Applications of Celluar Neural Networks for Shape from Shading Problem
MLDM '99 Proceedings of the First International Workshop on Machine Learning and Data Mining in Pattern Recognition
A neural network for recovering 3D shape from erroneous and few depth maps of shaded images
Pattern Recognition Letters
Improved SFS 3D measurement based on BP neural network
Image and Vision Computing
Novel Shape-From-Shading Methodology with Specular Reflectance Using Wavelet Networks
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Part II--Advances in Neural Networks
Multiple-view shape extraction from shading as local regression by analytic NN scheme
Mathematical and Computer Modelling: An International Journal
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The multilayer feedforward network has often been used for learning a nonlinear mapping based on a set of examples of the input-output data. In this paper, we present a novel use of the network, in which the example data are not explicitly given. We consider the problem of shape from shading in computer vision, where the input (image coordinates) and the output (surface depth) satisfy only a known differential equation. We use the feedforward network as a parametric representation of the object surface and reformulate the shape from shading problem as the minimization of an error function over the network weights. The stochastic gradient and conjugate gradient methods are used for the minimization. Boundary conditions for either surface depth or surface normal (or both) can be imposed by adjusting the same network at different levels. It is further shown that the light source direction can be estimated, based on an initial guess, by integrating the source estimation with the surface estimation. Extensions of the method to a wider class of problems are discussed. The efficiency of the method is verified by examples of both synthetic and real images