Self-Organising Maps for Implicit Surface Reconstruction

Abstract

This paper proposes an implicit surface reconstruction algorithm based on Self-Organising Maps (SOMs). The SOM has the connectivity of a regular 3D grid, each node storing its signed distance from the surface. At each iteration of the basic algorithm, a new training set is created by sampling regularly along the normals of the input points. The main training iteration consists of a competitive learning step, followed by several iterations of Laplacian smoothing. After each training iteration, we use extra sample validation to test for overfitting. At the end of the training process, a triangle mesh is extracted as the zero level set of the SOM grid. Validation tests and experiments show that the algorithm can cope with the noise of raw scan data. Timing measurements and comparisons show that the algorithm is fast, because the fixed and regular connectivity of the SOM means that the search of the node nearest to a sample can be done efficiently.