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.

We present a novel method for the geometric alignment of autoradiographs of the brain. The method is based on finding the spatial mapping and the one-to-one correspondences (or homologies) between point features extracted from the images and rejecting non-homologies as outliers. In this way, we attempt to account for the local natural and artifactual differences between the autoradiograph slices. We have executed the resulting automated algorithm on a set of left prefrontal cortex autoradiograph slices, specifically demonstrated its ability to perform point outlier rejection, validated it using synthetically generated spatial mappings and provided a visual comparison against the well known iterated closest point (ICP) algorithm. Visualization of a stack of aligned left prefrontal cortex autoradiograph slices is also provided.

A general variational framework for image approximation and segmentation is introduced. By using a continuous "line-process" to represent edge boundaries, it is possible to formulate a variational theory of image segmentation and approximation in which the boundary function has a simple explicit form in terms of the approximation function. At the same time, this variational framework is general enough to include the most commonly used objective functions. Application is made to Mumford--Shah type functionals as well as those considered by Geman and others. Employing arbitrary LLL ppp norms to measure smoothness and approximation allows the user to alternate between a least squares approach and one based on total variation, depending on the needs of a particular image. Since the optimal boundary function that minimizes the associated objective functional for a given approximation function can be found explicitly, the objective functional can be expressed in a reduced form that depends ...

The optical-flow approach has emerged as a major technique for estimating scene and object motion in image sequences. However, the results obtained by most optical flow techniques are strongly affected by motion discontinuities and by large illumination changes. While there do exist many separate techniques for robust estimation of optical flow in the presence of motion discontinuities and for dealing with the problems caused by illumination variations, only a few integrated approaches have been proposed. How-ever, most of these previously proposed integrated approaches use simple models of illumination variation; a common assumption being that illumination changes by either just a multiplicative factor or just an additive factor from frame to frame, but not both. Some other previously proposed integrated approaches are limited to specialized tasks such as image registration or change recovery. To remedy this shortcoming, this paper presents a new robust approach to general motion estimation in an integrated framework. Our approach deals simultaneously with motion discontinuities and large illumination variations. Our model of illumination variation is general, in the sense that it admits both multiplicative and additive effects. Keywords: Motion estimation, optical-flow, illumination, robust statistics. 1

. We introduce a new prior---the weak plate---to Bayesian tomographic reconstruction. The weak plate captures the piecewise ramplike spatial structure evident in primate autoradiograph source distributions. The weak plate is a part of a family of "mechanical" models---weak membrane (1st order), weak plate (2nd order), and weak quadric (3rd order)---in which a class of smoothness constraints derived from properties of ideal physical materials are used as models in the associated reconstruction problem. Since "weak" priors generate local minima in MAP estimation, we have designed novel Generalized Expectation--Maximization deterministic annealing algorithms to alleviate this problem. Our simulation studies qualitatively demonstrate the improvements over the weak membrane and maximum likelihood reconstructions. Key words: tomographic reconstruction, weak plate, piecewise smooth, deterministic annealing, expectation--maximization, free energy, saddle point. 1. Introduction Maximum likel...