diff --git a/modules/core/src/matrix_wrap.cpp b/modules/core/src/matrix_wrap.cpp
index 8d9e984bc83604493adedd27a3d301cd881cd6f3..f0b5b895c4bb7969c41c3be2c2ef21d65826276c 100644
--- a/modules/core/src/matrix_wrap.cpp
+++ b/modules/core/src/matrix_wrap.cpp
@@ -914,7 +914,7 @@ bool _InputArray::isContinuous(int i) const
     if( k == STD_ARRAY_MAT )
     {
         const Mat* vv = (const Mat*)obj;
-        CV_Assert(i > 0 && i < sz.height);
+        CV_Assert(i >= 0 && i < sz.height);
         return vv[i].isContinuous();
     }
 
@@ -948,21 +948,21 @@ bool _InputArray::isSubmatrix(int i) const
     if( k == STD_VECTOR_MAT )
     {
         const std::vector<Mat>& vv = *(const std::vector<Mat>*)obj;
-        CV_Assert((size_t)i < vv.size());
+        CV_Assert(i >= 0 && (size_t)i < vv.size());
         return vv[i].isSubmatrix();
     }
 
     if( k == STD_ARRAY_MAT )
     {
         const Mat* vv = (const Mat*)obj;
-        CV_Assert(i < sz.height);
+        CV_Assert(i >= 0 && i < sz.height);
         return vv[i].isSubmatrix();
     }
 
     if( k == STD_VECTOR_UMAT )
     {
         const std::vector<UMat>& vv = *(const std::vector<UMat>*)obj;
-        CV_Assert((size_t)i < vv.size());
+        CV_Assert(i >= 0 && (size_t)i < vv.size());
         return vv[i].isSubmatrix();
     }
 
@@ -993,9 +993,7 @@ size_t _InputArray::offset(int i) const
     if( k == STD_VECTOR_MAT )
     {
         const std::vector<Mat>& vv = *(const std::vector<Mat>*)obj;
-        if( i < 0 )
-            return 1;
-        CV_Assert( i < (int)vv.size() );
+        CV_Assert( i >= 0 && i < (int)vv.size() );
 
         return (size_t)(vv[i].ptr() - vv[i].datastart);
     }
@@ -1003,16 +1001,14 @@ size_t _InputArray::offset(int i) const
     if( k == STD_ARRAY_MAT )
     {
         const Mat* vv = (const Mat*)obj;
-        if( i < 0 )
-            return 1;
-        CV_Assert( i < sz.height );
+        CV_Assert( i >= 0 && i < sz.height );
         return (size_t)(vv[i].ptr() - vv[i].datastart);
     }
 
     if( k == STD_VECTOR_UMAT )
     {
         const std::vector<UMat>& vv = *(const std::vector<UMat>*)obj;
-        CV_Assert((size_t)i < vv.size());
+        CV_Assert(i >= 0 && (size_t)i < vv.size());
         return vv[i].offset;
     }
 
@@ -1026,7 +1022,7 @@ size_t _InputArray::offset(int i) const
     if (k == STD_VECTOR_CUDA_GPU_MAT)
     {
         const std::vector<cuda::GpuMat>& vv = *(const std::vector<cuda::GpuMat>*)obj;
-        CV_Assert((size_t)i < vv.size());
+        CV_Assert(i >= 0 && (size_t)i < vv.size());
         return (size_t)(vv[i].data - vv[i].datastart);
     }
 
@@ -1056,25 +1052,21 @@ size_t _InputArray::step(int i) const
     if( k == STD_VECTOR_MAT )
     {
         const std::vector<Mat>& vv = *(const std::vector<Mat>*)obj;
-        if( i < 0 )
-            return 1;
-        CV_Assert( i < (int)vv.size() );
+        CV_Assert( i >= 0 && i < (int)vv.size() );
         return vv[i].step;
     }
 
     if( k == STD_ARRAY_MAT )
     {
         const Mat* vv = (const Mat*)obj;
-        if( i < 0 )
-            return 1;
-        CV_Assert( i < sz.height );
+        CV_Assert( i >= 0 && i < sz.height );
         return vv[i].step;
     }
 
     if( k == STD_VECTOR_UMAT )
     {
         const std::vector<UMat>& vv = *(const std::vector<UMat>*)obj;
-        CV_Assert((size_t)i < vv.size());
+        CV_Assert(i >= 0 && (size_t)i < vv.size());
         return vv[i].step;
     }
 
@@ -1086,7 +1078,7 @@ size_t _InputArray::step(int i) const
     if (k == STD_VECTOR_CUDA_GPU_MAT)
     {
         const std::vector<cuda::GpuMat>& vv = *(const std::vector<cuda::GpuMat>*)obj;
-        CV_Assert((size_t)i < vv.size());
+        CV_Assert(i >= 0 && (size_t)i < vv.size());
         return vv[i].step;
     }
 
diff --git a/modules/core/test/test_mat.cpp b/modules/core/test/test_mat.cpp
index 0bc3961fe2f856f3a140d9026adf227559648851..a2426ad977837c6b39e03f77daff39b77332cd02 100644
--- a/modules/core/test/test_mat.cpp
+++ b/modules/core/test/test_mat.cpp
@@ -9,6 +9,8 @@
 #include "opencv2/core/eigen.hpp"
 #endif
 
+#include "opencv2/core/cuda.hpp"
+
 namespace opencv_test { namespace {
 
 class Core_ReduceTest : public cvtest::BaseTest
@@ -1984,6 +1986,157 @@ TEST(Core_InputArray, fetch_MatExpr)
 }
 
 
+#ifdef CV_CXX11
+class TestInputArrayRangeChecking {
+    static const char *kind2str(cv::_InputArray ia)
+    {
+        switch (ia.kind())
+        {
+        #define C(x) case cv::_InputArray::x: return #x
+        C(MAT);
+        C(UMAT);
+        C(EXPR);
+        C(MATX);
+        C(STD_VECTOR);
+        C(STD_ARRAY);
+        C(NONE);
+        C(STD_VECTOR_VECTOR);
+        C(STD_BOOL_VECTOR);
+        C(STD_VECTOR_MAT);
+        C(STD_ARRAY_MAT);
+        C(STD_VECTOR_UMAT);
+        C(CUDA_GPU_MAT);
+        C(STD_VECTOR_CUDA_GPU_MAT);
+        #undef C
+        default:
+            return "<unsupported>";
+        }
+    }
+
+    static void banner(cv::_InputArray ia, const char *label, const char *name)
+    {
+        std::cout << std::endl
+                  << label << " = " << name << ", Kind: " << kind2str(ia)
+                  << std::endl;
+    }
+
+    template<typename I, typename F>
+    static void testA(I ia, F f, const char *mfname)
+    {
+        banner(ia, "f", mfname);
+        EXPECT_THROW(f(ia, -1), cv::Exception)
+            << "f(ia, " << -1 << ") should throw cv::Exception";
+        for (int i = 0; i < int(ia.size()); i++)
+        {
+            EXPECT_NO_THROW(f(ia, i))
+                << "f(ia, " << i << ") should not throw an exception";
+        }
+        EXPECT_THROW(f(ia, int(ia.size())), cv::Exception)
+            << "f(ia, " << ia.size() << ") should throw cv::Exception";
+    }
+
+    template<typename I, typename F>
+    static void testB(I ia, F f, const char *mfname)
+    {
+        banner(ia, "f", mfname);
+        EXPECT_THROW(f(ia, -1), cv::Exception)
+            << "f(ia, " << -1 << ") should throw cv::Exception";
+        for (int i = 0; i < int(ia.size()); i++)
+        {
+            EXPECT_NO_THROW(f(ia, i))
+                << "f(ia, " << i << ") should not throw an exception";
+        }
+        EXPECT_THROW(f(ia, int(ia.size())), cv::Exception)
+            << "f(ia, " << ia.size() << ") should throw cv::Exception";
+    }
+
+    static void test_isContinuous()
+    {
+        auto f = [](cv::_InputArray ia, int i) { (void)ia.isContinuous(i); };
+
+        cv::Mat M;
+        cv::UMat uM;
+
+        std::vector<cv::Mat> vec = {M, M};
+        std::array<cv::Mat, 2> arr = {M, M};
+        std::vector<cv::UMat> uvec = {uM, uM};
+
+        testA(vec, f, "isContinuous");
+        testA(arr, f, "isContinuous");
+        testA(uvec, f, "isContinuous");
+    }
+
+    static void test_isSubmatrix()
+    {
+        auto f = [](cv::_InputArray ia, int i) { (void)ia.isSubmatrix(i); };
+
+        cv::Mat M;
+        cv::UMat uM;
+
+        std::vector<cv::Mat> vec = {M, M};
+        std::array<cv::Mat, 2> arr = {M, M};
+        std::vector<cv::UMat> uvec = {uM, uM};
+
+        testA(vec, f, "isSubmatrix");
+        testA(arr, f, "isSubmatrix");
+        testA(uvec, f, "isSubmatrix");
+    }
+
+    static void test_offset()
+    {
+        auto f = [](cv::_InputArray ia, int i) { return ia.offset(i); };
+
+        cv::Mat M;
+        cv::UMat uM;
+        cv::cuda::GpuMat gM;
+
+        std::vector<cv::Mat> vec = {M, M};
+        std::array<cv::Mat, 2> arr = {M, M};
+        std::vector<cv::UMat> uvec = {uM, uM};
+        std::vector<cv::cuda::GpuMat> gvec = {gM, gM};
+
+        testB(vec, f, "offset");
+        testB(arr, f, "offset");
+        testB(uvec, f, "offset");
+        testB(gvec, f, "offset");
+    }
+
+    static void test_step()
+    {
+        auto f = [](cv::_InputArray ia, int i) { return ia.step(i); };
+
+        cv::Mat M;
+        cv::UMat uM;
+        cv::cuda::GpuMat gM;
+
+        std::vector<cv::Mat> vec = {M, M};
+        std::array<cv::Mat, 2> arr = {M, M};
+        std::vector<cv::UMat> uvec = {uM, uM};
+        std::vector<cv::cuda::GpuMat> gvec = {gM, gM};
+
+        testB(vec, f, "step");
+        testB(arr, f, "step");
+        testB(uvec, f, "step");
+        testB(gvec, f, "step");
+    }
+
+public:
+    static void run()
+    {
+        test_isContinuous();
+        test_isSubmatrix();
+        test_offset();
+        test_step();
+    }
+};
+
+TEST(Core_InputArray, range_checking)
+{
+    TestInputArrayRangeChecking::run();
+}
+#endif
+
+
 TEST(Core_Vectors, issue_13078)
 {
     float floats_[] = { 1, 2, 3, 4, 5, 6, 7, 8 };