diff --git a/modules/core/include/opencv2/core/types.hpp b/modules/core/include/opencv2/core/types.hpp
index 0b1d948156..82dedcb850 100644
--- a/modules/core/include/opencv2/core/types.hpp
+++ b/modules/core/include/opencv2/core/types.hpp
@@ -1895,13 +1895,33 @@ Rect_<_Tp>& operator -= ( Rect_<_Tp>& a, const Size_<_Tp>& b )
 template<typename _Tp> static inline
 Rect_<_Tp>& operator &= ( Rect_<_Tp>& a, const Rect_<_Tp>& b )
 {
-    _Tp x1 = std::max(a.x, b.x);
-    _Tp y1 = std::max(a.y, b.y);
-    a.width = std::min(a.x + a.width, b.x + b.width) - x1;
-    a.height = std::min(a.y + a.height, b.y + b.height) - y1;
-    a.x = x1;
-    a.y = y1;
-    if( a.width <= 0 || a.height <= 0 )
+    if (a.empty() || b.empty()) {
+        a = Rect();
+        return a;
+    }
+    const Rect_<_Tp>& Rx_min = (a.x < b.x) ? a : b;
+    const Rect_<_Tp>& Rx_max = (a.x < b.x) ? b : a;
+    const Rect_<_Tp>& Ry_min = (a.y < b.y) ? a : b;
+    const Rect_<_Tp>& Ry_max = (a.y < b.y) ? b : a;
+    // Looking at the formula below, we will compute Rx_min.width - (Rx_max.x - Rx_min.x)
+    // but we want to avoid overflows. Rx_min.width >= 0 and (Rx_max.x - Rx_min.x) >= 0
+    // by definition so the difference does not overflow. The only thing that can overflow
+    // is (Rx_max.x - Rx_min.x). And it can only overflow if Rx_min.x < 0.
+    // Let us first deal with the following case.
+    if ((Rx_min.x < 0 && Rx_min.x + Rx_min.width < Rx_max.x) ||
+        (Ry_min.y < 0 && Ry_min.y + Ry_min.height < Ry_max.y)) {
+        a = Rect();
+        return a;
+    }
+    // We now know that either Rx_min.x >= 0, or
+    // Rx_min.x < 0 && Rx_min.x + Rx_min.width >= Rx_max.x and therefore
+    // Rx_min.width >= (Rx_max.x - Rx_min.x) which means (Rx_max.x - Rx_min.x)
+    // is inferior to a valid int and therefore does not overflow.
+    a.width = std::min(Rx_min.width - (Rx_max.x - Rx_min.x), Rx_max.width);
+    a.height = std::min(Ry_min.height - (Ry_max.y - Ry_min.y), Ry_max.height);
+    a.x = Rx_max.x;
+    a.y = Ry_max.y;
+    if (a.empty())
         a = Rect();
     return a;
 }
diff --git a/modules/core/test/test_misc.cpp b/modules/core/test/test_misc.cpp
index 372aab7eb0..d9e9119230 100644
--- a/modules/core/test/test_misc.cpp
+++ b/modules/core/test/test_misc.cpp
@@ -784,4 +784,36 @@ TEST(Core_Check, testSize_1)
 }
 
 
+template <typename T> class Rect_Test : public testing::Test {};
+
+TYPED_TEST_CASE_P(Rect_Test);
+
+// Reimplement C++11 std::numeric_limits<>::lowest.
+template<typename T> T cv_numeric_limits_lowest();
+template<> int cv_numeric_limits_lowest<int>() { return INT_MIN; }
+template<> float cv_numeric_limits_lowest<float>() { return -FLT_MAX; }
+template<> double cv_numeric_limits_lowest<double>() { return -DBL_MAX; }
+
+TYPED_TEST_P(Rect_Test, Overflows) {
+  typedef Rect_<TypeParam> R;
+  TypeParam num_max = std::numeric_limits<TypeParam>::max();
+  TypeParam num_lowest = cv_numeric_limits_lowest<TypeParam>();
+  EXPECT_EQ(R(0, 0, 10, 10), R(0, 0, 10, 10) & R(0, 0, 10, 10));
+  EXPECT_EQ(R(5, 6, 4, 3), R(0, 0, 10, 10) & R(5, 6, 4, 3));
+  EXPECT_EQ(R(5, 6, 3, 2), R(0, 0, 8, 8) & R(5, 6, 4, 3));
+  // Test with overflowing dimenions.
+  EXPECT_EQ(R(5, 0, 5, 10), R(0, 0, 10, 10) & R(5, 0, num_max, num_max));
+  // Test with overflowing dimensions for floats/doubles.
+  EXPECT_EQ(R(num_max, 0, num_max / 4, 10), R(num_max, 0, num_max / 2, 10) & R(num_max, 0, num_max / 4, 10));
+  // Test with overflowing coordinates.
+  EXPECT_EQ(R(), R(20, 0, 10, 10) & R(num_lowest, 0, 10, 10));
+  EXPECT_EQ(R(), R(20, 0, 10, 10) & R(0, num_lowest, 10, 10));
+  EXPECT_EQ(R(), R(num_lowest, 0, 10, 10) & R(0, num_lowest, 10, 10));
+}
+REGISTER_TYPED_TEST_CASE_P(Rect_Test, Overflows);
+
+typedef ::testing::Types<int, float, double> RectTypes;
+INSTANTIATE_TYPED_TEST_CASE_P(Negative_Test, Rect_Test, RectTypes);
+
+
 }} // namespace