diff --git a/modules/imgproc/src/phasecorr_iterative.cpp b/modules/imgproc/src/phasecorr_iterative.cpp
index ced9339c87..c2b03190bd 100644
--- a/modules/imgproc/src/phasecorr_iterative.cpp
+++ b/modules/imgproc/src/phasecorr_iterative.cpp
@@ -1,11 +1,13 @@
 #include "precomp.hpp"
 #include <cmath>
+#include <limits>
 
 namespace {
 
 template <typename T>
 void calculateCrossPowerSpectrum(const cv::Mat& dft1, const cv::Mat& dft2, cv::Mat& cps)
 {
+    const T eps = std::numeric_limits<T>::epsilon();  // prevent div0 problems
     for (int row = 0; row < dft1.rows; ++row)
     {
         auto* cpsp = cps.ptr<cv::Vec<T, 2>>(row);
@@ -15,7 +17,7 @@ void calculateCrossPowerSpectrum(const cv::Mat& dft1, const cv::Mat& dft2, cv::M
         {
             const T re = dft1p[col][0] * dft2p[col][0] + dft1p[col][1] * dft2p[col][1];
             const T im = dft1p[col][0] * dft2p[col][1] - dft1p[col][1] * dft2p[col][0];
-            const T mag = std::sqrt(re * re + im * im);
+            const T mag = std::sqrt(re * re + im * im) + eps;
             cpsp[col][0] = re / mag;
             cpsp[col][1] = im / mag;
         }
diff --git a/modules/imgproc/test/test_ipc.cpp b/modules/imgproc/test/test_ipc.cpp
index 321b1f2fe3..5e26a6dd14 100644
--- a/modules/imgproc/test/test_ipc.cpp
+++ b/modules/imgproc/test/test_ipc.cpp
@@ -24,6 +24,17 @@ Mat GenerateTestImage(Size size)
     return image;
 }
 
+Mat GenerateGaussianImage(Size size, Point2d center)
+{
+    Mat image(size, CV_32F);
+    for (int row = 0; row < size.height; ++row)
+        for (int col = 0; col < size.width; ++col)
+            image.at<float>(row, col) = static_cast<float>(std::exp(
+                -((col - center.x) * (col - center.x) + (row - center.y) * (row - center.y)) /
+                32.));
+    return image;
+}
+
 void TestPhaseCorrelationIterative(const Size& size, const double maxShift)
 {
     const auto iters = std::max(201., maxShift * 10 + 1);
@@ -114,4 +125,17 @@ TEST(Imgproc_PhaseCorrelationIterative, accuracy_real_img)
     ASSERT_NEAR(ipcShift.y, (double)yShift, 1.);
 }
 
+TEST(Imgproc_PhaseCorrelationIterative, accuracy_32f_smooth_img)
+{
+    const Point2d center(30., 28.);
+    const Point2d shift(-3., 2.);
+    const Mat image1 = GenerateGaussianImage(Size(64, 64), center);
+    const Mat image2 = GenerateGaussianImage(Size(64, 64), center + shift);
+
+    const Point2d ipcShift = phaseCorrelateIterative(image1, image2);
+
+    ASSERT_NEAR(ipcShift.x, shift.x, 1.);
+    ASSERT_NEAR(ipcShift.y, shift.y, 1.);
+}
+
 }}  // namespace opencv_test