Absfrucf- We present a Markov random field model which allows realistic edge modeling while providing stable maximum a posteriori MAP solutions. The proposed model, which we refer to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisifies several desirable analytical and computational properties for MAP estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global mini-mum of the U posteriori log-likeihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography. I.

This paper presents a new approach to the estimation of two-dimensional motion vector fields from time-varying images. The approach is stochastic, both in its formulation and in the solution method. The formulation involves the specification of a deterministic structural model, along with stochastic observation and motion field models. Two motion models are proposed: a globally smooth model based on vector Markov random fields and a piecewise smooth model derived from coupled vector-binary Markov random fields. Two estimation criteria are studied. In the Maximum A Posteriori Probability (MAP) estimation the a posteriori probability of motion given data is maximized, while in the Minimum Expected Cost (MEC) estimation the expectation of a certain cost function is minimized. The MAP estimation is performed via simulated annealing, while the MEC algorithm performs iteration-wise averaging. Both algorithms generate sample fields by means of stochastic relaxation implemented via the Gibbs s...

This paper presents a multiple resolution algorithm for segmenting images into regions with differing statistical behavior. In addition, an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions. Both algorithms use a causal Gaussian autoregressive (AR) model to describe the mean, variance and spatial correlation of the image textures. Together the algorithms may be used to perform unsupervised texture segmentation. The multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified. This method results in accurate segmentations and requires significantly less computation than some previously known methods. The field containing the classification of each pixel in the image is modeled as a Markov random field (MRF). Segmentation at each resolution is then performed by maximizing the a posteriori prob...

this paper should be helpful to researchers and practitioners working in the fields of video compression and processing, as well as in computer vision. Although the understanding of issues involved in the computation of motion has significantly increased over the last decade, we are still far from generic, robust, real-time motion estimation algorithms. The selection of the best motion estimator is still highly dependent on the application. Nevertheless, a broad variety of estimation models, criteria and optimization schemes can be treated in a unified framework presented here, thus allowing a direct comparison and leading to a deeper understanding of the properties of the resulting estimators.

Introduction In this chapter we are concerned with the estimation of 2-D motion from timevarying images and with the application of the computed motion to image sequence processing. Our goal for motion estimation is to propose a general formulation that incorporates object acceleration, nonlinear motion trajectories, occlusion effects and multichannel (vector) observations. To achieve this objective we use Gibbs-Markov models linked together by the Maximum A Posteriori Probability criterion which results in minimization of a multiple-term cost function. The specific applications of motion-compensated processing of image sequences are prediction, noise reduction and spatiotemporal interpolation. Estimation of motion from dynamic images is a very difficult task due to its ill-posedness [4]. Despite this difficulty, however, many approaches to the problem have been proposed in the last dozen years [27],[24],[40]. This activity can certainly be attrib

: We discuss some of the fundamental issues in the design of highly-parallel, dense, low-power motion sensors in analog VLSI. Since photoreceptor circuits are an integral part of all visual motion sensors, we discuss how the sizing of photosensitive areas can affect the performance of such systems. We review the classic gradient and correlation algorithms and give a survey of analog motion-sensing architectures inspired by them. We calculate how the measurable speed range scales with signal-tonoise ratio for a classic Reichardt sensor with a fixed time constant. We show how this speed range may be improved using a nonlinear filter with an adaptive time constant, constructed out of a diode and a capacitor, and present data from a velocity sensor based on such a filter. Finally, we describe how arrays of such velocity sensors can be employed to compute the heading direction of a moving subject and to estimate the time-to-contact between the sensor and a moving object. Keywords: motion se...

This paper examines the construction of a 3-D surface model of an object rotating in front of a camera. Previous research in depth from motion has demonstrated the power of using an incremental approach to depth estimation. In this paper, we extend this approach to more general motion and use a full 3-D surface model instead of a 2 1 = 2 -D sketch. The algorithm starts with a flow field computed using local correlation. It then projects individual measurements into 3-D points with associated uncertainties. Nearby points from successive frames are merged to improve the position estimates. These points are then used to construct a finite element surface model, which is itself refined over time. We demonstrate the application of our new techniques to several real image sequences. Keywords: Computer vision, 3-D model construction, image sequence (motion) analysis, optic flow, Kalman filter, surface interpolation, computer aided design, computer graphics animation. c flDigital Equipment C...

INTRODUCTION Young disciplines often experience moments of doubt: "Are we doing the right thing?" or "Is this approach viable?" [1]. Nowhere is this better exemplified than in the study of computer vision [2]. While progress has been made, the goal of general vision, on the order of human visual perception, remains elusive. Recently, this has led * Please address all correspondence to Michael J. Tarr, P.O. Box 208205, New Haven, CT 06520-8205, E-mail address: tarr@cs.yale.edu to the suggestion that the entire endeavor is flawed, that we should discard the dominant paradigm, and that it should be replaced with a new, more practical alternative. While this position may not qualify as a "paradigm shift" [3], it certainly advocates a substantial change in direction. To justify this radical deviation, proponents of the new, so-called purposive approach muster three lines of support: first, that machines fall far short of the visual capabilities of humans; second, that current com

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We present a model for recovering the direction of heading of an observer who is moving relative to a scene that may contain self-moving objects. The model builds upon an algorithm proposed by Rieger and Lawton (1985), which is based on earlier work by Longuet-Higgins and Prazdny (1981). The algorithm uses velocity differences computed in regions of high depth variation to estimate the location of the .focus o.f ezpansion, which indicates the observer's heading direction. We relate the behavior of the proposed model to psychophysical observations regarding the ability of human observers to judge their heading direction, and show how the model can cope with self- moving objects in the environment. We also discuss this model in the broader context of a navigational system that performs tasks requiring rapid sensing and response through the interaction of simple task-specific routines.