diff --git a/modules/core/include/opencv2/core/eigen.hpp b/modules/core/include/opencv2/core/eigen.hpp
index 741648edb8fb..8c250efe4cd7 100644
--- a/modules/core/include/opencv2/core/eigen.hpp
+++ b/modules/core/include/opencv2/core/eigen.hpp
@@ -47,6 +47,11 @@
 
 #include "opencv2/core.hpp"
 
+#if EIGEN_WORLD_VERSION == 3 && EIGEN_MAJOR_VERSION >= 3
+#include <unsupported/Eigen/CXX11/Tensor>
+#define OPENCV_EIGEN_TENSOR_SUPPORT
+#endif // EIGEN_WORLD_VERSION == 3 && EIGEN_MAJOR_VERSION >= 3
+
 #if defined _MSC_VER && _MSC_VER >= 1200
 #pragma warning( disable: 4714 ) //__forceinline is not inlined
 #pragma warning( disable: 4127 ) //conditional expression is constant
@@ -59,6 +64,107 @@ namespace cv
 //! @addtogroup core_eigen
 //! @{
 
+#ifdef OPENCV_EIGEN_TENSOR_SUPPORT
+/** @brief Converts an Eigen::Tensor to a cv::Mat.
+
+The method converts an Eigen::Tensor with shape (H x W x C) to a cv::Mat where:
+ H = number of rows
+ W = number of columns
+ C = number of channels
+
+Usage:
+\code
+Eigen::Tensor<float, 3, Eigen::RowMajor> a_tensor(...);
+// populate tensor with values
+Mat a_mat;
+eigen2cv(a_tensor, a_mat);
+\endcode
+*/
+template <typename _Tp, int _layout> static inline
+void eigen2cv( const Eigen::Tensor<_Tp, 3, _layout> &src, OutputArray dst )
+{
+    if( !(_layout & Eigen::RowMajorBit) )
+    {
+        const std::array<int, 3> shuffle{2, 1, 0};
+        Eigen::Tensor<_Tp, 3, !_layout> row_major_tensor = src.swap_layout().shuffle(shuffle);
+        Mat _src(src.dimension(0), src.dimension(1), CV_MAKETYPE(DataType<_Tp>::type, src.dimension(2)), row_major_tensor.data());
+        _src.copyTo(dst);
+    }
+    else
+    {
+        Mat _src(src.dimension(0), src.dimension(1), CV_MAKETYPE(DataType<_Tp>::type, src.dimension(2)), (void *)src.data());
+        _src.copyTo(dst);
+    }
+}
+
+/** @brief Converts a cv::Mat to an Eigen::Tensor.
+
+The method converts a cv::Mat to an Eigen Tensor with shape (H x W x C) where:
+ H = number of rows
+ W = number of columns
+ C = number of channels
+
+Usage:
+\code
+Mat a_mat(...);
+// populate Mat with values
+Eigen::Tensor<float, 3, Eigen::RowMajor> a_tensor(...);
+cv2eigen(a_mat, a_tensor);
+\endcode
+*/
+template <typename _Tp, int _layout> static inline
+void cv2eigen( const Mat &src, Eigen::Tensor<_Tp, 3, _layout> &dst )
+{
+    if( !(_layout & Eigen::RowMajorBit) )
+    {
+        Eigen::Tensor<_Tp, 3, !_layout> row_major_tensor(src.rows, src.cols, src.channels());
+        Mat _dst(src.rows, src.cols, CV_MAKETYPE(DataType<_Tp>::type, src.channels()), row_major_tensor.data());
+        if (src.type() == _dst.type())
+            src.copyTo(_dst);
+        else
+            src.convertTo(_dst, _dst.type());
+        const std::array<int, 3> shuffle{2, 1, 0};
+        dst = row_major_tensor.swap_layout().shuffle(shuffle);
+    }
+    else
+    {
+        dst.resize(src.rows, src.cols, src.channels());
+        Mat _dst(src.rows, src.cols, CV_MAKETYPE(DataType<_Tp>::type, src.channels()), dst.data());
+        if (src.type() == _dst.type())
+            src.copyTo(_dst);
+        else
+            src.convertTo(_dst, _dst.type());
+    }
+}
+
+/** @brief Maps cv::Mat data to an Eigen::TensorMap.
+
+The method wraps an existing Mat data array with an Eigen TensorMap of shape (H x W x C) where:
+ H = number of rows
+ W = number of columns
+ C = number of channels
+
+Explicit instantiation of the return type is required.
+
+@note Caller should be aware of the lifetime of the cv::Mat instance and take appropriate safety measures.
+The cv::Mat instance will retain ownership of the data and the Eigen::TensorMap will lose access when the cv::Mat data is deallocated.
+
+The example below initializes a cv::Mat and produces an Eigen::TensorMap:
+\code
+float arr[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
+Mat a_mat(2, 2, CV_32FC3, arr);
+Eigen::TensorMap<Eigen::Tensor<float, 3, Eigen::RowMajor>> a_tensormap = cv2eigen_tensormap<float>(a_mat);
+\endcode
+*/
+template <typename _Tp> static inline
+Eigen::TensorMap<Eigen::Tensor<_Tp, 3, Eigen::RowMajor>> cv2eigen_tensormap(const cv::InputArray &src)
+{
+    Mat mat = src.getMat();
+    CV_CheckTypeEQ(mat.type(), CV_MAKETYPE(traits::Type<_Tp>::value, mat.channels()), "");
+    return Eigen::TensorMap<Eigen::Tensor<_Tp, 3, Eigen::RowMajor>>((_Tp *)mat.data, mat.rows, mat.cols, mat.channels());
+}
+#endif // OPENCV_EIGEN_TENSOR_SUPPORT
+
 template<typename _Tp, int _rows, int _cols, int _options, int _maxRows, int _maxCols> static inline
 void eigen2cv( const Eigen::Matrix<_Tp, _rows, _cols, _options, _maxRows, _maxCols>& src, OutputArray dst )
 {
diff --git a/modules/core/test/test_mat.cpp b/modules/core/test/test_mat.cpp
index 58eafd074821..43e0078ec8e0 100644
--- a/modules/core/test/test_mat.cpp
+++ b/modules/core/test/test_mat.cpp
@@ -2084,6 +2084,86 @@ TEST(Core_Eigen, eigen2cv_check_Mat_type)
 }
 #endif // HAVE_EIGEN
 
+#ifdef OPENCV_EIGEN_TENSOR_SUPPORT
+TEST(Core_Eigen, cv2eigen_check_tensor_conversion)
+{
+    Mat A(2, 3, CV_32FC3);
+    float value = 0;
+    for(int row=0; row<A.rows; row++)
+        for(int col=0; col<A.cols; col++)
+            for(int ch=0; ch<A.channels(); ch++)
+                A.at<Vec3f>(row,col)[ch] = value++;
+
+    Eigen::Tensor<float, 3, Eigen::RowMajor> row_tensor;
+    cv2eigen(A, row_tensor);
+
+    float* mat_ptr = (float*)A.data;
+    float* tensor_ptr = row_tensor.data();
+    for (int i=0; i< row_tensor.size(); i++)
+        ASSERT_FLOAT_EQ(mat_ptr[i], tensor_ptr[i]);
+
+    Eigen::Tensor<float, 3, Eigen::ColMajor> col_tensor;
+    cv2eigen(A, col_tensor);
+    value = 0;
+    for(int row=0; row<A.rows; row++)
+        for(int col=0; col<A.cols; col++)
+            for(int ch=0; ch<A.channels(); ch++)
+                ASSERT_FLOAT_EQ(value++, col_tensor(row,col,ch));
+}
+#endif // OPENCV_EIGEN_TENSOR_SUPPORT
+
+#ifdef OPENCV_EIGEN_TENSOR_SUPPORT
+TEST(Core_Eigen, eigen2cv_check_tensor_conversion)
+{
+    Eigen::Tensor<float, 3, Eigen::RowMajor> row_tensor(2,3,3);
+    Eigen::Tensor<float, 3, Eigen::ColMajor> col_tensor(2,3,3);
+    float value = 0;
+    for(int row=0; row<row_tensor.dimension(0); row++)
+        for(int col=0; col<row_tensor.dimension(1); col++)
+            for(int ch=0; ch<row_tensor.dimension(2); ch++)
+            {
+                row_tensor(row,col,ch) = value;
+                col_tensor(row,col,ch) = value;
+                value++;
+            }
+
+    Mat A;
+    eigen2cv(row_tensor, A);
+
+    float* tensor_ptr = row_tensor.data();
+    float* mat_ptr = (float*)A.data;
+    for (int i=0; i< row_tensor.size(); i++)
+        ASSERT_FLOAT_EQ(tensor_ptr[i], mat_ptr[i]);
+
+    Mat B;
+    eigen2cv(col_tensor, B);
+
+    value = 0;
+    for(int row=0; row<B.rows; row++)
+        for(int col=0; col<B.cols; col++)
+            for(int ch=0; ch<B.channels(); ch++)
+                ASSERT_FLOAT_EQ(value++, B.at<Vec3f>(row,col)[ch]);
+}
+#endif // OPENCV_EIGEN_TENSOR_SUPPORT
+
+#ifdef OPENCV_EIGEN_TENSOR_SUPPORT
+TEST(Core_Eigen, cv2eigen_tensormap_check_tensormap_access)
+{
+    float arr[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
+    Mat a_mat(2, 2, CV_32FC3, arr);
+    Eigen::TensorMap<Eigen::Tensor<float, 3, Eigen::RowMajor>> a_tensor = cv2eigen_tensormap<float>(a_mat);
+
+    for(int i=0; i<a_mat.rows; i++) {
+        for (int j=0; j<a_mat.cols; j++) {
+            for (int ch=0; ch<a_mat.channels(); ch++) {
+                ASSERT_FLOAT_EQ(a_mat.at<Vec3f>(i,j)[ch], a_tensor(i,j,ch));
+                ASSERT_EQ(&a_mat.at<Vec3f>(i,j)[ch], &a_tensor(i,j,ch));
+            }
+        }
+    }
+}
+#endif // OPENCV_EIGEN_TENSOR_SUPPORT
+
 TEST(Mat, regression_12943)  // memory usage: ~4.5 Gb
 {
     applyTestTag(CV_TEST_TAG_MEMORY_6GB);