Cloth is a complex visual pattern with flexible 3D shape and illumination variations. Computing the 3D shape of cloth from a single image is of great interest to both computer graphics and vision researches. However, the acquisition of 3D cloth shape by Shape from Shading (SFS) is still a challenge. In this paper, we present a two-layer generative model for representing both the 2D cloth image and the 3D cloth surface. The first layer represents all the folds on cloth, which are called "shading primitives" in [4], and thus captures the overall "skeleton structures" of cloth. We learn a number of typical 3D fold primitives using some training images obtained through photometric stereo. The 3D fold primitives yield a dictionary of 2D shading primitives for cloth images. The second layer represents non-fold parts with very smooth (often flat) surface or shading, which interpolates the primitives in the first layer with a smoothness prior like conventional SFS. Then we present an algorithm called "cloth sketching" to find all the shading primitives on cloth image and simultaneously recover their 3D shape by fitting to the 3D fold primitives. Our sketch representation can be viewed as a 2-layer Markov random field (MRF), and it introduces some prior knowledge on the folds and has lower dimension and is more robust than the traditional shape-from-shading representation which assumes a MRF model on pixels. We show a number of experiments with satisfactory results in comparison to previous work.
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