diff --git a/modules/calib3d/include/opencv2/calib3d.hpp b/modules/calib3d/include/opencv2/calib3d.hpp
index b3709c8cc2..5fe7fb9596 100644
--- a/modules/calib3d/include/opencv2/calib3d.hpp
+++ b/modules/calib3d/include/opencv2/calib3d.hpp
@@ -3797,10 +3797,12 @@ namespace fisheye
     @param R Rectification transformation in the object space: 3x3 1-channel, or vector: 3x1/1x3
     1-channel or 1x1 3-channel
     @param P New camera intrinsic matrix (3x3) or new projection matrix (3x4)
+    @param criteria Termination criteria
     @param undistorted Output array of image points, 1xN/Nx1 2-channel, or vector\<Point2f\> .
      */
     CV_EXPORTS_W void undistortPoints(InputArray distorted, OutputArray undistorted,
-        InputArray K, InputArray D, InputArray R = noArray(), InputArray P  = noArray());
+        InputArray K, InputArray D, InputArray R = noArray(), InputArray P  = noArray(),
+                TermCriteria criteria = TermCriteria(TermCriteria::MAX_ITER + TermCriteria::EPS, 10, 1e-8));
 
     /** @brief Computes undistortion and rectification maps for image transform by #remap. If D is empty zero
     distortion is used, if R or P is empty identity matrixes are used.
diff --git a/modules/calib3d/src/fisheye.cpp b/modules/calib3d/src/fisheye.cpp
index 43b679f9e4..9a73132cbe 100644
--- a/modules/calib3d/src/fisheye.cpp
+++ b/modules/calib3d/src/fisheye.cpp
@@ -318,7 +318,8 @@ void cv::fisheye::distortPoints(InputArray undistorted, OutputArray distorted, I
 //////////////////////////////////////////////////////////////////////////////////////////////////////////////
 /// cv::fisheye::undistortPoints
 
-void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted, InputArray K, InputArray D, InputArray R, InputArray P)
+void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted, InputArray K, InputArray D,
+                                   InputArray R, InputArray P, TermCriteria criteria)
 {
     CV_INSTRUMENT_REGION();
 
@@ -330,6 +331,8 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
     CV_Assert(R.empty() || R.size() == Size(3, 3) || R.total() * R.channels() == 3);
     CV_Assert(D.total() == 4 && K.size() == Size(3, 3) && (K.depth() == CV_32F || K.depth() == CV_64F));
 
+    CV_Assert(criteria.isValid());
+
     cv::Vec2d f, c;
     if (K.depth() == CV_32F)
     {
@@ -372,6 +375,15 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
     size_t n = distorted.total();
     int sdepth = distorted.depth();
 
+    const bool isEps = criteria.type & TermCriteria::EPS;
+
+    /* Define max count for solver iterations */
+    int maxCount = std::numeric_limits<int>::max();
+    if (criteria.type & TermCriteria::MAX_ITER) {
+        maxCount = criteria.maxCount;
+    }
+
+
     for(size_t i = 0; i < n; i++ )
     {
         Vec2d pi = sdepth == CV_32F ? (Vec2d)srcf[i] : srcd[i];  // image point
@@ -389,13 +401,11 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
 
         double scale = 0.0;
 
-        if (fabs(theta_d) > 1e-8)
+        if (!isEps || fabs(theta_d) > criteria.epsilon)
         {
             // compensate distortion iteratively
 
-            const double EPS = 1e-8; // or std::numeric_limits<double>::epsilon();
-
-            for (int j = 0; j < 10; j++)
+            for (int j = 0; j < maxCount; j++)
             {
                 double theta2 = theta*theta, theta4 = theta2*theta2, theta6 = theta4*theta2, theta8 = theta6*theta2;
                 double k0_theta2 = k[0] * theta2, k1_theta4 = k[1] * theta4, k2_theta6 = k[2] * theta6, k3_theta8 = k[3] * theta8;
@@ -403,7 +413,8 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
                 double theta_fix = (theta * (1 + k0_theta2 + k1_theta4 + k2_theta6 + k3_theta8) - theta_d) /
                                    (1 + 3*k0_theta2 + 5*k1_theta4 + 7*k2_theta6 + 9*k3_theta8);
                 theta = theta - theta_fix;
-                if (fabs(theta_fix) < EPS)
+
+                if (isEps && (fabs(theta_fix) < criteria.epsilon))
                 {
                     converged = true;
                     break;
@@ -422,7 +433,7 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
         // so we can check whether theta has changed the sign during the optimization
         bool theta_flipped = ((theta_d < 0 && theta > 0) || (theta_d > 0 && theta < 0));
 
-        if (converged && !theta_flipped)
+        if ((converged || !isEps) && !theta_flipped)
         {
             Vec2d pu = pw * scale; //undistorted point