Geometric Neural Computing for 2D Contour and 3D Surface Reconstruction

Abstract

In this work we present an algorithm to approximate the surface of 2D or 3D objects combining concepts from geometric algebra and artificial neural networks. Our approach is based on the self-organized neural network called Growing Neural Gas (GNG), incorporating versors of the geometric algebra in its neural units; such versors are the transformations that will be determined during the training stage and then applied to a point to approximate the surface of the object. We also incorporate the information given by the generalized gradient vector flow to select automatically the input patterns, and also in the learning stage in order to improve the performance of the net. Several examples using medical images are presented, as well as images of automatic visual inspection. We compared the results obtained using snakes against the GSOM incorporating the gradient information and using versors. Such results confirm that our approach is very promising. As a second application, a kind of morphing or registration procedure is shown; namely the algorithm can be used when transforming one model at time t ₁ into another at time t ₂. We include also examples applying the same procedure, now extended to models based on spheres.