A Two-Level Generative Model for Cloth Representation and Shape from Shading

In this paper, we present a two-level generative model for representing the images and surface depth maps of drapery and clothes. The upper level consists of a number of folds which will generate the high contrast (ridge) areas with a dictionary of shading primitives (for 2D images) and fold primitives (for 3D depth maps). These primitives are represented in parametric forms and are learned in a supervised learning phase using 3D surfaces of clothes acquired through photometric stereo. The lower level consists of the remaining flat areas which fill between the folds with a smoothness prior (Markov random field). We show that the classical ill-posed problem-shape from shading (SFS) can be much improved by this two-level model for its reduced dimensionality and incorporation of middle-level visual knowledge, i.e., the dictionary of primitives. Given an input image, we first infer the folds and compute a sketch graph using a sketch pursuit algorithm as in the primal sketch (Guo et al., 2003). The 3D folds are estimated by parameter fitting using the fold dictionary and they form the "skeleton" of the drapery/cloth surfaces. Then, the lower level is computed by conventional SFS method using the fold areas as boundary conditions. The two levels interact at the final stage by optimizing a joint Bayesian posterior probability on the depth map. We show a number of experiments which demonstrate more robust results in comparison with state-of-the-art work. In a broader scope, our representation can be viewed as a two-level inhomogeneous MRF model which is applicable to general shape-from-X problems. Our study is an attempt to revisit Marr\´s idea (Marr and Freeman, 1982) of computing the 2frac12D sketch from primal sketch. In a companion paper (Barbu and Zhu, 2005), we study shape from stereo based on a similar two-level generative sketch representation.