Abstract-The scale-space technique introduced by Witkin involves generating coarser resolution images by convolving the original image with a Gaussian kernel. This approach has a major drawback: it is difficult to obtain accurately the locations of the “semantically mean-ingful ” edges at coarse scales. In this paper we suggest a new definition of scale-space, and introduce a class of algorithms that realize it using a diffusion process. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing in preference to interregion smoothing. It is shown that the “no new maxima should be generated at coarse scales ” property of conventional scale space is pre-served. As the region boundaries in our approach remain sharp, we obtain a high quality edge detector which successfully exploits global information. Experimental results are shown on a number of images. The algorithm involves elementary, local operations replicated over the image making parallel hardware implementations feasible. Index Terms-Adaptive filtering, analog VLSI, edge detection, edge enhancement, nonlinear diffusion, nonlinear filtering, parallel algo-

A major goal of research on networks of neuron-like processing units is to discover efficient learning procedures that allow these networks to construct complex internal representations of their environment. The learning procedures must be capable of modifying the connection strengths in such a way that internal units which are not part of the input or output come to represent important features of the task domain. Several interesting gradient-descent procedures have recently been discovered. Each connection computes the derivative, with respect to the connection strength, of a global measure of the error in the performance of the network. The strength is then adjusted in the direction that decreases the error. These relatively simple, gradient-descent learning procedures work well for small tasks and the new challenge is to find ways of improving their convergence rate and their generalization abilities so that they can be applied to larger, more realistic tasks.

Abstract—Many image processing problems are ill posed and must be regularized. Usually, a roughness penalty is imposed on the solution. The difficulty is to avoid the smoothing of edges, which are very important attributes of the image. In this paper, we first give conditions for the design of such an edge-preserving regularization. Under these conditions, we show that it is possible to introduce an auxiliary variable whose role is twofold. First, it marks the discontinuities and ensures their preservation from smoothing. Second, it makes the criterion half-quadratic. The optimization is then easier. We propose a deterministic strategy, based on alternate minimizations on the image and the auxiliary variable. This leads to the definition of an original reconstruction algorithm, called ARTUR. Some theoretical properties of ARTUR are discussed. Experimental results illustrate the behavior of the algorithm. These results are shown in the field of tomography, but this method can be applied in a large number of applications in image processing. 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...

DCPS is a connectionist production system interpreter that uses distributed repre-sentations. As a connectionist model it consists of many simple, richly intercon-nected neuron-like computing units that cooperate to solve problems in parallel. One motivation far constructing DCPS was to demonstrate that connectionist models ore copable of representing and using explicit rules. A second motivation was to show how “coarse coding ” or “distributed representations ” can be used to construct a working memory that requires far fewer units than the number of dif-ferent facts that can potentially be stored. The simulation we present is intended as a detailed demonstration of the feasibility of certain ideas and should not be viewed as a full implementation of production systems. Our current model only has o few of the many interesting emergent properties that we eventually hope to demonstrate: It is damage-resistant, it performs matching and variable bind-ing by massively parallel constraint satisfaction, and the capacity of its working memory is dependent on the similarity of the items being stored. 1.

Given a collection of similar signals that have been deformed with respect to each other, the general signal-matching problem is to recover the deformation. We formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term. The minimization reduces to a dynamic system governed by a set of coupled, first-order differential equations. The dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale. Among the major themes in recent work on visual signal matching have been the notions of matching as constrained opti-mization, of variational surface reconstruction, and of coarse-to-fine matching. Our solution captures these in a precise, succinct, and unified form. Results are presented for one-dimensional signals, a motion sequence, and a stereo pair. 1

Many problems in early vision can be formulated in terms of minimizing an' energy or cost function. Examples are shape-from-shading, edge detection, motion snatysis, structure from motion and surface interpolation (Poggio, Torre and Koch, 1985). It has been shown that all quadratic variational problems, an important subset of early vision tasks, can be "solved" by linear, analog electrical or chemical networks (Poggio and Koch, 1985). In a variety of situations the cost function is non-quadratic, however, for instance in the presence of discontinuities. The use of non-quadratic cost functions raises the question of designing efficient algorithms for computing the optimal solution. Recently. Hopfield and Tank (1985) have shown that networks of nonlinear analog "neurons" can be effect. lye in computing the solution of optimization problems, In this paper, we show how these networks can be generalized to solve the non-convex energy functionals of early vision. We illustrate this approach by implementing a specific network solving the problem of reconstructing a smooth surface while preserving its discontinuities from sparsely sampled data (Geman and Geman, 1984; Marroquin, 1984; Terzopoulos, 1984). These results suggest a novel computational strategy for solving such problems for both biological and artificial vision systems.

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...

A constrained optimization method, called the Lagrange-Hopfield (LH) method, is presented for solving Markov random field (MRF) based Bayesian image estimation problems for restoration and segmentation. The method combines the augmented Lagrangian multiplier technique with the Hopfield network to solve a constrained optimization problem into which the original Bayesian estimation problem is reformulated. The LH method effectively overcomes instabilities that are inherent in the penalty method (e.g. Hopfield network) or the Lagrange multiplier method in constrained optimization. An additional advantage of the LH method is its suitability for neural-like analog implementation. Experimental results are presented which show that LH yields good quality solutions at reasonable computational costs. 1. INTRODUCTION Image restoration is to recover a degraded image and segmentation is to partition an image into regions of similar image properties. Both can be posed generally as image estimation...

Sensitivity to variations in illumination is a fundamental and challenging problem in face recognition. In this paper, we describe a new method based on symmetric shape-from-shading (SFS) to develop a face recognition system that is robust to changes in illumination. The basic idea of this approach is to use the symmetric SFS algorithm as a tool to obtain a prototype image which is illumination-normalized. Applying traditional SFS algorithms to real images of complex objects (in terms of their shape and albedo variations) such as faces is very challenging. It is shown that the symmetric SFS algorithm has a unique point-wise solution. In practice, given a single real face image with complex shape and varying albedo, even the symmetric SFS algorithm cannot guarantee the recovery of accurate and complete shape information. For the particular problem of face recognition, we utilize the fact that all faces share a similar shape making the direct computation of the prototype image from a giv...