Growing self-organizing surface map: learning a surface topology from a point cloud

Area of Science:

• Computational geometry
• Computer vision
• Machine learning

Background:

• Surface reconstruction from point clouds is a fundamental problem in computer graphics and vision.
• Existing methods like neural meshes (NM) have limitations in handling arbitrary data sequences and ensuring complete surface topology.
• There is a need for robust surface reconstruction models that can accurately represent complex, folded surfaces.

Purpose of the Study:

• To introduce and detail the growing self-organizing surface map (GSOSM) model for 3D surface reconstruction.
• To present a novel connection learning rule, competitive connection Hebbian learning (CCHL), for generating complete triangulations.
• To evaluate the accuracy and topological integrity of GSOSM reconstructions and compare its performance against other models.

Main Methods:

• The GSOSM model incrementally reconstructs a surface from a dense point cloud using a mesh of equilateral triangles.
• It employs competitive connection Hebbian learning (CCHL) to establish surface topology, accepting any sequence of sample presentation.
• The model focuses on building a complete and accurate surface representation without false or overlapping faces.

Main Results:

• GSOSM successfully reconstructs folded surfaces immersed in 3D space from point cloud data.
• The use of CCHL results in complete triangulations, avoiding common artifacts like false or overlapping faces.
• Comparative analysis indicates that GSOSM achieves high accuracy and topological robustness.

Conclusions:

• The GSOSM model offers a significant advancement in 3D surface reconstruction, particularly for complex and folded surfaces.
• Its ability to build surface topology robustly and produce accurate triangulations makes it a valuable tool.
• GSOSM demonstrates superior performance compared to existing models in terms of accuracy and topological completeness.