Abstract. Stereo matching is one of the most active research areas in computer vision. While a large number of algorithms for stereo correspondence have been developed, relatively little work has been done on characterizing their performance. In this paper, we present a taxonomy of dense, two-frame stereo methods. Our taxonomy is designed to assess the different components and design decisions made in individual stereo algorithms. Using this taxonomy, we compare existing stereo methods and present experiments evaluating the performance of many different variants. In order to establish a common software platform and a collection of data sets for easy evaluation, we have designed a stand-alone, flexible C++ implementation that enables the evaluation of individual components and that can easily be extended to include new algorithms. We have also produced several new multi-frame stereo data sets with ground truth and are making both the code and data sets available on the Web. Finally, we include a comparative evaluation of a large set of today’s best-performing stereo algorithms.

In this paper we consider the problem of computing the 3D shape of an unknown, arbitrarily-shaped scene from multiple photographs taken at known but arbitrarilydistributed viewpoints. By studying the equivalence class of all 3D shapes that reproduce the input photographs, we prove the existence of a special member of this class, the photo hull, that (1) can be computed directly from photographs of the scene, and (2) subsumes all other members of this class. We then give a provably-correct algorithm, called Space Carving, for computing this shape and present experimental results on complex real-world scenes. The approach is designed to (1) build photorealistic shapes that accurately model scene appearance from a wide range of viewpoints, and (2) account for the complex interactions between occlusion, parallax, shading, and their effects on arbitrary views of a 3D scene. 1.

This paper describes a new algorithm for solving the N-camera stereo correspondence problem by transforming it into a maximum-flow problem. Once solved, the minimum-cut associated to the maximumflow yields a disparity surface for the whole image at once. This global approach to stereo analysis provides a more accurate and coherent depth map than the traditional line-by-line stereo. Moreover, the optimality of the depth surface is guaranteed and can be shown to be a generalization of the dynamic programming approach that is widely used in standard stereo. Results show improved depth estimation as well as better handling of depth discontinuities. While the worst case running time is O(n 2 d 2 log(nd)), the observed average running time is O(n 1:2 d 1:3 ) for an image size of n pixels and depth resolution d. 1 Introduction It is well known that depth related displacements in stereo pairs always occur along lines associated to the camera motion, the epipolar lines. These lines r...

In this paper, we formulate the stereo matching problem as a Markov network and solve it using Bayesian belief propagation. The stereo Markov network consists of three coupled Markov random fields that model the following: a smooth field for depth/disparity, a line process for depth discontinuity, and a binary process for occlusion. After eliminating the line process and the binary process by introducing two robust functions, we apply the belief propagation algorithm to obtain the maximum a posteriori (MAP) estimation in the Markov network. Other low-level visual cues (e.g., image segmentation) can also be easily incorporated in our stereo model to obtain better stereo results. Experiments demonstrate that our methods are comparable to the state-of-the-art stereo algorithms for many test cases.

Markov Random Fields (MRF’s) can be used for a wide variety of vision problems. In this paper we focus on MRF’s with two-valued clique potentials, which form a generalized Potts model. We show that the maximum a posteriori estimate of such an MRF can be obtained by solving a multiway minimum cut problem on a graph. We develop efficient algorithms for computing good approximations to the minimum multiway cut. The visual correspondence problem can be formulated as an MRF in our framework; this yields quite promising results on real data with ground truth. We also apply our techniques to MRF’s with linear clique potentials. 1

Proceedings of the 1998IEEE International Conference on Computer Vision, Bombay, India An algorithm to detect depth discontinuities from a stereo pair of images is presented. The algorithm matches individual pixels in corresponding scanline pairs while allowing occluded pixels to remain unmatched, then propagates the information between scanlines by means of a fast postprocessor. The algorithm handles large untextured regions, uses a measure of pixel dissimilarity that is insensitive to image sampling, and prunes bad search nodes to increase the speed of dynamic programming. The computation is relatively fast, taking about 1.5 microseconds per pixel per disparity on a workstation. Approximate disparity mapsand precise depth discontinuities (along both horizontal and vertical boundaries) are shown for five stereo images containing textured, untextured, fronto-parallel, and slanted objects. 1 Introduction Cartoon artists have known the perceptual importance of depth discontinuities for...

A method for solving the stereo matching problem in the presence of large occlusion is presented. A data structure — the disparity space image — is defined to facilitate the description of the effects of occlusion on the stereo matching process and in particular on dynamic programming (DP) solutions that find matches and occlusions simultaneously. We significantly improve upon existing DP stereo matching methods by showing that while some cost must be assigned to unmatched pixels, sensitivity to occlusion-cost and algorithmic complexity can be significantly reduced when highly-reliable matches, or ground control points, are incorporated into the matching process. The use of ground control points eliminates both the need for biasing the process towards a smooth solution and the task of selecting critical prior probabilities describing image formation. Finally, we describe how the detection of intensity edges can be used to bias the recovered solution such that occlusion boundaries will tend to be proposed along such edges, reflecting the observation that occlusion boundaries usually cause intensity discontinuities.

In this paper, we propose a symmetric stereo model to handle occlusion in dense two-frame stereo. Our occlusion reasoning is directly based on the visibility constraint that is more general than both ordering and uniqueness constraints used in previous work. The visibility constraint requires occlusion in one image and disparity in the other to be consistent. We embed the visibility constraint within an energy minimization framework, resulting in a symmetric stereo model that treats left and right images equally. An iterative optimization algorithm is used to approximate the minimum of the energy using belief propagation. Our stereo model can also incorporate segmentation as a soft constraint. Experimental results on the Middlebury stereo images show that our algorithm is state-of-the-art. 1

A stereo vision system that is required to support high-level object based tasks in a tele-operated environment is described. Stereo vision is computationally expensive, due to having to find corresponding pixels. Correlation is a fast, standard way to solve the correspondence problem. This paper analyses the behaviour of correlation based stereo to find ways to improve its quality while maintaining its realtime suitability. Three methods are suggested. Two of them aim to improve the disparity image especially at depth discontinuities, while one targets the identification of possible errors in general. Results are given on real stereo images with ground truth. A comparison with five standard correlation methods shows that improvements of simple stereo correlation are possible in real-time on current computer hardware.

In this paper a new rectification method is proposed. The method is both simple and efficient and can deal with all possible camera motions. A minimal image size without any pixel loss is guaranteed. The only required information is the oriented fundamental matrix. The whole rectification process is carried out directly in the images. The idea consists of using a polar parametrization of the image around the epipole. The transfer between the images is obtained through the fundamental matrix. The proposed method has important advantages compared to the traditional rectification schemes. In some cases these approaches yield very large images or can not rectify at all. Even the recently proposed cylindrical rectification method can encounter problems in some cases. These problems are mainly due to the fact that the matching ambiguity is not reduced to half epipolar lines. Although this last method is more complex than the one proposed in this paper the resulting images are in general larger. The performance of the new approach is illustrated with some results on real image pairs. 1.