A neural network for recovering 3D shape from erroneous and few depth maps of shaded images

In this paper, we present a new neural network (NN) for three-dimensional (3D) shape reconstruction. This NN provides an analytic mapping of an initial 3D polyhedral model into its projection depth images. Through this analytic mapping, the NN can analytically refine vertices position of the model using error back-propagation learning. This learning is based on shape-from-shading (SFS) depth maps taken from multiple views. The depth maps are obtained by Tsai–Shah SFS algorithm. They are considered as partial 3D shapes of the object to be reconstructed. The task is to reconstruct an accurate and complete representation of a given object relying only on a limited number of views and erroneous SFS depth maps. Through hierarchical reconstruction and annealing reinforcement strategies, our reconstruction system gives more exact and stable results. In addition, it corrects and smoothly fuses the erroneous SFS depth maps. The implementation of this neural network algorithm used in this paper is available at http://kumazawawww.cs.titech.ac.jp/~fanany/MV-SPRNN/mv-sprnn.html. 2003 Elsevier B.V. All rights reserved.