In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an α-βswap: for a pair of labels α, β, this move exchanges the labels between an arbitrary set of pixels labeled α and another arbitrary set labeled β. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an α-expansion: for a label α, this move assigns an arbitrary set of pixels the label α. Our second

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.

Relations between anisotropic diffusion and robust statistics are described in this paper. Specifically, we show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The "edge-stopping" function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework. This connection leads to a new "edge-stopping" function based on Tukey's biweight robust estimator, that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in an image that has been smoothed with anisotropic diffusion. Additionally, we derive a relationship between anisotropic diffusion and regularization with line processes. Adding constraints on the spatial organization of the ...

The modeling of spatial discontinuities for problems such as surface recovery, segmentation, image reconstruction, and optical flow has been intensely studied in computer vision. While "line-process" models of discontinuities have received a great deal of attention, there has been recent interest in the use of robust statistical techniques to account for discontinuities. This paper unifies the two approaches. To achieve this we generalize the notion of a "line process" to that of an analog "outlier process" and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics. We also characterize a class of robust statistical problems for which an equivalent outlier-process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier-process formulation. We show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier-process formulation. These results indicate that the outlier-process approach provides a general framework which subsumes the traditional line-process approaches as well as a wide class of robust estimation problems. Examples in surface reconstruction, image segmentation, and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited. An appendix provides a catalog of common robust error norms and their equivalent outlier-process formulations.

Abstract. One of the most exciting advances in early vision has been the development of efficient energy minimization algorithms. Many early vision tasks require labeling each pixel with some quantity such as depth or texture. While many such problems can be elegantly expressed in the language of Markov Random Fields (MRF’s), the resulting energy minimization problems were widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the top-performing stereo methods. Unfortunately, most papers define their own energy function, which is minimized with a specific algorithm of their choice. As a result, the tradeoffs among different energy minimization algorithms are not well understood. In this paper we describe a set of energy minimization benchmarks, which we use to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods—graph cuts, LBP, and tree-reweighted message passing—as well as the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching and interactive segmentation. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods with minimal overhead. We expect that the availability of our benchmarks and interface will make it significantly easier for vision researchers to adopt the best method for their specific problems. Benchmarks, code, results and images are available at

While stereo matching was originally formulated as the recovery of 3D shape from a pair of images, it is now generally recognized that using more than two images can dramatically improve the quality of the reconstruction. Unfortunately, as more images are added, the prevalence of semioccluded regions (pixels visible in some but not all images) also increases. In this paper, we propose some novel techniques to deal with this problem. Our first idea is to use a combination of shiftable windows and a dynamically selected subset of the neighboring images to do the matches. Our second idea is to explicitly label occluded pixels within a global energy minimization framework, and to reason about visibility within this framework so that only truly visible pixels are matched. Experimental results show a dramatic improvement using the first idea over conventional multibaseline stereo, especially when used in conjunction with a global energy minimization technique. These results also show that explicit occlusion labeling and visibility reasoning do help, but not significantly, if the spatial and temporal selection is applied first.

A selective vision system sequentially collects evidence to support a specified hypothesis about a scene, as long as the additional evidence is worth the effort of obtaining it. Efficiency comes from processing the scene only where necessary, to the level of detail necessary, and with only the necessary operators. Knowledge representation and sequential decision-making are central issues for selective vision, which takes advantage of prior knowledge of a domain's abstract and geometrical structure and models for the expected performance and cost of visual operators. The TEA-1 selective vision system uses Bayes nets for representation and benefitcost analysis for control of visual and non-visual actions. It is the high-level control for an active vision system, enabling purposive behavior, the use of qualitative vision modules and a pointable multiresolution sensor. TEA-1 demonstrates that Bayes nets and decision theoretic techniques provide a general, re-usable framework for constructi...

ms (we show that exact minimization in NP-hard in these cases). These algorithms produce a local minimum in interesting large move spaces. Furthermore, one of them nds a solution within a known factor from the optimum. The algorithms are iterative and compute several graph cuts at each iteration. The running time at each iteration is eectively linear due to the special graph structure. In practice it takes just a few iterations to converge. Moreover most of the progress happens during the rst iteration. For a certain piecewise constant prior we adapt the algorithms developed for the piecewise smooth prior. One of them nds a solution within a factor of two from the optimum. In addition we develop a third algorithm which nds a local minimum in yet another move space. We demonstrate the eectiveness of our approach on image restoration, stereo, and motion. For the data with ground truth, our methods signicantly outperform standard methods. Biographical Sketch Olga

. This paper presents a novel variational method for image segmentation that unifies boundary and region-based information sources under the Geodesic Active Region framework. A statistical analysis based on the Minimum Description Length criterion and the Maximum Likelihood Principle for the observed density function (image histogram) using a mixture of Gaussian elements, indicates the number of the different regions and their intensity properties. Then, the boundary information is determined using a probabilistic edge detector, while the region information is estimated using the Gaussian components of the mixture model. The defined objective function is minimized using a gradientdescent method where a level set approach is used to implement the resulting PDE system. According to the motion equations, the set of initial curves is propagated toward the segmentation result under the influence of boundary and region-based segmentation forces, and being constrained by a regul...

We present a Bayesian framework that combines motion (optical flow) estimation and segmentation based on a representation of the motion field as the sum of a parametric field and a residual field. The parameters describing the parametric component are found by a least squares procedure given the best estimates of the motion and segmentation fields. The motion field is updated by estimating the minimum-norm residual field given the best estimate of the parametric field, under the constraint that motion field be smooth within each segment. The segmentation field is updated to yield the minimum-norm residual field given the best estimate of the motion field, using Gibbsian priors. The solution to successive optimization problems are obtained using the highest confidence first (HCF) or iterated conditional mode (ICM) optimization methods. Experimental results on real video are shown. 1 Introduction Robust motion estimation and segmentation are fundamental to such applications as multiple...