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A new formulation of the image partitioning problem is presented: construct a complete and stable description of an image, in terms of a specified descriptive language, that is simplest in the sense of being shortest. We show that a descriptive language limited to a low-order polynomial description of the intensity variation within each region and a chain-code-like description of the region boundaries yields intuitively satisfying partitions for a wide class of images. The advantage of this formulation is that it can be extended to deal with subsequent steps of the image-understanding problem (or to deal with other image attributes, such as texture) in a natural way by augmenting the descriptive language. Experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge-detection techniques. 1 Introduction The partitioning proble...

Adaptive meshes are dynamic networks of nodal masses interconnected by adjustable springs. They are useful for nonuniformly sampling and reconstructing visual data. This paper extends the adaptive mesh model in the following ways: it (i) develops open adaptive meshes and closed adaptive shells based on triangular and rectangular elements, (ii) proposes a discontinuity detection and preservation algorithm suitable for the model, and (iii) develops techniques for adaptive hierarchical subdivision of adaptive meshes and shells. The extended model is applied to image and 3D surface data.

A variety of analytic and probabilistic models in connection to Markov random fields (MRFs) have been proposed in the last decade for solving low level vision problems involving discontinuities. This paper presents a systematic study on these models and defines a general discontinuity adaptive (DA) MRF model. By analyzing the Euler equation associated with the energy minimization, it shows that the fundamental difference between different models lies in the behavior of interaction between neighboring points, which is determined by the a priori smoothness constraint encoded into the energy function An important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing. This forms the basis on which a class of adaptive interaction functions (AIFs) is defined. The DA model is defined in terms of the Euler equation constrained by this class of AIFs. Its solution is C 1 continuous and allows arbitrarily large but bounded slopes in dealing...

Discontinuity-preserving Bayesian image restoration typically involves two Markov random fields: one representing the image intensities/gray levels to be recovered and another one signaling discontinuities/edges to be preserved. The usual strategy is to perform joint maximum a posteriori (MAP) estimation of the image and its edges, which requires the specification of priors for both fields. In this paper, instead of taking an edge prior, we interpret discontinuities (in fact their locations) as deterministic unknown parameters of the compound Gauss--Markov random field (CGMRF), which is assumed to model the intensities. This strategy should allow inferring the discontinuity locations directly from the image with no further assumptions. However, an additional problem emerges: The number of parameters (edges) is unknown. To deal with it, we invoke the minimum description length (MDL) principle; according to MDL, the best edge configuration is the one that allows the shortest description of the image and its edges. Taking the other model parameters (noise and CGMRF variances) also as unknown, we propose a new unsupervised discontinuity-preserving image restoration criterion. Implementation is carried out by a continuation-type iterative algorithm which provides estimates of the number of discontinuities, their locations, the noise variance, the original image variance, and the original image itself (restored image). Experimental results with real and synthetic images are reported.

We propose a unified approach to solve low, intermediate and high level computer vision problems for 3D object recognition from range images. All three levels of computation are cast in an optimization framework and can be implemented on neural network style architecture. In the low level computation, the tasks are to estimate curvature images from the input range data. Subsequent processing at the intermediate level is concerned with segmenting these curvature images into coherent curvature sign maps. In the high level, image features are matched against model features based on an object description called attributed relational graph (ARG). We show that the above computational tasks at each of the three different levels can all be formulated as optimizing a two-term energy function. The first term encodes unary constraints while the second term binary ones. These energy functions are minimized using parallel and distributed relaxation-based algorithms which are well suited for neural...

We derive an analytic expression for the distribution of contours x(t) generated by fluctuations in x(t) = @x(t)=@t due to random impulses of two limiting types. The first type are frequent but weak while the second are infrequent but strong. The result has applications in computational theories of figural completion and illusory contours because it can be used to model the prior probability distribution of short, smooth completion shapes punctuated by occasional discontinuities in orientation (i.e., corners). This work extends our previous work on characterizing the distribution of completion shapes which dealt only with the case of frequently acting weak impulses. 1 Introduction In a previous paper[1] we derived an analytic expression characterizing a distribution of short, smooth contours. This result has applications in ongoing work on figural completion[2] and perceptual saliency[3]. The idea that the prior probability distribution of boundary completion shapes can be characteri...

Discontinuity adaptive MRF priors have been used for modeling vision problems involving discontinuities and robust statistics models for solving regression problems involving outliers. This paper presents a comparative study of the two kinds of models. We analyze the mechanisms of adaptation (to discontinuities) and robustness (to outliers) and give a necessary condition for the adaptation and the robustness. We then give a common definition of both models. The definition captures the essence of the adaptation ability and gives in theory infinitely many choices of functions suitable for the adaptation in MRF and robust models. The likeness between the two models suggests that results in the two areas are interchangeable to benefit each other. Index terms --- Discontinuities, Markov random fields, robust statistics. Introduction Markov random field (MRF) theory provides a theoretic basis for modeling joint prior probabilities to prior contextual constraints by specifying appropriate ...

In this paper, we use vertically invariant morphological filters for time-varying or adaptive signal processing. The morphological filters adopted in this paper are vertically invariant openings and closings. Vertically invariant openings and closings have intuitive geometric interpretations and can provide different filtering scales with respect to different spacial positions. Hence, they are suitable for adaptive signal filtering. To adaptively asssign structuring elements of the vertically invariant openings or closings, we develop the progressive umbra-filling (PUF) procedure. Experimental results have shown that our approach can successfully eliminate noises without oversmoothing the important features of a signal.

: Resource discovery and information management are important problems in distributed multimedia systems. Resource discovery is based on two principal mechanisms, searching and browsing. While text based resource discovery and retrieval is currently adequately supported this is not true for non-textual media. This paper investigates the mechanisms available to support resource discovery and content based retrieval in visual data. 1. INTRODUCTION There is a growing trend in distributed information systems to incorporate increasingly greater amounts of multimedia data. While good support for resource discovery and retrieval services exists for textual data, this is simply not the case for visual data such as images and videos. This situation is unfortunate in light of the current transition away from textual data to multimedia data in many information systems. In this scenario adequate support for retrieval and mechanisms for resource discovery of visual data becomes imperious to the l...