diff --git a/modules/core/include/opencv2/core/mat.hpp b/modules/core/include/opencv2/core/mat.hpp
index 84df297bf9..eeb83c0744 100644
--- a/modules/core/include/opencv2/core/mat.hpp
+++ b/modules/core/include/opencv2/core/mat.hpp
@@ -2011,6 +2011,11 @@ public:
     template<typename _Tp> MatIterator_<_Tp> begin();
     template<typename _Tp> MatConstIterator_<_Tp> begin() const;
 
+    /** @brief Same as begin() but for inverse traversal
+     */
+    template<typename _Tp> std::reverse_iterator<MatIterator_<_Tp>> rbegin();
+    template<typename _Tp> std::reverse_iterator<MatConstIterator_<_Tp>> rbegin() const;
+
     /** @brief Returns the matrix iterator and sets it to the after-last matrix element.
 
     The methods return the matrix read-only or read-write iterators, set to the point following the last
@@ -2019,6 +2024,12 @@ public:
     template<typename _Tp> MatIterator_<_Tp> end();
     template<typename _Tp> MatConstIterator_<_Tp> end() const;
 
+    /** @brief Same as end() but for inverse traversal
+     */
+    template<typename _Tp> std::reverse_iterator< MatIterator_<_Tp>> rend();
+    template<typename _Tp> std::reverse_iterator< MatConstIterator_<_Tp>> rend() const;
+
+
     /** @brief Runs the given functor over all matrix elements in parallel.
 
     The operation passed as argument has to be a function pointer, a function object or a lambda(C++11).
@@ -2250,6 +2261,12 @@ public:
     const_iterator begin() const;
     const_iterator end() const;
 
+    //reverse iterators
+    std::reverse_iterator<iterator> rbegin();
+    std::reverse_iterator<iterator> rend();
+    std::reverse_iterator<const_iterator> rbegin() const;
+    std::reverse_iterator<const_iterator> rend() const;
+
     //! template methods for for operation over all matrix elements.
     // the operations take care of skipping gaps in the end of rows (if any)
     template<typename Functor> void forEach(const Functor& operation);
diff --git a/modules/core/include/opencv2/core/mat.inl.hpp b/modules/core/include/opencv2/core/mat.inl.hpp
index f07c820f33..886b82c6a0 100644
--- a/modules/core/include/opencv2/core/mat.inl.hpp
+++ b/modules/core/include/opencv2/core/mat.inl.hpp
@@ -1015,6 +1015,17 @@ MatConstIterator_<_Tp> Mat::begin() const
     return MatConstIterator_<_Tp>((const Mat_<_Tp>*)this);
 }
 
+template<typename _Tp> inline
+std::reverse_iterator<MatConstIterator_<_Tp>> Mat::rbegin() const
+{
+    if (empty())
+        return std::reverse_iterator<MatConstIterator_<_Tp>>();
+    CV_DbgAssert( elemSize() == sizeof(_Tp) );
+    MatConstIterator_<_Tp> it((const Mat_<_Tp>*)this);
+    it += total();
+    return std::reverse_iterator<MatConstIterator_<_Tp>> (it);
+}
+
 template<typename _Tp> inline
 MatConstIterator_<_Tp> Mat::end() const
 {
@@ -1026,6 +1037,15 @@ MatConstIterator_<_Tp> Mat::end() const
     return it;
 }
 
+template<typename _Tp> inline
+std::reverse_iterator<MatConstIterator_<_Tp>> Mat::rend() const
+{
+    if (empty())
+        return std::reverse_iterator<MatConstIterator_<_Tp>>();
+    CV_DbgAssert( elemSize() == sizeof(_Tp) );
+    return std::reverse_iterator<MatConstIterator_<_Tp>>((const Mat_<_Tp>*)this);
+}
+
 template<typename _Tp> inline
 MatIterator_<_Tp> Mat::begin()
 {
@@ -1035,6 +1055,17 @@ MatIterator_<_Tp> Mat::begin()
     return MatIterator_<_Tp>((Mat_<_Tp>*)this);
 }
 
+template<typename _Tp> inline
+std::reverse_iterator<MatIterator_<_Tp>> Mat::rbegin()
+{
+    if (empty())
+        return std::reverse_iterator<MatIterator_<_Tp>>();
+    CV_DbgAssert( elemSize() == sizeof(_Tp) );
+    MatIterator_<_Tp> it((Mat_<_Tp>*)this);
+    it += total();
+    return std::reverse_iterator<MatIterator_<_Tp>>(it);
+}
+
 template<typename _Tp> inline
 MatIterator_<_Tp> Mat::end()
 {
@@ -1046,6 +1077,15 @@ MatIterator_<_Tp> Mat::end()
     return it;
 }
 
+template<typename _Tp> inline
+std::reverse_iterator<MatIterator_<_Tp>> Mat::rend()
+{
+    if (empty())
+        return std::reverse_iterator<MatIterator_<_Tp>>();
+    CV_DbgAssert( elemSize() == sizeof(_Tp) );
+    return std::reverse_iterator<MatIterator_<_Tp>>(MatIterator_<_Tp>((Mat_<_Tp>*)this));
+}
+
 template<typename _Tp, typename Functor> inline
 void Mat::forEach(const Functor& operation) {
     this->forEach_impl<_Tp>(operation);
@@ -1713,24 +1753,48 @@ MatConstIterator_<_Tp> Mat_<_Tp>::begin() const
     return Mat::begin<_Tp>();
 }
 
+template<typename _Tp> inline
+std::reverse_iterator<MatConstIterator_<_Tp>> Mat_<_Tp>::rbegin() const
+{
+    return Mat::rbegin<_Tp>();
+}
+
 template<typename _Tp> inline
 MatConstIterator_<_Tp> Mat_<_Tp>::end() const
 {
     return Mat::end<_Tp>();
 }
 
+template<typename _Tp> inline
+std::reverse_iterator<MatConstIterator_<_Tp>> Mat_<_Tp>::rend() const
+{
+    return Mat::rend<_Tp>();
+}
+
 template<typename _Tp> inline
 MatIterator_<_Tp> Mat_<_Tp>::begin()
 {
     return Mat::begin<_Tp>();
 }
 
+template<typename _Tp> inline
+std::reverse_iterator<MatIterator_<_Tp>> Mat_<_Tp>::rbegin()
+{
+    return Mat::rbegin<_Tp>();
+}
+
 template<typename _Tp> inline
 MatIterator_<_Tp> Mat_<_Tp>::end()
 {
     return Mat::end<_Tp>();
 }
 
+template<typename _Tp> inline
+std::reverse_iterator<MatIterator_<_Tp>> Mat_<_Tp>::rend()
+{
+    return Mat::rend<_Tp>();
+}
+
 template<typename _Tp> template<typename Functor> inline
 void Mat_<_Tp>::forEach(const Functor& operation) {
     Mat::forEach<_Tp, Functor>(operation);
diff --git a/modules/core/test/test_mat.cpp b/modules/core/test/test_mat.cpp
index 9686f77ebc..a5d844e7ad 100644
--- a/modules/core/test/test_mat.cpp
+++ b/modules/core/test/test_mat.cpp
@@ -2371,4 +2371,82 @@ TEST(Mat, ptrVecni_20044)
     EXPECT_EQ(int(6), *(ci));
 }
 
+TEST(Mat, reverse_iterator_19967)
+{
+    // empty iterator (#16855)
+    cv::Mat m_empty;
+    EXPECT_NO_THROW(m_empty.rbegin<uchar>());
+    EXPECT_NO_THROW(m_empty.rend<uchar>());
+    EXPECT_TRUE(m_empty.rbegin<uchar>() == m_empty.rend<uchar>());
+
+    // 1D test
+    std::vector<uchar> data{0, 1, 2, 3};
+    const std::vector<int> sizes_1d{4};
+
+    //Base class
+    cv::Mat m_1d(sizes_1d, CV_8U, data.data());
+    auto mismatch_it_pair_1d = std::mismatch(data.rbegin(), data.rend(), m_1d.rbegin<uchar>());
+    EXPECT_EQ(mismatch_it_pair_1d.first, data.rend());  // expect no mismatch
+    EXPECT_EQ(mismatch_it_pair_1d.second, m_1d.rend<uchar>());
+
+    //Templated derived class
+    cv::Mat_<uchar> m_1d_t(static_cast<int>(sizes_1d.size()), sizes_1d.data(), data.data());
+    auto mismatch_it_pair_1d_t = std::mismatch(data.rbegin(), data.rend(), m_1d_t.rbegin());
+    EXPECT_EQ(mismatch_it_pair_1d_t.first, data.rend());  // expect no mismatch
+    EXPECT_EQ(mismatch_it_pair_1d_t.second, m_1d_t.rend());
+
+
+    // 2D test
+    const std::vector<int> sizes_2d{2, 2};
+
+    //Base class
+    cv::Mat m_2d(sizes_2d, CV_8U, data.data());
+    auto mismatch_it_pair_2d = std::mismatch(data.rbegin(), data.rend(), m_2d.rbegin<uchar>());
+    EXPECT_EQ(mismatch_it_pair_2d.first, data.rend());
+    EXPECT_EQ(mismatch_it_pair_2d.second, m_2d.rend<uchar>());
+
+    //Templated derived class
+    cv::Mat_<uchar> m_2d_t(static_cast<int>(sizes_2d.size()),sizes_2d.data(), data.data());
+    auto mismatch_it_pair_2d_t = std::mismatch(data.rbegin(), data.rend(), m_2d_t.rbegin());
+    EXPECT_EQ(mismatch_it_pair_2d_t.first, data.rend());
+    EXPECT_EQ(mismatch_it_pair_2d_t.second, m_2d_t.rend());
+
+    // 3D test
+    std::vector<uchar> data_3d{0, 1, 2, 3, 4, 5, 6, 7};
+    const std::vector<int> sizes_3d{2, 2, 2};
+
+    //Base class
+    cv::Mat m_3d(sizes_3d, CV_8U, data_3d.data());
+    auto mismatch_it_pair_3d = std::mismatch(data_3d.rbegin(), data_3d.rend(), m_3d.rbegin<uchar>());
+    EXPECT_EQ(mismatch_it_pair_3d.first, data_3d.rend());
+    EXPECT_EQ(mismatch_it_pair_3d.second, m_3d.rend<uchar>());
+
+    //Templated derived class
+    cv::Mat_<uchar> m_3d_t(static_cast<int>(sizes_3d.size()),sizes_3d.data(), data_3d.data());
+    auto mismatch_it_pair_3d_t = std::mismatch(data_3d.rbegin(), data_3d.rend(), m_3d_t.rbegin());
+    EXPECT_EQ(mismatch_it_pair_3d_t.first, data_3d.rend());
+    EXPECT_EQ(mismatch_it_pair_3d_t.second, m_3d_t.rend());
+
+    // const test base class
+    const cv::Mat m_1d_const(sizes_1d, CV_8U, data.data());
+
+    auto mismatch_it_pair_1d_const = std::mismatch(data.rbegin(), data.rend(), m_1d_const.rbegin<uchar>());
+    EXPECT_EQ(mismatch_it_pair_1d_const.first, data.rend());  // expect no mismatch
+    EXPECT_EQ(mismatch_it_pair_1d_const.second, m_1d_const.rend<uchar>());
+
+    EXPECT_FALSE((std::is_assignable<decltype(m_1d_const.rend<uchar>()), uchar>::value)) << "Constness of const iterator violated.";
+    EXPECT_FALSE((std::is_assignable<decltype(m_1d_const.rbegin<uchar>()), uchar>::value)) << "Constness of const iterator violated.";
+
+    // const test templated dervied class
+    const cv::Mat_<uchar> m_1d_const_t(static_cast<int>(sizes_1d.size()), sizes_1d.data(), data.data());
+
+    auto mismatch_it_pair_1d_const_t = std::mismatch(data.rbegin(), data.rend(), m_1d_const_t.rbegin());
+    EXPECT_EQ(mismatch_it_pair_1d_const_t.first, data.rend());  // expect no mismatch
+    EXPECT_EQ(mismatch_it_pair_1d_const_t.second, m_1d_const_t.rend());
+
+    EXPECT_FALSE((std::is_assignable<decltype(m_1d_const_t.rend()), uchar>::value)) << "Constness of const iterator violated.";
+    EXPECT_FALSE((std::is_assignable<decltype(m_1d_const_t.rbegin()), uchar>::value)) << "Constness of const iterator violated.";
+
+}
+
 }} // namespace