Belief propagation (BP) has been successfully used to approximate the solutions of various Markov random field (MRF) formulated energy minimization problems. However, large MRFs require a significant amount of memory to store the intermediate belief messages. We observe that these messages have redundant information due to the imposed smoothness prior. In this paper, we study the feasibility of applying compression techniques to the messages in the min-sum/max-product BP algorithm with 1D labels to improve the memory efficiency and reduce the read/write bandwidth. We articulate properties that an efficient message representation should satisfy. We investigate two common compression schemes, predictive coding and linear transform coding (PCA), and then propose a novel envelope point transform (EPT) method. Predictive coding is efficient and supports linear operations directly in the compressed domain, but it is only compatible with the L1smoothness function. PCA has the disadvantage that it does not guarantee the preservation of the minimal label. EPT is not limited to L1smoothness cost and allows a flexible quality vs. compression ratio tradeoff compared with predictive coding. Experiments on dense stereo reconstruction have shown that the predictive scheme and EPT can achieve 8times or more compression without significant loss of depth accuracy.

Similarity-based retrieval from shape databases typically employs a pairwise shape matcher and one or more indexing techniques. In this paper, we focus specifically on the design of a pairwise matcher for retrieval of 2-D shape contours. In the past, the matchers used for the one-to-many problem of shape retrieval were often designed for the problem of matching an isolated pair of shapes. This approach fails to exploit two characteristics of the one-to-many matching problem that distinguish it from the one-to-one matching problem. First, the output of shape retrieval systems tends to be dominated by matches to relatively similar shapes. In this paper, we demonstrate that by not expending computational resources on unneeded accuracy of matching, both the speed and the accuracy of retrieval can be increased. Second, the shape database is a large statistical sample of the population of shapes. We introduce a probabilistic model for exploiting that statistical knowledge to further increase retrieval accuracy. The model has several benefits: (1) It does not require class labels on the database shapes, thus supporting unlabeled retrieval. (2) It does not require feature independence. (3) It is parameter-free. (4) It has a fast runtime implementation. The probabilistic model is general and thus potentially applicable to other one-to-many matching problems.

Both example-based and model-based approaches for classifying contour shapes can encounter difficulties when dealing with classes that have large nonlinear variability, especially when the variability is structural or due to articulation. This paper proposes a part-based approach to address this problem. Bayesian classification is performed within a three-level framework, which consists of models for contour segments, for classes, and for the entire database of training examples. The class model enables different parts of different exemplars of a class to contribute to the recognition of an input shape. The method is robust to occlusion and is invariant to planar rotation, translation, and scaling. Furthermore, the method is completely automated. It achieves 98% classification accuracy on a large database with many classes.

This paper presents a one-stage stereo algorithm that yields 3D planar surface patches directly from matching image patch intensity information. The method allows an arbitrary rotation and translation between the cameras; it is not limited to parallel-axis, narrow-baseline, or vergent geometries. The key to the approach is to match image patches that have positions, shapes, sizes, orientations, and samplings consistent with a hypothesized surface patch and with each other. The match error then reflects only the mismatch of patch contents and not the mismatch of patch geometries or samplings. The algorithm is quantitatively evaluated against ground truth on real images with difficult viewing geometries, and demonstrates an average accuracy of about 1% in estimating surface depths and 10/spl deg/ in estimating surface normals.

Presents a non-feature-based solution to the problem of computing the shape of curved surfaces from texture information. First, the use of local spatial-frequency spectra and their moments to describe texture is discussed and motivated. A new, more accurate method for measuring the local spatial-frequency moments of an image texture using Gabor elementary functions and their derivatives is presented. Also described is a technique for separating shading from texture information, which makes the shape-from-texture algorithm robust to the shading effects found in real imagery. Second, a detailed model for the projection of local spectra and spectral moments of any surface reflectance patterns (not just textures) is developed. Third, the conditions under which the projection model can be solved for the orientation of the surface at each point are explored. Unlike earlier non-feature-based, curved surface shape-from-texture approaches, the assumption that the surface texture is isotropic is not required; surface texture homogeneity can be assumed instead. The algorithm's ability to operate on anisotropic and nondeterministic textures, and on both smooth- and rough-textured surfaces, is demonstrated.>

A closed-form solution to the problem of computing 3D curved-surface shape from texture cues is presented. An expression showing the dependence of localized image spectral moments on localized surface spectral moments and on local surface orientation is derived. The local image spectra are measured with wavelets, and the expression is solved for the surface orientation at each point. Because the method uses localized spectral information, it operates at a very low level in the visual hierarchy. No extraction of texture or edge elements is required. The wavelet-based computation used is biologically plausible, easily parallelized for rapid computation, and has been shown to be the basis for effective solutions to a variety of other vision tasks. The method is demonstrated on a number of real-world examples.>