diff --git a/modules/cudaarithm/include/opencv2/cudaarithm.hpp b/modules/cudaarithm/include/opencv2/cudaarithm.hpp
index bb74ea18918..a16c271881e 100644
--- a/modules/cudaarithm/include/opencv2/cudaarithm.hpp
+++ b/modules/cudaarithm/include/opencv2/cudaarithm.hpp
@@ -433,6 +433,17 @@ CV_EXPORTS_W void magnitudeSqr(InputArray x, InputArray y, OutputArray magnitude
  */
 CV_EXPORTS_W void phase(InputArray x, InputArray y, OutputArray angle, bool angleInDegrees = false, Stream& stream = Stream::Null());
 
+/** @brief Computes polar angles of complex matrix elements.
+
+@param xy Source matrix containing real and imaginary components ( CV_32FC2 ).
+@param angle Destination matrix of angles ( CV_32FC1 ).
+@param angleInDegrees Flag for angles that must be evaluated in degrees.
+@param stream Stream for the asynchronous version.
+
+@sa phase
+*/
+CV_EXPORTS_W void phase(InputArray xy, OutputArray angle, bool angleInDegrees = false, Stream& stream = Stream::Null());
+
 /** @brief Converts Cartesian coordinates into polar.
 
 @param x Source matrix containing real components ( CV_32FC1 ).
@@ -446,6 +457,29 @@ CV_EXPORTS_W void phase(InputArray x, InputArray y, OutputArray angle, bool angl
  */
 CV_EXPORTS_W void cartToPolar(InputArray x, InputArray y, OutputArray magnitude, OutputArray angle, bool angleInDegrees = false, Stream& stream = Stream::Null());
 
+/** @brief Converts Cartesian coordinates into polar.
+
+@param xy Source matrix containing real and imaginary components ( CV_32FC2 ).
+@param magnitude Destination matrix of float magnitudes ( CV_32FC1 ).
+@param angle Destination matrix of angles ( CV_32FC1 ).
+@param angleInDegrees Flag for angles that must be evaluated in degrees.
+@param stream Stream for the asynchronous version.
+
+@sa cartToPolar
+*/
+CV_EXPORTS_W void cartToPolar(InputArray xy, OutputArray magnitude, OutputArray angle, bool angleInDegrees = false, Stream& stream = Stream::Null());
+
+/** @brief Converts Cartesian coordinates into polar.
+
+@param xy Source matrix containing real and imaginary components ( CV_32FC2 ).
+@param magnitudeAngle Destination matrix of float magnitudes and angles ( CV_32FC2 ).
+@param angleInDegrees Flag for angles that must be evaluated in degrees.
+@param stream Stream for the asynchronous version.
+
+@sa cartToPolar
+*/
+CV_EXPORTS_W void cartToPolar(InputArray xy, OutputArray magnitudeAngle, bool angleInDegrees = false, Stream& stream = Stream::Null());
+
 /** @brief Converts polar coordinates into Cartesian.
 
 @param magnitude Source matrix containing magnitudes ( CV_32FC1 or CV_64FC1 ).
@@ -457,6 +491,25 @@ CV_EXPORTS_W void cartToPolar(InputArray x, InputArray y, OutputArray magnitude,
  */
 CV_EXPORTS_W void polarToCart(InputArray magnitude, InputArray angle, OutputArray x, OutputArray y, bool angleInDegrees = false, Stream& stream = Stream::Null());
 
+/** @brief Converts polar coordinates into Cartesian.
+
+@param magnitude Source matrix containing magnitudes ( CV_32FC1 or CV_64FC1 ).
+@param angle Source matrix containing angles ( same type as magnitude ).
+@param xy Destination matrix of real and imaginary components ( same depth as magnitude, i.e. CV_32FC2 or CV_64FC2 ).
+@param angleInDegrees Flag that indicates angles in degrees.
+@param stream Stream for the asynchronous version.
+*/
+CV_EXPORTS_W void polarToCart(InputArray magnitude, InputArray angle, OutputArray xy, bool angleInDegrees = false, Stream& stream = Stream::Null());
+
+/** @brief Converts polar coordinates into Cartesian.
+
+@param magnitudeAngle Source matrix containing magnitudes and angles ( CV_32FC2 or CV_64FC2 ).
+@param xy Destination matrix of real and imaginary components ( same depth as source ).
+@param angleInDegrees Flag that indicates angles in degrees.
+@param stream Stream for the asynchronous version.
+*/
+CV_EXPORTS_W void polarToCart(InputArray magnitudeAngle, OutputArray xy, bool angleInDegrees = false, Stream& stream = Stream::Null());
+
 //! @} cudaarithm_elem
 
 //! @addtogroup cudaarithm_core
diff --git a/modules/cudaarithm/src/cuda/polar_cart.cu b/modules/cudaarithm/src/cuda/polar_cart.cu
index 12980e424ff..725f5741d81 100644
--- a/modules/cudaarithm/src/cuda/polar_cart.cu
+++ b/modules/cudaarithm/src/cuda/polar_cart.cu
@@ -52,8 +52,10 @@
 #include "opencv2/cudev.hpp"
 #include "opencv2/core/private.cuda.hpp"
 
-using namespace cv;
-using namespace cv::cuda;
+//do not use implicit cv::cuda to avoid clash of tuples from ::cuda::std
+/*using namespace cv;
+using namespace cv::cuda;*/
+
 using namespace cv::cudev;
 
 void cv::cuda::magnitude(InputArray _x, InputArray _y, OutputArray _dst, Stream& stream)
@@ -66,11 +68,7 @@ void cv::cuda::magnitude(InputArray _x, InputArray _y, OutputArray _dst, Stream&
 
     GpuMat dst = getOutputMat(_dst, x.size(), CV_32FC1, stream);
 
-    GpuMat_<float> xc(x.reshape(1));
-    GpuMat_<float> yc(y.reshape(1));
-    GpuMat_<float> magc(dst.reshape(1));
-
-    gridTransformBinary(xc, yc, magc, magnitude_func<float>(), stream);
+    gridTransformBinary(globPtr<float>(x), globPtr<float>(y), globPtr<float>(dst), magnitude_func<float>(), stream);
 
     syncOutput(dst, _dst, stream);
 }
@@ -85,11 +83,7 @@ void cv::cuda::magnitudeSqr(InputArray _x, InputArray _y, OutputArray _dst, Stre
 
     GpuMat dst = getOutputMat(_dst, x.size(), CV_32FC1, stream);
 
-    GpuMat_<float> xc(x.reshape(1));
-    GpuMat_<float> yc(y.reshape(1));
-    GpuMat_<float> magc(dst.reshape(1));
-
-    gridTransformBinary(xc, yc, magc, magnitude_sqr_func<float>(), stream);
+    gridTransformBinary(globPtr<float>(x), globPtr<float>(y), globPtr<float>(dst), magnitude_sqr_func<float>(), stream);
 
     syncOutput(dst, _dst, stream);
 }
@@ -104,14 +98,26 @@ void cv::cuda::phase(InputArray _x, InputArray _y, OutputArray _dst, bool angleI
 
     GpuMat dst = getOutputMat(_dst, x.size(), CV_32FC1, stream);
 
-    GpuMat_<float> xc(x.reshape(1));
-    GpuMat_<float> yc(y.reshape(1));
-    GpuMat_<float> anglec(dst.reshape(1));
+    if (angleInDegrees)
+        gridTransformBinary(globPtr<float>(x), globPtr<float>(y), globPtr<float>(dst), direction_func<float, true>(), stream);
+    else
+        gridTransformBinary(globPtr<float>(x), globPtr<float>(y), globPtr<float>(dst), direction_func<float, false>(), stream);
+
+    syncOutput(dst, _dst, stream);
+}
+
+void cv::cuda::phase(InputArray _xy, OutputArray _dst, bool angleInDegrees, Stream& stream)
+{
+    GpuMat xy = getInputMat(_xy, stream);
+
+    CV_Assert( xy.type() == CV_32FC2 );
+
+    GpuMat dst = getOutputMat(_dst, xy.size(), CV_32FC1, stream);
 
     if (angleInDegrees)
-        gridTransformBinary(xc, yc, anglec, direction_func<float, true>(), stream);
+        gridTransformUnary(globPtr<float2>(xy), globPtr<float>(dst), direction_interleaved_func<float2, true>(), stream);
     else
-        gridTransformBinary(xc, yc, anglec, direction_func<float, false>(), stream);
+        gridTransformUnary(globPtr<float2>(xy), globPtr<float>(dst), direction_interleaved_func<float2, false>(), stream);
 
     syncOutput(dst, _dst, stream);
 }
@@ -127,10 +133,10 @@ void cv::cuda::cartToPolar(InputArray _x, InputArray _y, OutputArray _mag, Outpu
     GpuMat mag = getOutputMat(_mag, x.size(), CV_32FC1, stream);
     GpuMat angle = getOutputMat(_angle, x.size(), CV_32FC1, stream);
 
-    GpuMat_<float> xc(x.reshape(1));
-    GpuMat_<float> yc(y.reshape(1));
-    GpuMat_<float> magc(mag.reshape(1));
-    GpuMat_<float> anglec(angle.reshape(1));
+    GpuMat_<float> xc(x);
+    GpuMat_<float> yc(y);
+    GpuMat_<float> magc(mag);
+    GpuMat_<float> anglec(angle);
 
     if (angleInDegrees)
         gridTransformBinary(xc, yc, magc, anglec, magnitude_func<float>(), direction_func<float, true>(), stream);
@@ -141,6 +147,69 @@ void cv::cuda::cartToPolar(InputArray _x, InputArray _y, OutputArray _mag, Outpu
     syncOutput(angle, _angle, stream);
 }
 
+void cv::cuda::cartToPolar(InputArray _xy, OutputArray _mag, OutputArray _angle, bool angleInDegrees, Stream& stream)
+{
+    GpuMat xy = getInputMat(_xy, stream);
+
+    CV_Assert( xy.type() == CV_32FC2 );
+
+    GpuMat mag = getOutputMat(_mag, xy.size(), CV_32FC1, stream);
+    GpuMat angle = getOutputMat(_angle, xy.size(), CV_32FC1, stream);
+
+    GpuMat_<float> magc(mag);
+    GpuMat_<float> anglec(angle);
+
+    if (angleInDegrees)
+    {
+        auto f1 = magnitude_interleaved_func<float2>();
+        auto f2 = direction_interleaved_func<float2, true>();
+        cv::cudev::tuple<decltype(f1), decltype(f2)> f12 = cv::cudev::make_tuple(f1, f2);
+        gridTransformTuple(globPtr<float2>(xy),
+                           tie(magc, anglec),
+                           f12,
+                           stream);
+    }
+    else
+    {
+        auto f1 = magnitude_interleaved_func<float2>();
+        auto f2 = direction_interleaved_func<float2, false>();
+        cv::cudev::tuple<decltype(f1), decltype(f2)> f12 = cv::cudev::make_tuple(f1, f2);
+        gridTransformTuple(globPtr<float2>(xy),
+                           tie(magc, anglec),
+                           f12,
+                           stream);
+    }
+
+    syncOutput(mag, _mag, stream);
+    syncOutput(angle, _angle, stream);
+}
+
+void cv::cuda::cartToPolar(InputArray _xy, OutputArray _magAngle, bool angleInDegrees, Stream& stream)
+{
+    GpuMat xy = getInputMat(_xy, stream);
+
+    CV_Assert( xy.type() == CV_32FC2 );
+
+    GpuMat magAngle = getOutputMat(_magAngle, xy.size(), CV_32FC2, stream);
+    
+    if (angleInDegrees)
+    {
+        gridTransformUnary(globPtr<float2>(xy),
+            globPtr<float2>(magAngle),
+            magnitude_direction_interleaved_func<float2, true>(),
+            stream);
+    }
+    else
+    {
+        gridTransformUnary(globPtr<float2>(xy),
+            globPtr<float2>(magAngle),
+            magnitude_direction_interleaved_func<float2, false>(),
+            stream);
+    }
+
+    syncOutput(magAngle, _magAngle, stream);
+}
+
 namespace
 {
     template <typename T> struct sincos_op
@@ -159,12 +228,12 @@ namespace
     };
 
     template <typename T, bool useMag>
-    __global__ void polarToCartImpl_(const GlobPtr<T> mag, const GlobPtr<T> angle, GlobPtr<T> xmat, GlobPtr<T> ymat, const T scale, const int rows, const int cols)
+    __global__ void polarToCartImpl_(const PtrStep<T> mag, const PtrStepSz<T> angle, PtrStep<T> xmat, PtrStep<T> ymat, const T scale)
     {
         const int x = blockDim.x * blockIdx.x + threadIdx.x;
         const int y = blockDim.y * blockIdx.y + threadIdx.y;
 
-        if (x >= cols || y >= rows)
+        if (x >= angle.cols || y >= angle.rows)
             return;
 
         const T mag_val = useMag ? mag(y, x) : static_cast<T>(1.0);
@@ -178,23 +247,90 @@ namespace
         ymat(y, x) = mag_val * sin_a;
     }
 
+    template <typename T, bool useMag>
+    __global__ void polarToCartDstInterleavedImpl_(const PtrStep<T> mag, const PtrStepSz<T> angle, PtrStep<typename MakeVec<T, 2>::type > xymat, const T scale)
+    {
+        typedef typename MakeVec<T, 2>::type T2;
+        const int x = blockDim.x * blockIdx.x + threadIdx.x;
+        const int y = blockDim.y * blockIdx.y + threadIdx.y;
+
+        if (x >= angle.cols || y >= angle.rows)
+            return;
+
+        const T mag_val = useMag ? mag(y, x) : static_cast<T>(1.0);
+        const T angle_val = angle(y, x);
+
+        T sin_a, cos_a;
+        sincos_op<T> op;
+        op(scale * angle_val, &sin_a, &cos_a);
+
+        const T2 xy = {mag_val * cos_a, mag_val * sin_a};
+        xymat(y, x) = xy;
+    }
+
+    template <typename T>
+    __global__ void polarToCartInterleavedImpl_(const PtrStepSz<typename MakeVec<T, 2>::type > magAngle, PtrStep<typename MakeVec<T, 2>::type > xymat, const T scale)
+    {
+        typedef typename MakeVec<T, 2>::type T2;
+        const int x = blockDim.x * blockIdx.x + threadIdx.x;
+        const int y = blockDim.y * blockIdx.y + threadIdx.y;
+
+        if (x >= magAngle.cols || y >= magAngle.rows)
+            return;
+
+        const T2 magAngle_val = magAngle(y, x);
+        const T mag_val = magAngle_val.x;
+        const T angle_val = magAngle_val.y;
+
+        T sin_a, cos_a;
+        sincos_op<T> op;
+        op(scale * angle_val, &sin_a, &cos_a);
+
+        const T2 xy = {mag_val * cos_a, mag_val * sin_a};
+        xymat(y, x) = xy;
+    }
+
     template <typename T>
     void polarToCartImpl(const GpuMat& mag, const GpuMat& angle, GpuMat& x, GpuMat& y, bool angleInDegrees, cudaStream_t& stream)
     {
-        GpuMat_<T> xc(x.reshape(1));
-        GpuMat_<T> yc(y.reshape(1));
-        GpuMat_<T> magc(mag.reshape(1));
-        GpuMat_<T> anglec(angle.reshape(1));
+        const dim3 block(32, 8);
+        const dim3 grid(divUp(angle.cols, block.x), divUp(angle.rows, block.y));
+
+        const T scale = angleInDegrees ? static_cast<T>(CV_PI / 180.0) : static_cast<T>(1.0);
+
+        if (mag.empty())
+            polarToCartImpl_<T, false> << <grid, block, 0, stream >> >(mag, angle, x, y, scale);
+        else
+            polarToCartImpl_<T, true> << <grid, block, 0, stream >> >(mag, angle, x, y, scale);
+    }
+
+    template <typename T>
+    void polarToCartDstInterleavedImpl(const GpuMat& mag, const GpuMat& angle, GpuMat& xy, bool angleInDegrees, cudaStream_t& stream)
+    {
+        typedef typename MakeVec<T, 2>::type T2;
 
         const dim3 block(32, 8);
-        const dim3 grid(divUp(anglec.cols, block.x), divUp(anglec.rows, block.y));
+        const dim3 grid(divUp(angle.cols, block.x), divUp(angle.rows, block.y));
 
         const T scale = angleInDegrees ? static_cast<T>(CV_PI / 180.0) : static_cast<T>(1.0);
 
-        if (magc.empty())
-            polarToCartImpl_<T, false> << <grid, block, 0, stream >> >(shrinkPtr(magc), shrinkPtr(anglec), shrinkPtr(xc), shrinkPtr(yc), scale, anglec.rows, anglec.cols);
+        if (mag.empty())
+            polarToCartDstInterleavedImpl_<T, false> << <grid, block, 0, stream >> >(mag, angle, xy, scale);
         else
-            polarToCartImpl_<T, true> << <grid, block, 0, stream >> >(shrinkPtr(magc), shrinkPtr(anglec), shrinkPtr(xc), shrinkPtr(yc), scale, anglec.rows, anglec.cols);
+            polarToCartDstInterleavedImpl_<T, true> << <grid, block, 0, stream >> >(mag, angle, xy, scale);
+    }
+
+    template <typename T>
+    void polarToCartInterleavedImpl(const GpuMat& magAngle, GpuMat& xy, bool angleInDegrees, cudaStream_t& stream)
+    {
+        typedef typename MakeVec<T, 2>::type T2;
+
+        const dim3 block(32, 8);
+        const dim3 grid(divUp(magAngle.cols, block.x), divUp(magAngle.rows, block.y));
+
+        const T scale = angleInDegrees ? static_cast<T>(CV_PI / 180.0) : static_cast<T>(1.0);
+
+        polarToCartInterleavedImpl_<T> << <grid, block, 0, stream >> >(magAngle, xy, scale);
     }
 }
 
@@ -223,4 +359,48 @@ void cv::cuda::polarToCart(InputArray _mag, InputArray _angle, OutputArray _x, O
         CV_CUDEV_SAFE_CALL( cudaDeviceSynchronize() );
 }
 
+void cv::cuda::polarToCart(InputArray _mag, InputArray _angle, OutputArray _xy, bool angleInDegrees, Stream& _stream)
+{
+    typedef void(*func_t)(const GpuMat& mag, const GpuMat& angle, GpuMat& xy, bool angleInDegrees, cudaStream_t& stream);
+    static const func_t funcs[7] = { 0, 0, 0, 0, 0, polarToCartDstInterleavedImpl<float>, polarToCartDstInterleavedImpl<double> };
+
+    GpuMat mag = getInputMat(_mag, _stream);
+    GpuMat angle = getInputMat(_angle, _stream);
+
+    CV_Assert(angle.depth() == CV_32F || angle.depth() == CV_64F);
+    CV_Assert( mag.empty() || (mag.type() == angle.type() && mag.size() == angle.size()) );
+
+    GpuMat xy = getOutputMat(_xy, angle.size(), CV_MAKETYPE(angle.depth(), 2), _stream);
+
+    cudaStream_t stream = StreamAccessor::getStream(_stream);
+    funcs[angle.depth()](mag, angle, xy, angleInDegrees, stream);
+    CV_CUDEV_SAFE_CALL( cudaGetLastError() );
+
+    syncOutput(xy, _xy, _stream);
+
+    if (stream == 0)
+        CV_CUDEV_SAFE_CALL( cudaDeviceSynchronize() );
+}
+
+void cv::cuda::polarToCart(InputArray _magAngle, OutputArray _xy, bool angleInDegrees, Stream& _stream)
+{
+    typedef void(*func_t)(const GpuMat& magAngle, GpuMat& xy, bool angleInDegrees, cudaStream_t& stream);
+    static const func_t funcs[7] = { 0, 0, 0, 0, 0, polarToCartInterleavedImpl<float>, polarToCartInterleavedImpl<double> };
+
+    GpuMat magAngle = getInputMat(_magAngle, _stream);
+
+    CV_Assert(magAngle.type() == CV_32FC2 || magAngle.type() == CV_64FC2);
+
+    GpuMat xy = getOutputMat(_xy, magAngle.size(), magAngle.type(), _stream);
+
+    cudaStream_t stream = StreamAccessor::getStream(_stream);
+    funcs[magAngle.depth()](magAngle, xy, angleInDegrees, stream);
+    CV_CUDEV_SAFE_CALL( cudaGetLastError() );
+
+    syncOutput(xy, _xy, _stream);
+
+    if (stream == 0)
+        CV_CUDEV_SAFE_CALL( cudaDeviceSynchronize() );
+}
+
 #endif
diff --git a/modules/cudaarithm/test/test_element_operations.cpp b/modules/cudaarithm/test/test_element_operations.cpp
index d2e314b10d9..a15ad7b3ee5 100644
--- a/modules/cudaarithm/test/test_element_operations.cpp
+++ b/modules/cudaarithm/test/test_element_operations.cpp
@@ -2765,6 +2765,47 @@ INSTANTIATE_TEST_CASE_P(CUDA_Arithm, Phase, testing::Combine(
     testing::Values(AngleInDegrees(false), AngleInDegrees(true)),
     WHOLE_SUBMAT));
 
+PARAM_TEST_CASE(PhaseInterleaved, cv::cuda::DeviceInfo, cv::Size, AngleInDegrees, UseRoi)
+{
+    cv::cuda::DeviceInfo devInfo;
+    cv::Size size;
+    bool angleInDegrees;
+    bool useRoi;
+
+    virtual void SetUp()
+    {
+        devInfo = GET_PARAM(0);
+        size = GET_PARAM(1);
+        angleInDegrees = GET_PARAM(2);
+        useRoi = GET_PARAM(3);
+
+        cv::cuda::setDevice(devInfo.deviceID());
+    }
+};
+
+CUDA_TEST_P(PhaseInterleaved, Accuracy)
+{
+    cv::Mat x = randomMat(size, CV_32FC1);
+    cv::Mat y = randomMat(size, CV_32FC1);
+    cv::Mat xy;
+    std::vector<cv::Mat> xyChannels = {x, y};
+    cv::merge(xyChannels, xy);
+
+    cv::cuda::GpuMat dst = createMat(size, CV_32FC1, useRoi);
+    cv::cuda::phase(loadMat(xy, useRoi), dst, angleInDegrees);
+
+    cv::Mat dst_gold;
+    cv::phase(x, y, dst_gold, angleInDegrees);
+
+    EXPECT_MAT_NEAR(dst_gold, dst, angleInDegrees ? 1e-2 : 1e-3);
+}
+
+INSTANTIATE_TEST_CASE_P(CUDA_Arithm, PhaseInterleaved, testing::Combine(
+    ALL_DEVICES,
+    DIFFERENT_SIZES,
+    testing::Values(AngleInDegrees(false), AngleInDegrees(true)),
+    WHOLE_SUBMAT));
+
 ////////////////////////////////////////////////////////////////////////////////
 // CartToPolar
 
@@ -2809,6 +2850,97 @@ INSTANTIATE_TEST_CASE_P(CUDA_Arithm, CartToPolar, testing::Combine(
     testing::Values(AngleInDegrees(false), AngleInDegrees(true)),
     WHOLE_SUBMAT));
 
+PARAM_TEST_CASE(CartToPolarInterleavedXY, cv::cuda::DeviceInfo, cv::Size, AngleInDegrees, UseRoi)
+{
+    cv::cuda::DeviceInfo devInfo;
+    cv::Size size;
+    bool angleInDegrees;
+    bool useRoi;
+
+    virtual void SetUp()
+    {
+        devInfo = GET_PARAM(0);
+        size = GET_PARAM(1);
+        angleInDegrees = GET_PARAM(2);
+        useRoi = GET_PARAM(3);
+
+        cv::cuda::setDevice(devInfo.deviceID());
+    }
+};
+
+CUDA_TEST_P(CartToPolarInterleavedXY, Accuracy)
+{
+    cv::Mat x = randomMat(size, CV_32FC1);
+    cv::Mat y = randomMat(size, CV_32FC1);
+    cv::Mat xy;
+    std::vector<cv::Mat> xyChannels = {x, y};
+    cv::merge(xyChannels, xy);
+
+    cv::cuda::GpuMat mag = createMat(size, CV_32FC1, useRoi);
+    cv::cuda::GpuMat angle = createMat(size, CV_32FC1, useRoi);
+    cv::cuda::cartToPolar(loadMat(xy, useRoi), mag, angle, angleInDegrees);
+
+    cv::Mat mag_gold;
+    cv::Mat angle_gold;
+    cv::cartToPolar(x, y, mag_gold, angle_gold, angleInDegrees);
+
+    EXPECT_MAT_NEAR(mag_gold, mag, 1e-4);
+    EXPECT_MAT_NEAR(angle_gold, angle, angleInDegrees ? 1e-2 : 1e-3);
+}
+
+INSTANTIATE_TEST_CASE_P(CUDA_Arithm, CartToPolarInterleavedXY, testing::Combine(
+    ALL_DEVICES,
+    DIFFERENT_SIZES,
+    testing::Values(AngleInDegrees(false), AngleInDegrees(true)),
+    WHOLE_SUBMAT));
+
+PARAM_TEST_CASE(CartToPolarInterleavedXYMagAngle, cv::cuda::DeviceInfo, cv::Size, AngleInDegrees, UseRoi)
+{
+    cv::cuda::DeviceInfo devInfo;
+    cv::Size size;
+    bool angleInDegrees;
+    bool useRoi;
+
+    virtual void SetUp()
+    {
+        devInfo = GET_PARAM(0);
+        size = GET_PARAM(1);
+        angleInDegrees = GET_PARAM(2);
+        useRoi = GET_PARAM(3);
+
+        cv::cuda::setDevice(devInfo.deviceID());
+    }
+};
+
+CUDA_TEST_P(CartToPolarInterleavedXYMagAngle, Accuracy)
+{
+    cv::Mat x = randomMat(size, CV_32FC1);
+    cv::Mat y = randomMat(size, CV_32FC1);
+    cv::Mat xy;
+    std::vector<cv::Mat> xyChannels = {x, y};
+    cv::merge(xyChannels, xy);
+
+    cv::cuda::GpuMat magAngle = createMat(size, CV_32FC2, useRoi);
+    cv::cuda::cartToPolar(loadMat(xy, useRoi), magAngle, angleInDegrees);
+    std::vector<cv::cuda::GpuMat> magAngleChannels;
+    cv::cuda::split(magAngle, magAngleChannels);
+    cv::cuda::GpuMat& mag = magAngleChannels[0];
+    cv::cuda::GpuMat& angle = magAngleChannels[1];
+
+    cv::Mat mag_gold;
+    cv::Mat angle_gold;
+    cv::cartToPolar(x, y, mag_gold, angle_gold, angleInDegrees);
+
+    EXPECT_MAT_NEAR(mag_gold, mag, 1e-4);
+    EXPECT_MAT_NEAR(angle_gold, angle, angleInDegrees ? 1e-2 : 1e-3);
+}
+
+INSTANTIATE_TEST_CASE_P(CUDA_Arithm, CartToPolarInterleavedXYMagAngle, testing::Combine(
+    ALL_DEVICES,
+    DIFFERENT_SIZES,
+    testing::Values(AngleInDegrees(false), AngleInDegrees(true)),
+    WHOLE_SUBMAT));
+
 ////////////////////////////////////////////////////////////////////////////////
 // polarToCart
 
@@ -2857,5 +2989,104 @@ INSTANTIATE_TEST_CASE_P(CUDA_Arithm, PolarToCart, testing::Combine(
     testing::Values(AngleInDegrees(false), AngleInDegrees(true)),
     WHOLE_SUBMAT));
 
+PARAM_TEST_CASE(PolarToCartInterleaveXY, cv::cuda::DeviceInfo, cv::Size, MatType, AngleInDegrees, UseRoi)
+{
+    cv::cuda::DeviceInfo devInfo;
+    cv::Size size;
+    int type;
+    bool angleInDegrees;
+    bool useRoi;
+
+    virtual void SetUp()
+    {
+        devInfo = GET_PARAM(0);
+        size = GET_PARAM(1);
+        type = GET_PARAM(2);
+        angleInDegrees = GET_PARAM(3);
+        useRoi = GET_PARAM(4);
+
+        cv::cuda::setDevice(devInfo.deviceID());
+    }
+};
+
+CUDA_TEST_P(PolarToCartInterleaveXY, Accuracy)
+{
+    cv::Mat magnitude = randomMat(size, type);
+    cv::Mat angle = randomMat(size, type);
+    const double tol = (type == CV_32FC1 ? 1.6e-4 : 1e-4) * (angleInDegrees ? 1.0 : 19.47);
+
+    cv::cuda::GpuMat xy = createMat(size, CV_MAKETYPE(CV_MAT_DEPTH(type), 2), useRoi);
+    cv::cuda::polarToCart(loadMat(magnitude, useRoi), loadMat(angle, useRoi), xy, angleInDegrees);
+    std::vector<cv::cuda::GpuMat> xyChannels;
+    cv::cuda::split(xy, xyChannels);
+    cv::cuda::GpuMat& x = xyChannels[0];
+    cv::cuda::GpuMat& y = xyChannels[1];
+
+    cv::Mat x_gold;
+    cv::Mat y_gold;
+    cv::polarToCart(magnitude, angle, x_gold, y_gold, angleInDegrees);
+
+    EXPECT_MAT_NEAR(x_gold, x, tol);
+    EXPECT_MAT_NEAR(y_gold, y, tol);
+}
+
+INSTANTIATE_TEST_CASE_P(CUDA_Arithm, PolarToCartInterleaveXY, testing::Combine(
+    ALL_DEVICES,
+    DIFFERENT_SIZES,
+    testing::Values(CV_32FC1, CV_64FC1),
+    testing::Values(AngleInDegrees(false), AngleInDegrees(true)),
+    WHOLE_SUBMAT));
+
+PARAM_TEST_CASE(PolarToCartInterleaveMagAngleXY, cv::cuda::DeviceInfo, cv::Size, MatType, AngleInDegrees, UseRoi)
+{
+    cv::cuda::DeviceInfo devInfo;
+    cv::Size size;
+    int type;
+    bool angleInDegrees;
+    bool useRoi;
+
+    virtual void SetUp()
+    {
+        devInfo = GET_PARAM(0);
+        size = GET_PARAM(1);
+        type = GET_PARAM(2);
+        angleInDegrees = GET_PARAM(3);
+        useRoi = GET_PARAM(4);
+
+        cv::cuda::setDevice(devInfo.deviceID());
+    }
+};
+
+CUDA_TEST_P(PolarToCartInterleaveMagAngleXY, Accuracy)
+{
+    cv::Mat magnitude = randomMat(size, type);
+    cv::Mat angle = randomMat(size, type);
+    std::vector<cv::Mat> magAngleChannels = {magnitude, angle};
+    cv::Mat magAngle;
+    cv::merge(magAngleChannels, magAngle);
+    const double tol = (type == CV_32FC1 ? 1.6e-4 : 1e-4) * (angleInDegrees ? 1.0 : 19.47);
+
+    cv::cuda::GpuMat xy = createMat(size, CV_MAKETYPE(CV_MAT_DEPTH(type), 2), useRoi);
+    cv::cuda::polarToCart(loadMat(magAngle, useRoi), xy, angleInDegrees);
+    std::vector<cv::cuda::GpuMat> xyChannels;
+    cv::cuda::split(xy, xyChannels);
+    cv::cuda::GpuMat& x = xyChannels[0];
+    cv::cuda::GpuMat& y = xyChannels[1];
+
+    cv::Mat x_gold;
+    cv::Mat y_gold;
+    cv::polarToCart(magnitude, angle, x_gold, y_gold, angleInDegrees);
+
+    EXPECT_MAT_NEAR(x_gold, x, tol);
+    EXPECT_MAT_NEAR(y_gold, y, tol);
+}
+
+INSTANTIATE_TEST_CASE_P(CUDA_Arithm, PolarToCartInterleaveMagAngleXY, testing::Combine(
+    ALL_DEVICES,
+    DIFFERENT_SIZES,
+    testing::Values(CV_32FC1, CV_64FC1),
+    testing::Values(AngleInDegrees(false), AngleInDegrees(true)),
+    WHOLE_SUBMAT));
+
 }} // namespace
 #endif // HAVE_CUDA
diff --git a/modules/cudawarping/include/opencv2/cudawarping.hpp b/modules/cudawarping/include/opencv2/cudawarping.hpp
index 45cca1ccf86..b9ca957358e 100644
--- a/modules/cudawarping/include/opencv2/cudawarping.hpp
+++ b/modules/cudawarping/include/opencv2/cudawarping.hpp
@@ -70,6 +70,8 @@ namespace cv { namespace cuda {
 @param ymap Y values. Only CV_32FC1 type is supported.
 @param interpolation Interpolation method (see resize ). INTER_NEAREST , INTER_LINEAR and
 INTER_CUBIC are supported for now.
+The extra flag WARP_RELATIVE_MAP can be ORed to the interpolation method
+(e.g. INTER_LINEAR | WARP_RELATIVE_MAP)
 @param borderMode Pixel extrapolation method (see borderInterpolate ). BORDER_REFLECT101 ,
 BORDER_REPLICATE , BORDER_CONSTANT , BORDER_REFLECT and BORDER_WRAP are supported for now.
 @param borderValue Value used in case of a constant border. By default, it is 0.
@@ -79,6 +81,10 @@ The function transforms the source image using the specified map:
 
 \f[\texttt{dst} (x,y) =  \texttt{src} (xmap(x,y), ymap(x,y))\f]
 
+with the WARP_RELATIVE_MAP flag :
+
+\f[\texttt{dst} (x,y) =  \texttt{src} (x+map_x(x,y),y+map_y(x,y))\f]
+
 Values of pixels with non-integer coordinates are computed using the bilinear interpolation.
 
 @sa remap
diff --git a/modules/cudawarping/src/cuda/remap.cu b/modules/cudawarping/src/cuda/remap.cu
index 38edf19ae24..8f698a2ffb4 100644
--- a/modules/cudawarping/src/cuda/remap.cu
+++ b/modules/cudawarping/src/cuda/remap.cu
@@ -68,9 +68,23 @@ namespace cv { namespace cuda { namespace device
             }
         }
 
+        template <typename Ptr2D, typename T> __global__ void remap_relative(const Ptr2D src, const PtrStepf mapx, const PtrStepf mapy, PtrStepSz<T> dst)
+        {
+            const int x = blockDim.x * blockIdx.x + threadIdx.x;
+            const int y = blockDim.y * blockIdx.y + threadIdx.y;
+
+            if (x < dst.cols && y < dst.rows)
+            {
+                const float xcoo = x+mapx.ptr(y)[x];
+                const float ycoo = y+mapy.ptr(y)[x];
+
+                dst.ptr(y)[x] = saturate_cast<T>(src(ycoo, xcoo));
+            }
+        }
+
         template <template <typename> class Filter, template <typename> class B, typename T> struct RemapDispatcherStream
         {
-            static void call(PtrStepSz<T> src, PtrStepSzf mapx, PtrStepSzf mapy, PtrStepSz<T> dst, const float* borderValue, cudaStream_t stream, bool)
+            static void call(PtrStepSz<T> src, PtrStepSzf mapx, PtrStepSzf mapy, PtrStepSz<T> dst, const float* borderValue, cudaStream_t stream, bool, bool isRelative)
             {
                 typedef typename TypeVec<float, VecTraits<T>::cn>::vec_type work_type;
 
@@ -81,14 +95,17 @@ namespace cv { namespace cuda { namespace device
                 BorderReader<PtrStep<T>, B<work_type>> brdSrc(src, brd);
                 Filter<BorderReader<PtrStep<T>, B<work_type>>> filter_src(brdSrc);
 
-                remap<<<grid, block, 0, stream>>>(filter_src, mapx, mapy, dst);
+                if (isRelative)
+                  remap_relative<<<grid, block, 0, stream>>>(filter_src, mapx, mapy, dst);
+                else
+                  remap<<<grid, block, 0, stream>>>(filter_src, mapx, mapy, dst);
                 cudaSafeCall( cudaGetLastError() );
             }
         };
 
         template <template <typename> class Filter, template <typename> class B, typename T> struct RemapDispatcherNonStream
         {
-            static void call(PtrStepSz<T> src, PtrStepSz<T> srcWhole, int xoff, int yoff, PtrStepSzf mapx, PtrStepSzf mapy, PtrStepSz<T> dst, const float* borderValue, bool)
+            static void call(PtrStepSz<T> src, PtrStepSz<T> srcWhole, int xoff, int yoff, PtrStepSzf mapx, PtrStepSzf mapy, PtrStepSz<T> dst, const float* borderValue, bool, bool isRelative)
             {
                 CV_UNUSED(srcWhole);
                 CV_UNUSED(xoff);
@@ -102,7 +119,10 @@ namespace cv { namespace cuda { namespace device
                 BorderReader<PtrStep<T>, B<work_type>> brdSrc(src, brd);
                 Filter<BorderReader<PtrStep<T>, B<work_type>>> filter_src(brdSrc);
 
-                remap<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                if (isRelative)
+                  remap_relative<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                else
+                  remap<<<grid, block>>>(filter_src, mapx, mapy, dst);
                 cudaSafeCall( cudaGetLastError() );
 
                 cudaSafeCall( cudaDeviceSynchronize() );
@@ -112,7 +132,7 @@ namespace cv { namespace cuda { namespace device
         template <template <typename> class Filter, template <typename> class B, typename T> struct RemapDispatcherNonStreamTex
         {
             static void call(PtrStepSz< T > src, PtrStepSz< T > srcWhole, int xoff, int yoff, PtrStepSzf mapx, PtrStepSzf mapy,
-                PtrStepSz< T > dst, const float* borderValue, bool cc20)
+                PtrStepSz< T > dst, const float* borderValue, bool cc20, bool isRelative)
             {
                 typedef typename TypeVec<float, VecTraits< T >::cn>::vec_type work_type;
                 dim3 block(32, cc20 ? 8 : 4);
@@ -123,7 +143,10 @@ namespace cv { namespace cuda { namespace device
                     B<work_type> brd(src.rows, src.cols, VecTraits<work_type>::make(borderValue));
                     BorderReader<cudev::TexturePtr<T>, B<work_type>> brdSrc(texSrcWhole, brd);
                     Filter<BorderReader<cudev::TexturePtr<T>, B<work_type>>> filter_src(brdSrc);
-                    remap<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                    if (isRelative)
+                        remap_relative<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                    else
+                        remap<<<grid, block>>>(filter_src, mapx, mapy, dst);
 
                 }
                 else {
@@ -131,7 +154,10 @@ namespace cv { namespace cuda { namespace device
                     B<work_type> brd(src.rows, src.cols, VecTraits<work_type>::make(borderValue));
                     BorderReader<cudev::TextureOffPtr<T>, B<work_type>> brdSrc(texSrcWhole, brd);
                     Filter<BorderReader<cudev::TextureOffPtr<T>, B<work_type>>> filter_src(brdSrc);
-                    remap<<<grid, block >>>(filter_src, mapx, mapy, dst);
+                    if (isRelative)
+                        remap_relative<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                    else
+                        remap<<<grid, block >>>(filter_src, mapx, mapy, dst);
                 }
 
                 cudaSafeCall( cudaGetLastError() );
@@ -142,7 +168,7 @@ namespace cv { namespace cuda { namespace device
         template <template <typename> class Filter, typename T> struct RemapDispatcherNonStreamTex<Filter, BrdReplicate, T>
         {
             static void call(PtrStepSz< T > src, PtrStepSz< T > srcWhole, int xoff, int yoff, PtrStepSzf mapx, PtrStepSzf mapy,
-                PtrStepSz< T > dst, const float*, bool)
+                PtrStepSz< T > dst, const float*, bool, bool isRelative)
             {
                 dim3 block(32, 8);
                 dim3 grid(divUp(dst.cols, block.x), divUp(dst.rows, block.y));
@@ -150,7 +176,10 @@ namespace cv { namespace cuda { namespace device
                 {
                     cudev::Texture<T> texSrcWhole(srcWhole);
                     Filter<cudev::TexturePtr<T>> filter_src(texSrcWhole);
-                    remap<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                    if (isRelative)
+                        remap_relative<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                    else
+                        remap<<<grid, block>>>(filter_src, mapx, mapy, dst);
                 }
                 else
                 {
@@ -158,7 +187,10 @@ namespace cv { namespace cuda { namespace device
                     BrdReplicate<T> brd(src.rows, src.cols);
                     BorderReader<cudev::TextureOffPtr<T>, BrdReplicate<T>> brdSrc(texSrcWhole, brd);
                     Filter<BorderReader<cudev::TextureOffPtr<T>, BrdReplicate<T>>> filter_src(brdSrc);
-                    remap<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                    if (isRelative)
+                        remap_relative<<<grid, block>>>(filter_src, mapx, mapy, dst);
+                    else
+                        remap<<<grid, block>>>(filter_src, mapx, mapy, dst);
                 }
                 cudaSafeCall( cudaGetLastError() );
                 cudaSafeCall( cudaDeviceSynchronize() );
@@ -203,20 +235,20 @@ namespace cv { namespace cuda { namespace device
         template <template <typename> class Filter, template <typename> class B, typename T> struct RemapDispatcher
         {
             static void call(PtrStepSz<T> src, PtrStepSz<T> srcWhole, int xoff, int yoff, PtrStepSzf mapx, PtrStepSzf mapy,
-                PtrStepSz<T> dst, const float* borderValue, cudaStream_t stream, bool cc20)
+                PtrStepSz<T> dst, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative)
             {
                 if (stream == 0)
-                    RemapDispatcherNonStream<Filter, B, T>::call(src, srcWhole, xoff, yoff, mapx, mapy, dst, borderValue, cc20);
+                    RemapDispatcherNonStream<Filter, B, T>::call(src, srcWhole, xoff, yoff, mapx, mapy, dst, borderValue, cc20, isRelative);
                 else
-                    RemapDispatcherStream<Filter, B, T>::call(src, mapx, mapy, dst, borderValue, stream, cc20);
+                    RemapDispatcherStream<Filter, B, T>::call(src, mapx, mapy, dst, borderValue, stream, cc20, isRelative);
             }
         };
 
         template <typename T> void remap_gpu(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap,
-            PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20)
+            PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative)
         {
             typedef void (*caller_t)(PtrStepSz<T> src, PtrStepSz<T> srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap,
-                PtrStepSz<T> dst, const float* borderValue, cudaStream_t stream, bool cc20);
+                PtrStepSz<T> dst, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
 
             static const caller_t callers[3][5] =
             {
@@ -244,24 +276,24 @@ namespace cv { namespace cuda { namespace device
             };
 
             callers[interpolation][borderMode](static_cast<PtrStepSz<T>>(src), static_cast<PtrStepSz<T>>(srcWhole), xoff, yoff, xmap, ymap,
-                static_cast<PtrStepSz<T>>(dst), borderValue, stream, cc20);
+                static_cast<PtrStepSz<T>>(dst), borderValue, stream, cc20, isRelative);
         }
 
-        template void remap_gpu<uchar >(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
-        template void remap_gpu<uchar3>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
-        template void remap_gpu<uchar4>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
+        template void remap_gpu<uchar >(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
+        template void remap_gpu<uchar3>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
+        template void remap_gpu<uchar4>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
 
-        template void remap_gpu<ushort >(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
-        template void remap_gpu<ushort3>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
-        template void remap_gpu<ushort4>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
+        template void remap_gpu<ushort >(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
+        template void remap_gpu<ushort3>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
+        template void remap_gpu<ushort4>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
 
-        template void remap_gpu<short >(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
-        template void remap_gpu<short3>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
-        template void remap_gpu<short4>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
+        template void remap_gpu<short >(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
+        template void remap_gpu<short3>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
+        template void remap_gpu<short4>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
 
-        template void remap_gpu<float >(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
-        template void remap_gpu<float3>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
-        template void remap_gpu<float4>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
+        template void remap_gpu<float >(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
+        template void remap_gpu<float3>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
+        template void remap_gpu<float4>(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
     } // namespace imgproc
 }}} // namespace cv { namespace cuda { namespace cudev
 
diff --git a/modules/cudawarping/src/remap.cpp b/modules/cudawarping/src/remap.cpp
index c1351daf2d4..db276d5e8bf 100644
--- a/modules/cudawarping/src/remap.cpp
+++ b/modules/cudawarping/src/remap.cpp
@@ -54,7 +54,7 @@ namespace cv { namespace cuda { namespace device
     {
         template <typename T>
         void remap_gpu(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst,
-                       int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
+                       int interpolation, int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
     }
 }}}
 
@@ -62,8 +62,11 @@ void cv::cuda::remap(InputArray _src, OutputArray _dst, InputArray _xmap, InputA
 {
     using namespace cv::cuda::device::imgproc;
 
+    const bool hasRelativeFlag = ((interpolation & WARP_RELATIVE_MAP) != 0);
+    interpolation &= ~WARP_RELATIVE_MAP;
+
     typedef void (*func_t)(PtrStepSzb src, PtrStepSzb srcWhole, int xoff, int yoff, PtrStepSzf xmap, PtrStepSzf ymap, PtrStepSzb dst, int interpolation,
-        int borderMode, const float* borderValue, cudaStream_t stream, bool cc20);
+        int borderMode, const float* borderValue, cudaStream_t stream, bool cc20, bool isRelative);
     static const func_t funcs[6][4] =
     {
         {remap_gpu<uchar>      , 0 /*remap_gpu<uchar2>*/ , remap_gpu<uchar3>     , remap_gpu<uchar4>     },
@@ -98,7 +101,7 @@ void cv::cuda::remap(InputArray _src, OutputArray _dst, InputArray _xmap, InputA
     src.locateROI(wholeSize, ofs);
 
     func(src, PtrStepSzb(wholeSize.height, wholeSize.width, src.datastart, src.step), ofs.x, ofs.y, xmap, ymap,
-        dst, interpolation, borderMode, borderValueFloat.val, StreamAccessor::getStream(stream), deviceSupports(FEATURE_SET_COMPUTE_20));
+        dst, interpolation, borderMode, borderValueFloat.val, StreamAccessor::getStream(stream), deviceSupports(FEATURE_SET_COMPUTE_20), hasRelativeFlag);
 }
 
 #endif // HAVE_CUDA
diff --git a/modules/cudawarping/test/test_remap.cpp b/modules/cudawarping/test/test_remap.cpp
index b751072bbec..d56c871243c 100644
--- a/modules/cudawarping/test/test_remap.cpp
+++ b/modules/cudawarping/test/test_remap.cpp
@@ -204,5 +204,82 @@ INSTANTIATE_TEST_CASE_P(CUDA_Warping, RemapOutOfScope, testing::Combine(
         testing::Values(BorderType(cv::BORDER_CONSTANT)),
         WHOLE_SUBMAT));
 
+PARAM_TEST_CASE(RemapRelative, cv::cuda::DeviceInfo, MatType, Interpolation, BorderType)
+{
+    cv::cuda::DeviceInfo devInfo;
+    int type;
+    int interpolation;
+    int borderType;
+
+    cv::cuda::GpuMat gSrc;
+    cv::cuda::GpuMat gMapRelativeX32F;
+    cv::cuda::GpuMat gMapRelativeY32F;
+    cv::cuda::GpuMat gMapAbsoluteX32F;
+    cv::cuda::GpuMat gMapAbsoluteY32F;
+
+    virtual void SetUp()
+    {
+        devInfo = GET_PARAM(0);
+        type = GET_PARAM(1);
+        interpolation = GET_PARAM(2);
+        borderType = GET_PARAM(3);
+
+        cv::cuda::setDevice(devInfo.deviceID());
+
+        const int nChannels = CV_MAT_CN(type);
+        const cv::Size size(127, 61);
+        cv::Mat data64FC1(1, size.area()*nChannels, CV_64FC1);
+        data64FC1.forEach<double>([&](double& pixel, const int* position) {pixel = static_cast<double>(position[1]);});
+
+        cv::Mat src;
+        data64FC1.reshape(nChannels, size.height).convertTo(src, type);
+
+        cv::Mat mapRelativeX32F(size, CV_32FC1);
+        mapRelativeX32F.setTo(cv::Scalar::all(-0.33));
+
+        cv::Mat mapRelativeY32F(size, CV_32FC1);
+        mapRelativeY32F.setTo(cv::Scalar::all(-0.33));
+
+        cv::Mat mapAbsoluteX32F = mapRelativeX32F.clone();
+        mapAbsoluteX32F.forEach<float>([&](float& pixel, const int* position) {
+            pixel += static_cast<float>(position[1]);
+        });
+
+        cv::Mat mapAbsoluteY32F = mapRelativeY32F.clone();
+        mapAbsoluteY32F.forEach<float>([&](float& pixel, const int* position) {
+            pixel += static_cast<float>(position[0]);
+        });
+
+        gSrc.upload(src);
+        gMapRelativeX32F.upload(mapRelativeX32F);
+        gMapRelativeY32F.upload(mapRelativeY32F);
+        gMapAbsoluteX32F.upload(mapAbsoluteX32F);
+        gMapAbsoluteY32F.upload(mapAbsoluteY32F);
+    }
+};
+CUDA_TEST_P(RemapRelative, RemapRelative_Validity)
+{
+    cv::cuda::GpuMat gDstAbsolute;
+    cv::cuda::remap(gSrc, gDstAbsolute, gMapAbsoluteX32F, gMapAbsoluteY32F, interpolation, borderType);
+    cv::cuda::GpuMat gDstRelative;
+    cv::cuda::remap(gSrc, gDstRelative, gMapRelativeX32F, gMapRelativeY32F, interpolation | WARP_RELATIVE_MAP, borderType);
+
+    cv::Mat dstAbsolute;
+    gDstAbsolute.download(dstAbsolute);
+    cv::Mat dstRelative;
+    gDstRelative.download(dstRelative);
+
+    EXPECT_MAT_NEAR(dstAbsolute, dstRelative, (dstAbsolute.depth() == CV_32F) ? 1e-3 : 1.0);
+}
+
+INSTANTIATE_TEST_CASE_P(CUDA_RemapRelative, RemapRelative, testing::Combine(
+        ALL_DEVICES,
+        testing::Values(MatType(CV_8UC1), MatType(CV_8UC3), MatType(CV_8UC4),
+                        MatType(CV_16UC1), MatType(CV_16UC3), MatType(CV_16UC4),
+                        MatType(CV_16SC1), MatType(CV_16SC3), MatType(CV_16SC4),
+                        MatType(CV_32FC1), MatType(CV_32FC3), MatType(CV_32FC4)),
+        testing::Values(Interpolation(cv::INTER_NEAREST), Interpolation(cv::INTER_LINEAR), Interpolation(cv::INTER_CUBIC)),
+        testing::Values(BorderType(cv::BORDER_REFLECT101), BorderType(cv::BORDER_REPLICATE), BorderType(cv::BORDER_CONSTANT))));
+
 }} // namespace
 #endif // HAVE_CUDA
diff --git a/modules/cudev/include/opencv2/cudev/functional/functional.hpp b/modules/cudev/include/opencv2/cudev/functional/functional.hpp
index e4165358c28..ddf2cf809e3 100644
--- a/modules/cudev/include/opencv2/cudev/functional/functional.hpp
+++ b/modules/cudev/include/opencv2/cudev/functional/functional.hpp
@@ -619,6 +619,17 @@ template <typename T> struct magnitude_func : binary_function<T, T, typename fun
     }
 };
 
+template <typename T2> struct magnitude_interleaved_func : unary_function<T2, typename VecTraits<T2>::elem_type>
+{
+    typedef typename VecTraits<T2>::elem_type T;
+    typedef typename TypeTraits<T2>::parameter_type parameter_type;
+    __device__ __forceinline__ T operator ()(parameter_type ab) const
+    {
+        sqrt_func<typename functional_detail::FloatType<T>::type> f;
+        return f(ab.x * ab.x + ab.y * ab.y);
+    }
+};
+
 template <typename T> struct magnitude_sqr_func : binary_function<T, T, typename functional_detail::FloatType<T>::type>
 {
     __device__ __forceinline__ typename functional_detail::FloatType<T>::type operator ()(typename TypeTraits<T>::parameter_type a, typename TypeTraits<T>::parameter_type b) const
@@ -627,6 +638,16 @@ template <typename T> struct magnitude_sqr_func : binary_function<T, T, typename
     }
 };
 
+template <typename T2> struct magnitude_sqr_interleaved_func : unary_function<T2, typename VecTraits<T2>::elem_type>
+{
+    typedef typename VecTraits<T2>::elem_type T;
+    typedef typename TypeTraits<T2>::parameter_type parameter_type;
+    __device__ __forceinline__ T operator ()(parameter_type ab) const
+    {
+        return ab.x * ab.x + ab.y * ab.y;
+    }
+};
+
 template <typename T, bool angleInDegrees> struct direction_func : binary_function<T, T, T>
 {
     __device__ T operator ()(T x, T y) const
@@ -643,6 +664,35 @@ template <typename T, bool angleInDegrees> struct direction_func : binary_functi
     }
 };
 
+template <typename T2, bool angleInDegrees> struct direction_interleaved_func : unary_function<T2, typename VecTraits<T2>::elem_type>
+{
+    typedef typename VecTraits<T2>::elem_type T;
+    __device__ T operator ()(T2 xy) const
+    {
+        atan2_func<T> f;
+        typename atan2_func<T>::result_type angle = f(xy.y, xy.x);
+
+        angle += (angle < 0) * (2.0f * CV_PI_F);
+
+        if (angleInDegrees)
+            angle *= (180.0f / CV_PI_F);
+
+        return saturate_cast<T>(angle);
+    }
+};
+
+template <typename T2, bool angleInDegrees> struct magnitude_direction_interleaved_func : unary_function<T2, typename VecTraits<T2>::elem_type>
+{
+    typedef typename VecTraits<T2>::elem_type T;
+    __device__ T2 operator ()(T2 xy) const
+    {
+        const T mag = magnitude_interleaved_func<T2>()(xy);
+        const T angle = direction_interleaved_func<T2, angleInDegrees>()(xy);
+        const T2 magAngle = {saturate_cast<T>(mag), saturate_cast<T>(angle)};
+        return magAngle;
+    }
+};
+
 template <typename T> struct pow_func : binary_function<T, float, float>
 {
     __device__ __forceinline__ float operator ()(T val, float power) const