Impact of Wavelets and Multiwavelets Bases on Stereo Correspondence Estimation Problem

Finding correct corresponding points frommore than one perspective views in stereo vision is subject to number of potential problems, such as occlusion, ambiguity, illuminative variations and radial distortions. A number of algorithms has been proposed to address the problems as well as the solutions, in the context of stereo correspondence estimation. The majority of them can be categorized into three broad classes i.e. local search algorithms (LA) L. Di Stefano (2004); T. S. Huang (1994); Wang et al. (2006), global search algorithms (GA) Y. Boykov & Zabih (2001); Scharstein & Szeliski (1998) and hierarchical iterative search algorithms (HA) A. Bhatti (2008); C. L. Zitnick (2000). The algorithms belonging to the LA class try to establish correspondences over locally defined regions within the image space. Correlations techniques are commonly employed to estimate the similarities between the stereo image pair using pixel intensities, sensitive to illuminative variations. LA perform well in the presence of rich textured areas but have tendency of relatively lower performance in the featureless regions. Furthermore, local search using correlation windows usually lead to poor performance across the boundaries of image regions. On the other hand, algorithms belonging to GA group deals with the stereo correspondence estimation as a global cost-function optimization problem. These algorithms usually do not perform local search but rather try to find a correspondence assignment that minimizes a global objective function. GA group algorithms are generally considered to possess better performance over the rest of the algorithms. Despite of the fact of their overall better performance, these algorithms are not free of shortcomings and are dependent on how well the cost function represents the relationship between the disparity and some of its properties like smoothness, regularity. Moreover, how close that cost function representation is to the real world scenarios. Furthermore, the smoothness parameters makes disparity map smooth everywhere which may lead to poor performance at image discontinuities. Another disadvantage of these algorithms is their computational complexity, which makes them unsuitable for real-time and close-to-realtime applications. Third group of algorithms uses the concept of multi-resolution analysis Mallat (1999) in addressing the problem of stereo correspondence. In multi-resolution analysis, as is obvious from the name, the input signal (image) is divided into different resolutions, i.e. scales and spacesMallat (1999); A. Witkin & Kass (1987), before estimation of the correspondence. This group of algorithms do not explicitly state a global function that is to be minimized, but rather try to establishes correspondences in a hierarchical manner J. R. Bergen &Hingorani (1992); Q‘ingxiong Yang & Nister (2006), similar to iterative optimization algorithms Daubechies (1992). Generally, stereo correspondences established in lower resolutions are propagated to higher resolutions in an 2