Merge pull request #22798 from lamm45:distransform-large

Fix distransform to work with large images #22798

This attempts to fix the following bug which was caused by storing squares of large integers into 32-bit floating point variables:
https://github.com/opencv/opencv/issues/22732


### Pull Request Readiness Checklist

See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request

- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [x] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake

modules/imgproc/src/distransform.cpp

@@ -448,7 +448,7 @@ static void getDistanceTransformMask( int maskType, float *metrics )
 
 struct DTColumnInvoker : ParallelLoopBody
 {
-    DTColumnInvoker( const Mat* _src, Mat* _dst, const int* _sat_tab, const float* _sqr_tab)
+    DTColumnInvoker( const Mat* _src, Mat* _dst, const int* _sat_tab, const int* _sqr_tab)
     {
         src = _src;
         dst = _dst;
@@ -481,7 +481,7 @@ struct DTColumnInvoker : ParallelLoopBody
             {
                 dist = dist + 1 - sat_tab[dist - d[j]];
                 d[j] = dist;
-                dptr[0] = sqr_tab[dist];
+                dptr[0] = (float)sqr_tab[dist];
             }
         }
     }
@@ -489,12 +489,12 @@ struct DTColumnInvoker : ParallelLoopBody
     const Mat* src;
     Mat* dst;
     const int* sat_tab;
-    const float* sqr_tab;
+    const int* sqr_tab;
 };
 
 struct DTRowInvoker : ParallelLoopBody
 {
-    DTRowInvoker( Mat* _dst, const float* _sqr_tab, const float* _inv_tab )
+    DTRowInvoker( Mat* _dst, const int* _sqr_tab, const float* _inv_tab )
     {
         dst = _dst;
         sqr_tab = _sqr_tab;
@@ -529,7 +529,7 @@ struct DTRowInvoker : ParallelLoopBody
                 for(;;k--)
                 {
                     p = v[k];
-                    float s = (fq + sqr_tab[q] - d[p] - sqr_tab[p])*inv_tab[q - p];
+                    float s = (fq - d[p] + (sqr_tab[q]-sqr_tab[p]))*inv_tab[q - p];
                     if( s > z[k] )
                     {
                         k++;
@@ -552,28 +552,28 @@ struct DTRowInvoker : ParallelLoopBody
     }
 
     Mat* dst;
-    const float* sqr_tab;
+    const int* sqr_tab;
     const float* inv_tab;
 };
 
 static void
 trueDistTrans( const Mat& src, Mat& dst )
 {
-    const float inf = 1e15f;
+    const int inf = INT_MAX;
 
     CV_Assert( src.size() == dst.size() );
 
     CV_Assert( src.type() == CV_8UC1 && dst.type() == CV_32FC1 );
     int i, m = src.rows, n = src.cols;
 
-    cv::AutoBuffer<uchar> _buf(std::max(m*2*sizeof(float) + (m*3+1)*sizeof(int), n*2*sizeof(float)));
+    cv::AutoBuffer<uchar> _buf(std::max(m*2*sizeof(int) + (m*3+1)*sizeof(int), n*2*sizeof(float)));
     // stage 1: compute 1d distance transform of each column
-    float* sqr_tab = (float*)_buf.data();
+    int* sqr_tab = (int*)_buf.data();
     int* sat_tab = cv::alignPtr((int*)(sqr_tab + m*2), sizeof(int));
     int shift = m*2;
 
     for( i = 0; i < m; i++ )
-        sqr_tab[i] = (float)(i*i);
+        sqr_tab[i] = i*i;
     for( i = m; i < m*2; i++ )
         sqr_tab[i] = inf;
     for( i = 0; i < shift; i++ )
@@ -584,13 +584,14 @@ trueDistTrans( const Mat& src, Mat& dst )
     cv::parallel_for_(cv::Range(0, n), cv::DTColumnInvoker(&src, &dst, sat_tab, sqr_tab), src.total()/(double)(1<<16));
 
     // stage 2: compute modified distance transform for each row
-    float* inv_tab = sqr_tab + n;
+    float* inv_tab = (float*)sqr_tab + n;
 
-    inv_tab[0] = sqr_tab[0] = 0.f;
+    inv_tab[0] = 0.f;
+    sqr_tab[0] = 0;
     for( i = 1; i < n; i++ )
     {
         inv_tab[i] = (float)(0.5/i);
-        sqr_tab[i] = (float)(i*i);
+        sqr_tab[i] = i*i;
     }
 
     cv::parallel_for_(cv::Range(0, m), cv::DTRowInvoker(&dst, sqr_tab, inv_tab));
@@ -752,7 +753,9 @@ void cv::distanceTransform( InputArray _src, OutputArray _dst, OutputArray _labe
         CV_IPP_CHECK()
         {
 #if IPP_DISABLE_PERF_TRUE_DIST_MT
-            if(cv::getNumThreads()<=1 || (src.total()<(int)(1<<14)))
+            // IPP uses floats, but 4097 cannot be squared into a float
+            if((cv::getNumThreads()<=1 || (src.total()<(int)(1<<14))) &&
+                src.rows < 4097 && src.cols < 4097)
 #endif
             {
                 IppStatus status;