3D reconstruction of a structure of a real scene with an open surface

A non-transitory computer readable storage medium having recorded thereon a computer program comprising instructions for performing a method for 3D reconstruction of a structure of a real scene, the method comprising:

• obtaining a first open triangulated surface, the first open triangulated surface being a set of triangles of a tetrahedral meshing of a 3D point cloud representing at least a part of a structure;
• and
• determining a second open triangulated surface representing a skin of a portion of the structure, the determining exploring candidate open triangulated surfaces each being a set of triangles of the tetrahedral meshing and the determining penalizing a high rank of the candidate open triangulated surfaces according to a lexicographic order, the lexicographic order being based on a triangle order and the lexicographic order ordering a first candidate open triangulated surface having first triangles which are ordered according to a decreasing rank of the triangle order, relative to a second candidate open triangulated surface having second triangles which are ordered according to a decreasing rank of the triangle order, the triangle order penalizing a triangle size, the determined second open triangulated surface violating consistency of a labelling of the tetrahedral meshing with two given labels, a triangle respecting consistency of the labelling when the triangle belongs to the first open triangulated surface and separates two tetrahedrons having different labels, or when the triangle does not belong to the first open triangulated surface and separates two tetrahedrons having a same label,
• wherein the tetrahedral meshing presents the following properties:
• a union of the tetrahedrons of the tetrahedral meshing forms a convex envelop of the points of the 3D point cloud;
• and
• the intersection between any first tetrahedron of the tetrahedral meshing and any second tetrahedron of the tetrahedral meshing intersecting the first tetrahedron is a vertex of the first tetrahedron, an edge of the first tetrahedron, or a face of the first tetrahedron.

A computer comprising:

• a processor coupled to a memory, the memory having recorded thereon a computer program comprising instructions for 3D reconstruction of a structure of a real scene that when executed by the processor causes the processor to be configured to:
• obtain a first open triangulated surface, the first open triangulated surface being a set of triangles of a tetrahedral meshing of a 3D point cloud representing at least a part of a structure, and
• determine a second open triangulated surface representing a skin of a portion of the structure, the determination exploring candidate open triangulated surfaces each being a set of triangles of the tetrahedral meshing and the determining penalizing a high rank of the candidate open triangulated surfaces according to a lexicographic order, the lexicographic order being based on a triangle order and the lexicographic order ordering a first candidate open triangulated surface having first triangles which are ordered according to a decreasing rank of the triangle order, relative to a second candidate open triangulated surface having second triangles which are ordered according to a decreasing rank of the triangle order, the triangle order penalizing a triangle size, the determined second open triangulated surface violating consistency of a labelling of the tetrahedral meshing with two given labels, a triangle respecting consistency of the labelling when the triangle belongs to the first open triangulated surface and separates two tetrahedrons having different labels, or when the triangle does not belong to the first open triangulated surface and separates two tetrahedrons having a same label,
• wherein the tetrahedral meshing presents the following properties:
• a union of the tetrahedrons of the tetrahedral meshing forms a convex envelop of the points of the 3D point cloud;
• and
• the intersection between any first tetrahedron of the tetrahedral meshing and any second tetrahedron of the tetrahedral meshing intersecting the first tetrahedron is a vertex of the first tetrahedron, an edge of the first tetrahedron, or a face of the first tetrahedron.