Shift-Invariant Contourlet Transform and Its Application to Stereo Matching

Abstract

In this paper, we reformulate the conventional area-based stereo matching algorithm suffering from the windowing problem and solve it using shift-invariance contourlet transform. Multiple scale analysis has long been adopted in vision research. Investigation of the contourlet transform suggests that provide changeable window areas associated with the signal frequency components and hierarchically represent signals with multi-scale and multi-direction structure. The contourlet transform employs Laplacian pyramids to achieve multi-resolution decomposition and directional filter banks to achieve directional decomposition. It can capture the intrinsic geometrical structure that is key in visual information. Due to downsampling and upsampling, the contourlet transform is shift-variant. However, shift-invariance is desirable in stereo matching. In this paper we describe a generalization of the contourlet and the fully sampled a trous algorithm that provides approximate shift-invariance with an acceptable level of redundancy, and also discusses the advantages of applying contourlet transforms to stereo matching. An image pyramid is generated and used in the hierarchical stereo matching. That method consists of multiple passes which compute stereo matches with a coarse-to-fine and sparse-to-dense paradigm. Experimental results with real images are presented