -1, true);
 
     Mat _labels, best_labels = _bestLabels.getMat();
diff --git a/modules/core/test/test_math.cpp b/modules/core/test/test_math.cpp
index a572cd0d92..5dec97e8c1 100644
--- a/modules/core/test/test_math.cpp
+++ b/modules/core/test/test_math.cpp
@@ -2512,6 +2512,15 @@ TEST(Core_SVD, flt)
 
 // TODO: eigenvv, invsqrt, cbrt, fastarctan, (round, floor, ceil(?)),
 
+enum
+{
+    MAT_N_DIM_C1,
+    MAT_N_1_CDIM,
+    MAT_1_N_CDIM,
+    MAT_N_DIM_C1_NONCONT,
+    MAT_N_1_CDIM_NONCONT,
+    VECTOR
+};
 
 class CV_KMeansSingularTest : public cvtest::BaseTest
 {
@@ -2519,7 +2528,7 @@ public:
     CV_KMeansSingularTest() {}
     ~CV_KMeansSingularTest() {}
 protected:
-    void run(int)
+    void run(int inVariant)
     {
         int i, iter = 0, N = 0, N0 = 0, K = 0, dims = 0;
         Mat labels;
@@ -2531,20 +2540,70 @@ protected:
             for( iter = 0; iter < maxIter; iter++ )
             {
                 ts->update_context(this, iter, true);
-                dims = rng.uniform(1, MAX_DIM+1);
+                dims = rng.uniform(inVariant == MAT_1_N_CDIM ? 2 : 1, MAX_DIM+1);
                 N = rng.uniform(1, MAX_POINTS+1);
                 N0 = rng.uniform(1, MAX(N/10, 2));
                 K = rng.uniform(1, N+1);
 
-                Mat data0(N0, dims, CV_32F);
-                rng.fill(data0, RNG::UNIFORM, -1, 1);
+                if (inVariant == VECTOR)
+                {
+                    dims = 2;
 
-                Mat data(N, dims, CV_32F);
-                for( i = 0; i < N; i++ )
-                    data0.row(rng.uniform(0, N0)).copyTo(data.row(i));
+                    std::vector<cv::Point2f> data0(N0);
+                    rng.fill(data0, RNG::UNIFORM, -1, 1);
 
-                kmeans(data, K, labels, TermCriteria(TermCriteria::MAX_ITER+TermCriteria::EPS, 30, 0),
-                       5, KMEANS_PP_CENTERS);
+                    std::vector<cv::Point2f> data(N);
+                    for( i = 0; i < N; i++ )
+                        data[i] = data0[rng.uniform(0, N0)];
+
+                    kmeans(data, K, labels, TermCriteria(TermCriteria::MAX_ITER+TermCriteria::EPS, 30, 0),
+                           5, KMEANS_PP_CENTERS);
+                }
+                else
+                {
+                    Mat data0(N0, dims, CV_32F);
+                    rng.fill(data0, RNG::UNIFORM, -1, 1);
+
+                    Mat data;
+
+                    switch (inVariant)
+                    {
+                    case MAT_N_DIM_C1:
+                        data.create(N, dims, CV_32F);
+                        for( i = 0; i < N; i++ )
+                            data0.row(rng.uniform(0, N0)).copyTo(data.row(i));
+                        break;
+
+                    case MAT_N_1_CDIM:
+                        data.create(N, 1, CV_32FC(dims));
+                        for( i = 0; i < N; i++ )
+                            memcpy(data.ptr(i), data0.ptr(rng.uniform(0, N0)), dims * sizeof(float));
+                        break;
+
+                    case MAT_1_N_CDIM:
+                        data.create(1, N, CV_32FC(dims));
+                        for( i = 0; i < N; i++ )
+                            memcpy(data.data + i * dims * sizeof(float), data0.ptr(rng.uniform(0, N0)), dims * sizeof(float));
+                        break;
+
+                    case MAT_N_DIM_C1_NONCONT:
+                        data.create(N, dims + 5, CV_32F);
+                        data = data(Range(0, N), Range(0, dims));
+                        for( i = 0; i < N; i++ )
+                            data0.row(rng.uniform(0, N0)).copyTo(data.row(i));
+                        break;
+
+                    case MAT_N_1_CDIM_NONCONT:
+                        data.create(N, 3, CV_32FC(dims));
+                        data = data.colRange(0, 1);
+                        for( i = 0; i < N; i++ )
+                            memcpy(data.ptr(i), data0.ptr(rng.uniform(0, N0)), dims * sizeof(float));
+                        break;
+                    }
+
+                    kmeans(data, K, labels, TermCriteria(TermCriteria::MAX_ITER+TermCriteria::EPS, 30, 0),
+                           5, KMEANS_PP_CENTERS);
+                }
 
                 Mat hist(K, 1, CV_32S, Scalar(0));
                 for( i = 0; i < N; i++ )
@@ -2568,7 +2627,19 @@ protected:
     }
 };
 
-TEST(Core_KMeans, singular) { CV_KMeansSingularTest test; test.safe_run(); }
+TEST(Core_KMeans, singular) { CV_KMeansSingularTest test; test.safe_run(MAT_N_DIM_C1); }
+
+CV_ENUM(KMeansInputVariant, MAT_N_DIM_C1, MAT_N_1_CDIM, MAT_1_N_CDIM, MAT_N_DIM_C1_NONCONT, MAT_N_1_CDIM_NONCONT, VECTOR)
+
+typedef testing::TestWithParam<KMeansInputVariant> Core_KMeans_InputVariants;
+
+TEST_P(Core_KMeans_InputVariants, singular)
+{
+    CV_KMeansSingularTest test;
+    test.safe_run(GetParam());
+}
+
+INSTANTIATE_TEST_CASE_P(AllVariants, Core_KMeans_InputVariants, KMeansInputVariant::all());
 
 TEST(CovariationMatrixVectorOfMat, accuracy)
 {
diff --git a/samples/cpp/kmeans.cpp b/samples/cpp/kmeans.cpp
index 19e998379d..d475cf175c 100644
--- a/samples/cpp/kmeans.cpp
+++ b/samples/cpp/kmeans.cpp
@@ -33,7 +33,7 @@ int main( int /*argc*/, char** /*argv*/ )
     {
         int k, clusterCount = rng.uniform(2, MAX_CLUSTERS+1);
         int i, sampleCount = rng.uniform(1, 1001);
-        Mat points(sampleCount, 2, CV_32F), labels;
+        Mat points(sampleCount, 1, CV_32FC2), labels;
 
         clusterCount = MIN(clusterCount, sampleCount);
         Mat centers;