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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Image and Vision Computing, Volume 22, Issue 10, 1 September 2004, Pages 795–806
This paper describes an improvement to the dynamic programming approach for dense stereo. Traditionally dense stereo algorithms proceed independently for each pair of epipolar lines, and then a further step is used to smooth the estimated disparities between the epipolar lines. This typically results in a streaky disparity map along depth discontinuities. In order to overcome this problem the information from corner and edge matching algorithms are exploited. Indeed we present a unified dynamic programming/statistical framework that allows the incorporation of any partial knowledge about disparities, such as matched features and known surfaces within the scene. The result is a fully automatic dense stereo system with a faster run time and greater accuracy than the standard dynamic programming method.
Automatically generating 3D models from images is an on going topic of research. A successful image to model system has been developed by the research groups at Oxford  and Leuven . The method proceeds as a set of independent modules: first features are extracted and matched, second projection matrices and calibration recovered, third a dense stereo algorithm based on dynamic programming is used to extract depths and finally a 3D model is constructed. It can be seen that this process involves two representations, one sparse and feature based, the other a dense depth map yielded by dynamic programming. Within this paper the dynamic programming algorithm for recovering the dense depth map is discussed and various improvements to its speed and accuracy are advocated, which utilize the results already obtained by the sparse feature matcher. It will be seen that this unique synthesis of the sparse and dense matching techniques leads to improved results and run times. The problem of obtaining dense correspondence along pairs of corresponding epipolar lines may be solved using dynamic programming as an optimal path finding problem on a 2D plane. However, there is no corresponding efficient method to impose a smoothness constraint between the epipolar lines. The solution along consecutive epipolar lines can vary significantly, creating artifacts across depth discontinuities and in homogeneous patches of intensity. An example of this is shown in Fig. 1. It can be seen that indeed the estimated disparity along the depth discontinuities is poor, despite being estimated by a method that attempts to enforce inter epipolar line consistency  (the epipolar lines in this case run roughly horizontally). Full-size image (33 K) Fig. 1. (a,b) The left and right images of the Pentagon standard test stereo pair obtained from the CMU VASC database (http://www.vasc.ri.cmu.edu/idb/). (c) the disparity map generated by the Cox MLMH+V algorithm, typical of the dynamic programming approach  (lighter shades indicate larger disparity). What this disparity map does not show is those pixels that are unmatched (occlusion), this will be discussed in more detail in Section 5. Note the lack of consistency between epipolar lines, which run horizontally. Figure options There have been a variety of proposals to solve the ‘streaky’ artifact. Henderson  was the first to use dynamic programming to solve the structure from motion problem. He proposed a sequential approach to impose inter epipolar line constraints, starting at the top of the image and proceeding down through the epipolar lines using the result of the previous as a guide for the next. This method, however, suffers from an avalanche effect in the errors, in that small errors made early on can be magnified as the algorithm progresses. Baker and Binford  popularized dynamic programming for stereo, explaining it in terms of the Viterbi algorithm . First using Viterbi to match edges, and then a second round of Viterbi to match pixels between edges. However, their method does not adequately deal with occlusion and cannot recover if the edges are mismatched. A slightly different idea is put forward for edgel matching by Ohta and Kanade  who propose performing dynamic programming to solve a path planning problem in the product space of the epipolar lines. To impose consistency between epipolar lines they extend the dynamic programming to 3D. However, this furnished only a sparse representation in terms of edges. A problem with the above methods is that they do not deal with occlusion very well, and have no mechanism for detecting occluded pixels. A series of methods ,  and  that were developed roughly concurrently are all characterized by the modelling of an occlusion process together with a shift to estimate a per pixel disparity (as opposed to matching edges first as in Ref.  and ). Cox et al.  propose a purely maximum likelihood approach, whereas Belhumeur  and Geiger et al.  prescribe a Bayesian philosophy. The other difference is algorithmic, all the methods can be cast as one of finding the best path through a graph, but the structure of the graphs are different. However, the methods all operate on each pair of epipolar lines independently and rely on further iterative steps to enforce smoothness constraints between epipolar lines. Recently a new class of methods based on maximum flow/minimum cut algorithms has promised to generalize the dynamic programming approach to incorporate inter epipolar line constraints. Roy and Cox  introduced a maximum flow algorithm on an undirected graph for stereo, however, as pointed out in Ref.  their method does not really generalize dynamic programming and does not model discontinuities and occlusions as all pixels are forced to have a match. Ishikawa and Geiger  propose a max flow algorithm on a directed graph with the aim of imposing constraints between epipolar lines, this approach seems interesting but there is still evidence of the streaky effect at depth discontinuities suggesting that the algorithm does not adequately enforce inter epipolar line constraints. These algorithms are also very computationally intensive when compared with the pair-wise epipolar line solutions. None of these papers exploit prior information that might already have been gathered. Within this paper we explore a class of methods that combines the sparse but accurate representations yielded by feature detectors and matchers with the dense representation yielded by dynamic programming. This paper is laid out as follows: Section 2 explains the dynamic programming approach to dense stereo. Section 3 briefly describes the feature extraction and matching algorithms. It also suggests an improvement on the edge matching by making use of the results of the corner matching. Section 4 shows how the corner and edge information can be readily incorporated into the dynamic programming framework. A comparison of the disparity map computations for our methods and for that of Cox et al.  is given in Section 5.
نتیجه گیری انگلیسی
Within this paper a new integrated methodology has been put forward. Rather than considering the corner matching, curve matching and dense stereo matching parts of the SFM process in isolation, we propose that they should be strongly entwined. We consider the output of each stage as a prior for the next stage, i.e. corner matching helps the edge matching, the corner and edge matching help the dense stereo. To do this the method of pivoting is introduced which involves modifying the cost function in the dynamic programming method of estimating dense stereo. The new pivoting method helps to enforce constraints between epipolar lines and helps to reduce ambiguity within an epipolar line for disparity estimation. Furthermore, it is shown how the corner matching can speed up the edge matching and the corner and edge matching can speed up the dense matching. This increase in speed can be by as much as a factor four. These improvements have been demonstrated on standard test sequences. Finally, we have uploaded results of a simple application, based on our novel pivoted dense stereo algorithm, for generating 3D animations from a single stereo pair, the results can be seen at http://research.microsoft.com/virtuamsr/.