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The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model. We focus primarily on the case in which the model is only allowed to translate with respect to the image. Then we consider how to extend the techniques to rigid motion (translation and rotation). The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors as occur with edge detectors and other feature extraction methods. Moreover, we show how the method extends naturally to the problem of comparing a portion of a model against an i...

Abstract—This paper addresses the problem of retrieving images from large image databases. The method is based on local grayvalue invariants which are computed at automatically detected interest points. A voting algorithm and semilocal constraints make retrieval possible. Indexing allows for efficient retrieval from a database of more than 1,000 images. Experimental results show correct retrieval in the case of partial visibility, similarity transformations, extraneous features, and small perspective deformations. Index Terms—Image retrieval, image indexing, graylevel invariants, matching, interest points. 1

A heuristic method has been developed for registering two sets of 3-D curves obtained by using an edge-based stereo system, or two dense 3-D maps obtained by using a correlation-based stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3-D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subset-subset matching. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.

A method for building flexible shape models is presented in which a shape is represented by a set of labelled points. The technique determines the statistics of the points over a collection of example shapes. The mean positions of the points give an average shape and a number of modes of variation are determined describing the main ways in which the example shapes tend to deform from the average. In this way allowed variation in shape can be included in the model. The method produces a compact flexible 'Point Distribution Model' with a small number of linearly independent parameters, which can be used during image search. We demonstrate the application of the Point Distribution Model in describing two classes of shapes. 1

. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

Abstract. Estimation techniques in computer vision applications must estimate accurate model parameters despite small-scale noise in the data, occasional large-scale measurement errors (outliers), and measurements from multiple populations in the same data set. Increasingly, robust estimation techniques, some borrowed from the statistics literature and others described in the computer vision literature, have been used in solving these parameter estimation problems. Ideally, these techniques should effectively ignore the outliers and measurements from other populations, treating them as outliers, when estimating the parameters of a single population. Two frequently used techniques are least-median of

Object recognition from sensory data involves, in part, determining the pose of a model with respect to a scene. A common method for finding an object's pose is the generalized Hough transform, which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters. Large clusters of similar transformations in that space are taken as evidence of a correct match. In this article, we provide a theoretical analysis of the behavior of such methods. We derive bounds on the set of transformations consistent with each pairing of data and model features, in the presence of noise and occlusion in the image. We also provide bounds on the likelihood of false peaks in the parameter space, as a function of noise, occlusion, and tessellation effects. We argue that blithely applying such methods to complex recognition tasks is a risky proposition, as the probability of false positives can be very high.

Abstract | This paper addresses the problem of retrieving images from large image databases. The method is based on local greyvalue invariants which are computed at automatically detected interest points. Avoting algorithm and semi-local constraints make retrieval possible. Indexing allows for e cient retrieval from a database of more than 1000 images. Experimental results show correct retrieval in the case of partial visibility, similarity transformations, extraneous features, and small perspective deformations.

A selective vision system sequentially collects evidence to support a specified hypothesis about a scene, as long as the additional evidence is worth the effort of obtaining it. Efficiency comes from processing the scene only where necessary, to the level of detail necessary, and with only the necessary operators. Knowledge representation and sequential decision-making are central issues for selective vision, which takes advantage of prior knowledge of a domain's abstract and geometrical structure and models for the expected performance and cost of visual operators. The TEA-1 selective vision system uses Bayes nets for representation and benefitcost analysis for control of visual and non-visual actions. It is the high-level control for an active vision system, enabling purposive behavior, the use of qualitative vision modules and a pointable multiresolution sensor. TEA-1 demonstrates that Bayes nets and decision theoretic techniques provide a general, re-usable framework for constructi...