diff --git a/Point_set_shape_detection_3/test/Point_set_shape_detection_3/test_regularization.cpp b/Point_set_shape_detection_3/test/Point_set_shape_detection_3/test_regularization.cpp
index 1e1cc39bdd3..aef2e8bc985 100644
--- a/Point_set_shape_detection_3/test/Point_set_shape_detection_3/test_regularization.cpp
+++ b/Point_set_shape_detection_3/test/Point_set_shape_detection_3/test_regularization.cpp
@@ -160,13 +160,28 @@ int main()
     check_ransac_size (ransac, 2);
 
     std::vector<Plane> before = get_ransac_planes(ransac);
-    CGAL::regularize_planes (ransac, true, false, false, false, 5.);
+    
+    // Test regularization
+    typename Efficient_ransac::Plane_range planes = ransac.planes();
+    CGAL::regularize_planes (points,
+                             Point_map(),
+                             planes,
+                             CGAL::Shape_detection_3::Plane_map<Traits>(),
+                             CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                             true, false, false, false, 5.);
+    
     std::vector<Plane> after = get_ransac_planes(ransac);
 
     std::cerr << " * Nothing should change now..." << std::endl;
     check_planes_unchanged (before, after);
     
-    CGAL::regularize_planes (ransac, true, false, false, false, 15.);
+    CGAL::regularize_planes (points,
+                             Point_map(),
+                             planes,
+                             CGAL::Shape_detection_3::Plane_map<Traits>(),
+                             CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                             true, false, false, false, 15.);
+    
     after = get_ransac_planes(ransac);
 
     std::cerr << " * Something should change now..." << std::endl;
@@ -192,13 +207,27 @@ int main()
     check_ransac_size (ransac, 2);
 
     std::vector<Plane> before = get_ransac_planes(ransac);
-    CGAL::regularize_planes (ransac, false, true, false, true, 5.);
+
+    typename Efficient_ransac::Plane_range planes = ransac.planes();
+    CGAL::regularize_planes (points,
+                             Point_map(),
+                             planes,
+                             CGAL::Shape_detection_3::Plane_map<Traits>(),
+                             CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                             false, true, false, true, 5.);
+
     std::vector<Plane> after = get_ransac_planes(ransac);
 
     std::cerr << " * Nothing should change now..." << std::endl;
     check_planes_unchanged (before, after);
     
-    CGAL::regularize_planes (ransac, false, true, false, true, 15.);
+    CGAL::regularize_planes (points,
+                             Point_map(),
+                             planes,
+                             CGAL::Shape_detection_3::Plane_map<Traits>(),
+                             CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                             false, true, false, true, 15.);
+
     after = get_ransac_planes(ransac);
 
     std::cerr << " * Something should change now..." << std::endl;
@@ -223,13 +252,27 @@ int main()
     check_ransac_size (ransac, 2);
 
     std::vector<Plane> before = get_ransac_planes(ransac);
-    CGAL::regularize_planes (ransac, true, false, true, false, 5., 0.1);
+
+    typename Efficient_ransac::Plane_range planes = ransac.planes();
+    CGAL::regularize_planes (points,
+                             Point_map(),
+                             planes,
+                             CGAL::Shape_detection_3::Plane_map<Traits>(),
+                             CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                             true, false, true, false, 5., 0.1);
+
     std::vector<Plane> after = get_ransac_planes(ransac);
 
     std::cerr << " * Nothing should change now..." << std::endl;
     check_planes_unchanged (before, after);
     
-    CGAL::regularize_planes (ransac, true, false, true, false, 5., 0.3);
+    CGAL::regularize_planes (points,
+                             Point_map(),
+                             planes,
+                             CGAL::Shape_detection_3::Plane_map<Traits>(),
+                             CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                             true, false, true, false, 5., 0.3);
+
     after = get_ransac_planes(ransac);
 
     std::cerr << " * Something should change now..." << std::endl;
@@ -259,13 +302,26 @@ int main()
     check_ransac_size (ransac, 2);
 
     std::vector<Plane> before = get_ransac_planes(ransac);
-    CGAL::regularize_planes (ransac, false, false, false, true, 5., 0.01, Vector(1., 0., 0.));
+    typename Efficient_ransac::Plane_range planes = ransac.planes();
+    CGAL::regularize_planes (points,
+                             Point_map(),
+                             planes,
+                             CGAL::Shape_detection_3::Plane_map<Traits>(),
+                             CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                             false, false, false, true, 5., 0.01, Vector(1., 0., 0.));
+
     std::vector<Plane> after = get_ransac_planes(ransac);
 
     std::cerr << " * Nothing should change now..." << std::endl;
     check_planes_unchanged (before, after);
     
-    CGAL::regularize_planes (ransac, false, false, false, true, 15., 0.01, Vector(1., 0., 0.));
+    CGAL::regularize_planes (points,
+                             Point_map(),
+                             planes,
+                             CGAL::Shape_detection_3::Plane_map<Traits>(),
+                             CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                             false, false, false, true, 15., 0.01, Vector(1., 0., 0.));
+
     after = get_ransac_planes(ransac);
 
     std::cerr << " * Something should change now..." << std::endl;
diff --git a/Point_set_shape_detection_3/test/Point_set_shape_detection_3/test_scene.cpp b/Point_set_shape_detection_3/test/Point_set_shape_detection_3/test_scene.cpp
index b68753dd059..80b8f46f0a1 100644
--- a/Point_set_shape_detection_3/test/Point_set_shape_detection_3/test_scene.cpp
+++ b/Point_set_shape_detection_3/test/Point_set_shape_detection_3/test_scene.cpp
@@ -128,7 +128,13 @@ bool test_scene() {
   }
 
   // Test regularization
-  CGAL::regularize_planes (ransac, true, true, true, true,
+  typename Efficient_ransac::Plane_range planes = ransac.planes();
+  CGAL::regularize_planes (points,
+                           Point_map(),
+                           planes,
+                           CGAL::Shape_detection_3::Plane_map<Traits>(),
+                           CGAL::Shape_detection_3::Point_to_shape_index_map<Traits>(points, planes),
+                           true, true, true, true,
                            (FT)50., (FT)0.01);
   
   Point_index_range pts = ransac.indices_of_unassigned_points();