diff --git a/Shape_detection/examples/Shape_detection/region_growing_lines_on_segment_set.cpp b/Shape_detection/examples/Shape_detection/region_growing_lines_on_segment_set.cpp
index d5596eee720..694f96564d0 100644
--- a/Shape_detection/examples/Shape_detection/region_growing_lines_on_segment_set.cpp
+++ b/Shape_detection/examples/Shape_detection/region_growing_lines_on_segment_set.cpp
@@ -35,7 +35,7 @@ int main(int argc, char *argv[]) {
   const std::string filename = is_default_input ? CGAL::data_file_path("meshes/am.off") : argv[1];
 
   Surface_mesh surface_mesh;
-  if (!CGAL::IO::read_polygon_mesh(filename, surface_mesh, CGAL::parameters::all_default())) {
+  if (!CGAL::IO::read_polygon_mesh(filename, surface_mesh)) {
     std::cerr << "ERROR: cannot read the input file!" << std::endl;
     return EXIT_FAILURE;
   }
@@ -48,7 +48,7 @@ int main(int argc, char *argv[]) {
 
   // Find planar regions.
   One_ring_query one_ring_query(surface_mesh);
-  Plane_region plane_region(surface_mesh, CGAL::parameters::all_default());
+  Plane_region plane_region(surface_mesh);
   RG_planes rg_planes(face_range, one_ring_query, plane_region);
 
   std::vector< std::vector<std::size_t> > regions;
diff --git a/Shape_detection/examples/Shape_detection/region_growing_planes_on_polygon_mesh.cpp b/Shape_detection/examples/Shape_detection/region_growing_planes_on_polygon_mesh.cpp
index 00cee6c73ef..f0caab5c229 100644
--- a/Shape_detection/examples/Shape_detection/region_growing_planes_on_polygon_mesh.cpp
+++ b/Shape_detection/examples/Shape_detection/region_growing_planes_on_polygon_mesh.cpp
@@ -40,7 +40,7 @@ int main(int argc, char *argv[]) {
   CGAL::IO::set_ascii_mode(in);
 
   Polygon_mesh polygon_mesh;
-  if (!CGAL::IO::read_polygon_mesh(filename, polygon_mesh, CGAL::parameters::all_default())) {
+  if (!CGAL::IO::read_polygon_mesh(filename, polygon_mesh)) {
     std::cerr << "ERROR: cannot read the input file!" << std::endl;
     return EXIT_FAILURE;
   }
@@ -65,8 +65,7 @@ int main(int argc, char *argv[]) {
 
   // Sort face indices.
   Sorting sorting(
-    polygon_mesh, neighbor_query,
-    CGAL::parameters::all_default());
+    polygon_mesh, neighbor_query);
   sorting.sort();
 
   // Create an instance of the region growing class.
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/K_neighbor_query.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/K_neighbor_query.h
index b839ed5aca6..528cc95cf8b 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/K_neighbor_query.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/K_neighbor_query.h
@@ -131,10 +131,10 @@ namespace Point_set {
       \pre `input_range.size() > 0`
       \pre `K > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     K_neighbor_query(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::point_map), PointMap())),
@@ -188,15 +188,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // K_neighbor_query(
-    //   const InputRange& input_range) :
-    // K_neighbor_query(
-    //   input_range, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_circle_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_circle_fit_region.h
index bf4b37d7d89..e33f5738f61 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_circle_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_circle_fit_region.h
@@ -159,10 +159,10 @@ namespace Point_set {
       \pre `minimum_radius >= 0`
       \pre `maximum_radius >= minimum_radius`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_circle_fit_region(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::point_map), PointMap())),
@@ -274,15 +274,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_circle_fit_region(
-    //   const InputRange& input_range) :
-    // Least_squares_circle_fit_region(
-    //   input_range, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_circle_fit_sorting.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_circle_fit_sorting.h
index deebe8f7dd7..043130f21cd 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_circle_fit_sorting.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_circle_fit_sorting.h
@@ -112,11 +112,11 @@ namespace Point_set {
 
       \pre `input_range.size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_circle_fit_sorting(
       const InputRange& input_range,
       NeighborQuery& neighbor_query,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_neighbor_query(neighbor_query),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
@@ -162,16 +162,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_circle_fit_sorting(
-    //   const InputRange& input_range,
-    //   NeighborQuery& neighbor_query) :
-    // Least_squares_circle_fit_sorting(
-    //   input_range, neighbor_query, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Sorting
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_cylinder_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_cylinder_fit_region.h
index 5fd28eedec5..37ef7d7ccb6 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_cylinder_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_cylinder_fit_region.h
@@ -159,10 +159,10 @@ namespace Point_set {
       \pre `minimum_radius >= 0`
       \pre `maximum_radius >= minimum_radius`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_cylinder_fit_region(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::point_map), PointMap())),
@@ -274,15 +274,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_cylinder_fit_region(
-    //   const InputRange& input_range) :
-    // Least_squares_cylinder_fit_region(
-    //   input_range, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_cylinder_fit_sorting.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_cylinder_fit_sorting.h
index 77ec64f374b..355cb9abc28 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_cylinder_fit_sorting.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_cylinder_fit_sorting.h
@@ -123,11 +123,11 @@ namespace Point_set {
 
       \pre `input_range.size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_cylinder_fit_sorting(
       const InputRange& input_range,
       NeighborQuery& neighbor_query,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_neighbor_query(neighbor_query),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
@@ -180,16 +180,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_cylinder_fit_sorting(
-    //   const InputRange& input_range,
-    //   NeighborQuery& neighbor_query) :
-    // Least_squares_cylinder_fit_sorting(
-    //   input_range, neighbor_query, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Sorting
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_region.h
index 2c097dffa8c..f71b77188fb 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_region.h
@@ -145,10 +145,10 @@ namespace Point_set {
       \pre `cosine_value >= 0 && cosine_value <= 1`
       \pre `minimum_region_size > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_line_fit_region(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::point_map), PointMap())),
@@ -240,15 +240,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_line_fit_region(
-    //   const InputRange& input_range) :
-    // Least_squares_line_fit_region(
-    //   input_range, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_sorting.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_sorting.h
index dcea8805470..8bb9f67f89a 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_sorting.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_line_fit_sorting.h
@@ -112,11 +112,11 @@ namespace Point_set {
 
       \pre `input_range.size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_line_fit_sorting(
       const InputRange& input_range,
       NeighborQuery& neighbor_query,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_neighbor_query(neighbor_query),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
@@ -162,16 +162,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_line_fit_sorting(
-    //   const InputRange& input_range,
-    //   NeighborQuery& neighbor_query) :
-    // Least_squares_line_fit_sorting(
-    //   input_range, neighbor_query, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Sorting
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_region.h
index b9e49fcee0d..37814710117 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_region.h
@@ -145,10 +145,10 @@ namespace Point_set {
       \pre `cosine_value >= 0 && cosine_value <= 1`
       \pre `minimum_region_size > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_plane_fit_region(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::point_map), PointMap())),
@@ -239,16 +239,6 @@ namespace Point_set {
     { }
 
     #endif // CGAL_NO_DEPRECATED_CODE
-
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_plane_fit_region(
-    //   const InputRange& input_range) :
-    // Least_squares_plane_fit_region(
-    //   input_range, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_sorting.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_sorting.h
index 0c9582c4910..482d5c91232 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_sorting.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_plane_fit_sorting.h
@@ -112,11 +112,11 @@ namespace Point_set {
 
       \pre `input_range.size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_plane_fit_sorting(
       const InputRange& input_range,
       NeighborQuery& neighbor_query,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_neighbor_query(neighbor_query),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
@@ -162,16 +162,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_plane_fit_sorting(
-    //   const InputRange& input_range,
-    //   NeighborQuery& neighbor_query) :
-    // Least_squares_plane_fit_sorting(
-    //   input_range, neighbor_query, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Sorting
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_region.h
index 9cc235fc158..03cb2bffcd2 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_region.h
@@ -158,10 +158,10 @@ namespace Point_set {
       \pre `minimum_radius >= 0`
       \pre `maximum_radius >= minimum_radius`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_sphere_fit_region(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::point_map), PointMap())),
@@ -273,15 +273,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_sphere_fit_region(
-    //   const InputRange& input_range) :
-    // Least_squares_sphere_fit_region(
-    //   input_range, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_sorting.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_sorting.h
index fdcdb073be6..f84de44bec2 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_sorting.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Least_squares_sphere_fit_sorting.h
@@ -112,11 +112,11 @@ namespace Point_set {
 
       \pre `input_range.size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_sphere_fit_sorting(
       const InputRange& input_range,
       NeighborQuery& neighbor_query,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np= parameters::default_values()) :
     m_input_range(input_range),
     m_neighbor_query(neighbor_query),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
@@ -162,16 +162,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_sphere_fit_sorting(
-    //   const InputRange& input_range,
-    //   NeighborQuery& neighbor_query) :
-    // Least_squares_sphere_fit_sorting(
-    //   input_range, neighbor_query, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Sorting
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Sphere_neighbor_query.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Sphere_neighbor_query.h
index ff8b7786895..38b75f71402 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Sphere_neighbor_query.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_point_set/Sphere_neighbor_query.h
@@ -128,10 +128,10 @@ namespace Point_set {
       \pre `input_range.size() > 0`
       \pre `sphere_radius > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Sphere_neighbor_query(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_input_range(input_range),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::point_map), PointMap())),
@@ -183,15 +183,6 @@ namespace Point_set {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Sphere_neighbor_query(
-    //   const InputRange& input_range) :
-    // Sphere_neighbor_query(
-    //   input_range, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_region.h
index 48dd37195b9..85cf2a58414 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_region.h
@@ -159,10 +159,10 @@ namespace Polygon_mesh {
       \pre `cosine_value >= 0 && cosine_value <= 1`
       \pre `minimum_region_size > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_plane_fit_region(
       const PolygonMesh& pmesh,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_face_graph(pmesh),
     m_face_range(faces(m_face_graph)),
     m_vertex_to_point_map(parameters::choose_parameter(parameters::get_parameter(
@@ -247,15 +247,6 @@ namespace Polygon_mesh {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_plane_fit_region(
-    //   const PolygonMesh& pmesh) :
-    // Least_squares_plane_fit_region(
-    //   pmesh, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_sorting.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_sorting.h
index bbfd2cb994a..e764ab30b26 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_sorting.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Least_squares_plane_fit_sorting.h
@@ -118,11 +118,11 @@ namespace Polygon_mesh {
 
       \pre `faces(pmesh).size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename CGAL_NP_TEMPLATE_PARAMETERS>
     Least_squares_plane_fit_sorting(
       const PolygonMesh& pmesh,
       NeighborQuery& neighbor_query,
-      const NamedParameters& np) :
+      const CGAL_NP_CLASS& np = parameters::default_values()) :
     m_face_graph(pmesh),
     m_neighbor_query(neighbor_query),
     m_face_range(faces(m_face_graph)),
@@ -169,16 +169,6 @@ namespace Polygon_mesh {
 
     #endif // CGAL_NO_DEPRECATED_CODE
 
-    /// \cond SKIP_IN_MANUAL
-    // TODO: Should be off until the deprecated code is removed.
-    // Least_squares_plane_fit_sorting(
-    //   const PolygonMesh& pmesh,
-    //   NeighborQuery& neighbor_query) :
-    // Least_squares_plane_fit_sorting(
-    //   pmesh, neighbor_query, CGAL::parameters::all_default())
-    // { }
-    /// \endcond
-
     /// @}
 
     /// \name Sorting
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Polyline_graph.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Polyline_graph.h
index f7de1ef0a2f..141d977f650 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Polyline_graph.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polygon_mesh/Polyline_graph.h
@@ -162,10 +162,10 @@ namespace Polygon_mesh {
       \pre `faces(pmesh).size() > 0`
       \pre `edges(pmesh).size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename NamedParameters = parameters::Default_named_parameters>
     Polyline_graph(
       const PolygonMesh& pmesh,
-      const NamedParameters& np) :
+      const NamedParameters& np = parameters::default_values()) :
     m_face_graph(pmesh),
     m_face_range(faces(m_face_graph)),
     m_edge_range(edges(m_face_graph)),
@@ -182,14 +182,6 @@ namespace Polygon_mesh {
       build_graph();
     }
 
-    /// \cond SKIP_IN_MANUAL
-    Polyline_graph(
-      const PolygonMesh& pmesh) :
-    Polyline_graph(
-      pmesh, CGAL::parameters::all_default())
-    { }
-    /// \endcond
-
     /// \cond SKIP_IN_MANUAL
     void build_graph() {
 
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_region.h
index 58e9b78c5d0..3e5be5e9d07 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_region.h
@@ -139,10 +139,10 @@ namespace Polyline {
       \pre `cosine_value >= 0 && cosine_value <= 1`
       \pre `minimum_region_size > 0`
     */
-    template<typename NamedParameters>
+    template<typename NamedParameters = parameters::Default_named_parameters>
     Least_squares_line_fit_region(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const NamedParameters& np = parameters::default_values()) :
     m_input_range(input_range),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::point_map), PointMap())),
@@ -175,14 +175,6 @@ namespace Polyline {
       m_cos_value_threshold = cos_value;
     }
 
-    /// \cond SKIP_IN_MANUAL
-    Least_squares_line_fit_region(
-      const InputRange& input_range) :
-    Least_squares_line_fit_region(
-      input_range, CGAL::parameters::all_default())
-    { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_sorting.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_sorting.h
index 8467d22c37d..0c3bff990dd 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_sorting.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_sorting.h
@@ -117,11 +117,11 @@ namespace Polyline {
 
       \pre `input_range.size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename NamedParameters = parameters::Default_named_parameters>
     Least_squares_line_fit_sorting(
       const InputRange& input_range,
       NeighborQuery& neighbor_query,
-      const NamedParameters& np) :
+      const NamedParameters& np = parameters::default_values()) :
     m_input_range(input_range),
     m_neighbor_query(neighbor_query),
     m_point_map(parameters::choose_parameter(parameters::get_parameter(
@@ -136,15 +136,6 @@ namespace Polyline {
       m_scores.resize(m_input_range.size());
     }
 
-    /// \cond SKIP_IN_MANUAL
-    Least_squares_line_fit_sorting(
-      const InputRange& input_range,
-      NeighborQuery& neighbor_query) :
-    Least_squares_line_fit_sorting(
-      input_range, neighbor_query, CGAL::parameters::all_default())
-    { }
-    /// \endcond
-
     /// @}
 
     /// \name Sorting
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_segment_set/Least_squares_line_fit_region.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_segment_set/Least_squares_line_fit_region.h
index b5ee43d4137..0623e95732f 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_segment_set/Least_squares_line_fit_region.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_segment_set/Least_squares_line_fit_region.h
@@ -140,10 +140,10 @@ namespace Segment_set {
       \pre `cosine_value >= 0 && cosine_value <= 1`
       \pre `minimum_region_size > 0`
     */
-    template<typename NamedParameters>
+    template<typename NamedParameters = parameters::Default_named_parameters>
     Least_squares_line_fit_region(
       const InputRange& input_range,
-      const NamedParameters& np) :
+      const NamedParameters& np = parameters::default_values()) :
     m_input_range(input_range),
     m_segment_map(parameters::choose_parameter(parameters::get_parameter(
       np, internal_np::segment_map), SegmentMap())),
@@ -176,14 +176,6 @@ namespace Segment_set {
       m_cos_value_threshold = cos_value;
     }
 
-    /// \cond SKIP_IN_MANUAL
-    Least_squares_line_fit_region(
-      const InputRange& input_range) :
-    Least_squares_line_fit_region(
-      input_range, CGAL::parameters::all_default())
-    { }
-    /// \endcond
-
     /// @}
 
     /// \name Access
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_segment_set/Least_squares_line_fit_sorting.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_segment_set/Least_squares_line_fit_sorting.h
index b8964de4196..0d572769d02 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_segment_set/Least_squares_line_fit_sorting.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_segment_set/Least_squares_line_fit_sorting.h
@@ -117,11 +117,11 @@ namespace Segment_set {
 
       \pre `input_range.size() > 0`
     */
-    template<typename NamedParameters>
+    template<typename NamedParameters = parameters::Default_named_parameters>
     Least_squares_line_fit_sorting(
       const InputRange& input_range,
       NeighborQuery& neighbor_query,
-      const NamedParameters& np) :
+      const NamedParameters& np = parameters::default_values()) :
     m_input_range(input_range),
     m_neighbor_query(neighbor_query),
     m_segment_map(parameters::choose_parameter(parameters::get_parameter(
@@ -136,15 +136,6 @@ namespace Segment_set {
       m_scores.resize(m_input_range.size());
     }
 
-    /// \cond SKIP_IN_MANUAL
-    Least_squares_line_fit_sorting(
-      const InputRange& input_range,
-      NeighborQuery& neighbor_query) :
-    Least_squares_line_fit_sorting(
-      input_range, neighbor_query, CGAL::parameters::all_default())
-    { }
-    /// \endcond
-
     /// @}
 
     /// \name Sorting
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/internal/free_functions.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/internal/free_functions.h
index d4befbb97e2..7f85ec9ee63 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/internal/free_functions.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/internal/free_functions.h
@@ -33,9 +33,9 @@ namespace internal {
 template<
 typename InputRange,
 typename OutputIterator,
-typename NamedParameters>
+typename CGAL_NP_TEMPLATE_PARAMETERS>
 OutputIterator region_growing_lines(
-  const InputRange& points_with_normals, OutputIterator regions, const NamedParameters& np) {
+  const InputRange& points_with_normals, OutputIterator regions, const CGAL_NP_CLASS& np = parameters::default_values()) {
 
   using Input_range = InputRange;
   using Point_with_normal = typename Input_range::value_type;
@@ -60,22 +60,12 @@ OutputIterator region_growing_lines(
   return regions;
 }
 
-template<
-typename InputRange,
-typename OutputIterator>
-OutputIterator region_growing_lines(
-  const InputRange& points_with_normals, OutputIterator regions) {
-
-  return region_growing_lines(
-    points_with_normals, regions, CGAL::parameters::all_default());
-}
-
 template<
 typename InputRange,
 typename OutputIterator,
-typename NamedParameters>
+typename CGAL_NP_TEMPLATE_PARAMETERS>
 OutputIterator region_growing_planes(
-  const InputRange& points_with_normals, OutputIterator regions, const NamedParameters& np) {
+  const InputRange& points_with_normals, OutputIterator regions, const CGAL_NP_CLASS& np = parameters::default_values()) {
 
   using Input_range = InputRange;
   using Point_with_normal = typename Input_range::value_type;
@@ -100,23 +90,13 @@ OutputIterator region_growing_planes(
   return regions;
 }
 
-template<
-typename InputRange,
-typename OutputIterator>
-OutputIterator region_growing_planes(
-  const InputRange& points_with_normals, OutputIterator regions) {
-
-  return region_growing_planes(
-    points_with_normals, regions, CGAL::parameters::all_default());
-}
-
 template<
 typename PointType,
 typename VectorType,
 typename OutputIterator,
-typename NamedParameters>
+typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT>
 OutputIterator region_growing_planes(
-  const CGAL::Point_set_3<PointType, VectorType>& point_set, OutputIterator regions, const NamedParameters& np) {
+  const CGAL::Point_set_3<PointType, VectorType>& point_set, OutputIterator regions, const CGAL_NP_CLASS& np) {
 
   using Point_type = PointType;
   using Vector_type = VectorType;
@@ -158,10 +138,10 @@ OutputIterator region_growing_planes(
 template<
 typename GeomTraits,
 typename OutputIterator,
-typename NamedParameters>
+typename CGAL_NP_TEMPLATE_PARAMETERS>
 OutputIterator region_growing_planes(
   const CGAL::Polyhedron_3<GeomTraits, CGAL::Polyhedron_items_3, CGAL::HalfedgeDS_vector>& polyhedron,
-  OutputIterator regions, const NamedParameters& np) {
+  OutputIterator regions, const CGAL_NP_CLASS& np = parameters::default_values()) {
 
   using Traits = GeomTraits;
   using Polyhedron = CGAL::Polyhedron_3<Traits, CGAL::Polyhedron_items_3, CGAL::HalfedgeDS_vector>;
@@ -183,23 +163,12 @@ OutputIterator region_growing_planes(
   return regions;
 }
 
-template<
-typename GeomTraits,
-typename OutputIterator>
-OutputIterator region_growing_planes(
-  const CGAL::Polyhedron_3<GeomTraits, CGAL::Polyhedron_items_3, CGAL::HalfedgeDS_vector>& polyhedron,
-  OutputIterator regions) {
-
-  return region_growing_planes(
-    polyhedron, regions, CGAL::parameters::all_default());
-}
-
 template<
 typename PointType,
 typename OutputIterator,
-typename NamedParameters>
+typename CGAL_NP_TEMPLATE_PARAMETERS>
 OutputIterator region_growing_planes(
-  const CGAL::Surface_mesh<PointType>& surface_mesh, OutputIterator regions, const NamedParameters& np) {
+  const CGAL::Surface_mesh<PointType>& surface_mesh, OutputIterator regions, const CGAL_NP_CLASS& np = parameters::default_values()) {
 
   using Point_type = PointType;
   using Traits = typename Kernel_traits<Point_type>::Kernel;
@@ -222,22 +191,12 @@ OutputIterator region_growing_planes(
   return regions;
 }
 
-template<
-typename PointType,
-typename OutputIterator>
-OutputIterator region_growing_planes(
-  const CGAL::Surface_mesh<PointType>& surface_mesh, OutputIterator regions) {
-
-  return region_growing_planes(
-    surface_mesh, regions, CGAL::parameters::all_default());
-}
-
 template<
 typename InputRange,
 typename OutputIterator,
-typename NamedParameters>
+typename CGAL_NP_TEMPLATE_PARAMETERS>
 OutputIterator region_growing_polylines(
-  const InputRange& polyline, OutputIterator regions, const NamedParameters& np) {
+  const InputRange& polyline, OutputIterator regions, const CGAL_NP_CLASS& np = parameters::default_values()) {
 
   using Input_range = InputRange;
   using Point_type = typename Input_range::value_type;
@@ -260,16 +219,6 @@ OutputIterator region_growing_polylines(
   return regions;
 }
 
-template<
-typename InputRange,
-typename OutputIterator>
-OutputIterator region_growing_polylines(
-  const InputRange& polyline, OutputIterator regions) {
-
-  return region_growing_polylines(
-    polyline, regions, CGAL::parameters::all_default());
-}
-
 } // namespace internal
 } // namespace Shape_detection
 } // namespace CGAL
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/internal/utils.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/internal/utils.h
index d5778213566..d5ade9113a3 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/internal/utils.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/internal/utils.h
@@ -32,7 +32,7 @@
 
 // Named parameters.
 #include <CGAL/boost/graph/named_params_helper.h>
-#include <CGAL/boost/graph/Named_function_parameters.h>
+#include <CGAL/Named_function_parameters.h>
 
 // Face graph includes.
 #include <CGAL/Iterator_range.h>
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_basic.cpp b/Shape_detection/test/Shape_detection/test_region_growing_basic.cpp
index 72184785b8a..de47140ae76 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_basic.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_basic.cpp
@@ -45,8 +45,8 @@ int main(int argc, char *argv[]) {
   assert(input_range.size() == 3634);
 
   // Create parameter classes.
-  Neighbor_query neighbor_query(input_range, CGAL::parameters::all_default());
-  Region_type region_type(input_range, CGAL::parameters::all_default());
+  Neighbor_query neighbor_query(input_range);
+  Region_type region_type(input_range);
 
   // Run region growing.
   Region_growing region_growing(
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
index df1a1567272..b65e6fed294 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
@@ -71,8 +71,7 @@ bool test(int argc, char** argv, const std::string name, const std::size_t minr,
 
   // Sort indices.
   Sorting sorting(
-    input_range, neighbor_query,
-    CGAL::parameters::all_default());
+    input_range, neighbor_query);
   sorting.sort();
 
   // Run region growing.