CGAL How can I copy properties from Point_set to Surface mesh - c++

Question

First off, I'm aware of the CGAL GIS tutorial, but I just can't seem to copy properties from Point_set to surface mesh.
Any way, I'm loading the LIDAR point cloud to the point set as follows:
using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
using Point = Kernel::Point_3;
using Point_set = CGAL::Point_set_3<Point>;
std::ifstream ifile("input.ply", std::ios_base::binary);
ifile >> point_set;
std::cerr << point_set.size() << " point(s) read" << std::endl;
ifile.close();
I can get the properties via
auto props = point_set.properties();
for (const auto& item : props)
std::cerr << item << std::endl;
// I do know that there exist property "classification" that is of unsigned char type
Point_set::Property_map<unsigned char> original_class_map
= point_set.property_map<unsigned char>("classification").first;
Then, I had tried to set the mesh and had added vertex property, using the code from above mentioned CGAL tutorial. The code below set the point's z coordinate as a property.
auto idx_to_point_with_info
= [&](const Point_set::Index& idx) -> std::pair<Point, Point_set::Index> {
return std::make_pair(point_set.point(idx), idx);
};
using Vbi = CGAL::Triangulation_vertex_base_with_info_2<Point_set::Index, Projection_traits>;
using Fbi = CGAL::Triangulation_face_base_with_info_2<int, Projection_traits>;
using TDS = CGAL::Triangulation_data_structure_2<Vbi, Fbi>;
using TIN_with_info = CGAL::Delaunay_triangulation_2<Projection_traits, TDS>;
TIN_with_info tin_with_info(
boost::make_transform_iterator(point_set.begin(), idx_to_point_with_info),
boost::make_transform_iterator(point_set.end(), idx_to_point_with_info));
auto classification_value = [&](const TIN_with_info::Vertex_handle vh) -> double
{
return vh->point().z();
};
for (TIN_with_info::Vertex_handle vh : tin_with_info.all_vertex_handles())
{ // should work without classification_value, just plain vh->info() = vh->point().z();
vh->info() = classification_value(vh);
}
using Mesh = CGAL::Surface_mesh<Point>;
Mesh tin_class_mesh;
Mesh::Property_map<Mesh::Vertex_index, double> class_map
= tin_class_mesh.add_property_map<Mesh::Vertex_index, double>("v:class").first;
CGAL::copy_face_graph(tin_with_info, tin_class_mesh,
CGAL::parameters::vertex_to_vertex_output_iterator(
boost::make_function_output_iterator(class_lambda)));
std::cerr << tin_class_mesh.number_of_vertices() << " vs " << point_set.size() <<std::endl;
Now, this works just fine, I had successfully set the z coordinate as a property on a mesh.
But, I just can't figure out how can I copy the classification property from the point_set to the tin_class_mesh. I know that I'd need to change double to unsigned char in the code, but I don't know how to access the property from the point_set and assign it to the corresponding vertex in tin_class_mesh. What am I doing wrong?
As a side note, the interesting part here is that the number of tin_colored_mesh.number_of_vertices() differs slightly from the point_set.size(). Why is that?