Decoupling Noises and Features via Weighted -analysis Compressed Sensing
نویسندگان
چکیده
Many geometry processing applications are sensitive to noises and sharp features. Although there are a number of works on detecting noises and sharp features in the literature, they are heuristic. On the one hand, traditional denoising methods use filtering operators to remove the noises, however, may blur sharp features and shrink the object. On the other hand, noises make detection of features, which relies on computation of differential properties, unreliable and unstable. Therefore, detecting noises and features on discrete surfaces still remains challenging. In this paper, we present a novel approach for decoupling noises and features on 3D shapes. Our approach consists of two phases. In the first phase, an estimated base mesh is generated to approximate the true underlying surface of the input noisy mesh by a global Laplacian regularization denoising scheme. The base mesh is guaranteed to asymptotically converge to the underlying surface with probability one as the sample size goes to infinity. In the second phase, an `1-analysis compressed sensing optimization is proposed to recover sharp features from the residual between the base mesh and the input mesh. This is based on our discovery that sharp features can be sparsely represented in some coherent dictionary which is constructed by the pseudo-inverse matrix of the Laplacian of the shape. The features are recovered from the residual in a progressive way. Theoretical analysis and experimental results have shown that our approach reliably and robustly removes noises and extracts sharp features on 3D shapes.
منابع مشابه
Online Appendix to: Decoupling Noise and Features via Weighted 1-Analysis Compressed Sensing
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تاریخ انتشار 2013