Stereo Correspondence Estimation based on Wavelets and Multiwavelets Analysis

Stereo vision has long been studied and a number of techniques have been proposed to estimate the disparities and 3D depth of the objects in the scene. This is done by estimating the pixel correspondences of similar features in the stereo perspective views originated from the same 3D scene (O. Faugeras 2001; R. Hartley 2003). However, finding correct corresponding points is subject to a number of potential problems like occlusion, ambiguity, illuminative variations and radial distortions (D. Scharstein 2002). A number of algorithms have been proposed to address some of the aforementioned issues in stereo vision however it is still relatively an open problem. Current research in stereo vision has attracted a lot of focus on multiresolution techniques, based on wavelets/multiwavelets scale-space representation and analysis, for correspondence estimation (S. Mallat 1993; He-Ping Pan 1996). However, very little work has been reported in this regard. The main advantage of these algorithms is their hierarchical nature that exhibit behaviour similar to iterative optimization algorithms. These algorithms generally operate on an image pyramid where results from coarser levels are used to constrain regional search at finer levels. The coarse-to-fine techniques adopted in these algorithms are considered to be a middle approach unlike other existing algorithms where correspondences are established based either purely on local search (L. Di Stefano 2004; Q`ıngxiong Yang 2006) or as a global cost-function optimization problem (D. Scharstein 1998; M. Lin 2003) with their respective shortcomings. In this work, earlier contributions regarding the application of wavelet/multiwavelets in stereo vision is presented highlighting shortcomings, involved in those techniques such as translation and rotational variance (R. R. Coifman 1995; S. Mallat 1999) inherited in the discrete wavelet/multiwavelet transformation. Furthermore, correspondence estimation, directly using wavelet coefficients for aggregation costs, is very sensitive to noise and illuminative variation that generally exists in between the stereo perspective views. In addition, a new novel and robust algorithm is presented (Asim Bhatti 2008) using the hierarchical correspondence estimation approach where wavelets/multiwavelets transform modulus maxima (WTMM) are considered as corresponding features, addressing the issue of translation invariance. WTMM defines translation invariant features with phases pointing normal to the surface. The proposed algorithm introduced a new comprehensive selection criterion called strength of the candidate (SC) unlike many existing algorithms where selection O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m