Abstract: Inspired by recent developments in computational morphology, this paper discusses their potential impact on research undertaken in the field of spatial analysis addressing the characterization and recognition of form in point sets. A brief discussion of point pattern recognition methods now common in spatial analysis is included, pointing to their limitations and questioning their success. The main focus of the paper, however, is the examination of recent methods of geometric decomposition that appear more useful for solving questions concerning form. New techniques based in computational morphology may very well revolutionize the characterization of point sets for spatial analysts. Some of these techniques are referenced and briefly discussed here, including their potential applications to point pattern recognition problems in spatial analysis.

Abstract: A number of methods are available in the literature to estimate the class-conditional densities for pattern classification. The Parzen-window method of density estimation is studied with emphasis on techniques for optimal window-width estimation. We report the window-widths obtained by using the BOOTSTRAP technique and compare them with MSE, MEISER and the LEAVE-ONE-OUT techniques. The performance of classifiers based on the Parzen window density estimate is compared with other well-known classifiers such as linear, quadratic, K-Nearest Neighbor, and binary tree on several real data sets.

Abstract: In this paper we report on one aspect of work in progress in restricted-orientation geometry. We investigate various alternative definitions of convexity in this setting rather than the standard definition. At the same time, we indicate how a firm mathematical foundation for these notions can be obtained.

Abstract: Several algorithms for finding symmetries of geometrical objects have recently appeared. In this paper the results are surveyed, and some problems which remain open are described.

Abstract: Guard placement problems have been extensively studied by mathematicians as well as computer scientists. The classical guard problem posed by Victor Klee is to determine the number of guards sufficient to see any art gallery given as an n -vertex simple polygon. Here we study traditional (or rectilinear) art-galleries, i.e. galleries in which all interior angles are either 270° or 90°. The Rectilinear Art Gallery Theorem originally proved by Kahn, Klawe and Kleitman states that any n-vertex rectilinear art gallery can always be guarded by at most [ n /4 J guards. Here we examine the problem from its computational point-of-view by providing an algorithmic proof of the Rectilinear Art Gallery Theorem. It is demonstrated that guard placement in monotone rectilinear polygons can be done in linear time, while the problem can be solved for arbitrary, nvertex, rectilinear polygons in 0 ( n loglog n ) time.

Abstract: As tools for the construction of expert systems have become commonly available, workers in artificial intelligence (AI) have begun to pay increasing attention to the problems of building and maintaining large knowledge bases. In particular, considerable discussion has concentrated on the difficulty of eliciting useful and complete knowledge about a given application task from experts—a problem widely referred to as the knowledgeacquisition bottleneck. At the same time, AI researchers have often noted that the systems that they build are brittle, showing marked degradation in reasoning performance when confronted with unusual or atypical cases. Most expert systems, like pattern-recognition systems, are concerned with the classification of entities in the world. The process of building knowledge bases for expert systems that perform classification, like the process of developing statistical classifiers, requires that someone who is familiar with the application area both determine the relevant types of objects in the domain and identify the observable features of those objects that may be germane to the classification problem. In the case of both expert systems and pattern-recognition systems, developers must create models of the application area. Although the pattern-recognition literature does not generally mention concepts such as “knowledge acquisition” or “brittleness,” these problems are also important in the construction of statistical models. This paper shows how builders of expert and patternrecognition systems face many of the same challenges, and discusses ways in which the two research communities can learn from each other's experiences in creating different types of computational models for classification tasks.

Abstract: Two planar point sets S 1 and S 2 are circularly separable if there is a circle that encloses S 1 but excludes S 2 . In this note an O((| S 1 |+| S 2 |)log ((| S 1 |+| S 2 |)) algorithm is presented to determine the set S( S 1 , S 2 ) of points which are centers of circles that enclose S 1 but exclude S 2 . It is then shown that once S( S 1 , S 2 ) is known, all the smallest and the largest separating circles can be computed very easily.

Abstract: The symmetries in a neighbourhood of a gray value image are modelled by conjugate harmonic function pairs. These are shown to be a suitable curve linear coordinate pair, in which the model represents a neighbourhood. In this representation the image parts, which are symmetric with respect to the chosen function pair, have iso-gray value curves which are simple lines or parallel line patterns. The detection is modelled in the special Fourier domain corresponding to the new variables by minimizing an error function. It is shown that the minimization process or detection of these patterns can be carried out for the whole image entirely in the spatial domain by convolutions. What will be defined as the partial derivative image is the image which takes part in the convolution. The convolution kernel is complex valued, as are the partial derivative image and the result. The magnitudes of the result are shown to correspond to a well defined certainty measure, while the orientation is the least square estimate of an orientation in the Fourier transform corresponding to the harmonic coordinates. Applications to four symmetries are given. These are circular, linear, hyperbolic and parabolic symmetries. Experimental results are presented.

Abstract: We have developed and evaluated an edge detection scheme using a non-linear Laplace operator and the Marr-Hildreth model of edge detection. The technique is extremely effective and flexible in detecting one-pixel thick edges in images whose signal-to-noise ratios (SNR) range from 40 dB down to 0 dB. We have compared our results with those in the literature. For the test images we considered, our configuration performs at least as well - and in most cases far better - than other edge detectors. For these comparisons we have used Pratt's figure-of-merit as a quantitative performance measure. At very low signal-to-noise ratios ( Specific characterizations of the non-linear Laplacian are its adaptive orientation to the direction of the gradient, its inherent masks which permit the development of approximately circular (isotropic) filters, and its easy and fast implementation in software.

Abstract: This paper describes part of a system for chromosome aberration scoring by detecting dicentric chromosomes. Although it has been programmed in a traditional procedural computing style, it aims to combine multiple knowledge sources and to use model-determined constraints in an adaptive classifier to provide a high performance level. Chromosome centromere candidates are independendy hypothesised by structural analysis of the chromosome boundary and by analysis of the density distribution along the chromosome axis. For each candidate of either type, a common feature set which is based on a third, independent structural analysis, is measured in order to test the hypotheses. A classifier for centromere candidates is constructed from the set of candidates within a cell itself, by constraining feature space using strong model assumptions. The relationship of the analysis components described to a proposed complete system is outlined.

Abstract: In this article, we present neighbor relations among figures on a 2-D digitized picture. First those relations (the Voronoi neighbor, the relative neighbor, and the Gabriel neighbor) are extended to a set of connected components (arbitrary shapes of figures). Second, several procedures to obtain those neighbor relations from a given binary image are described with estimation of the amount of computation required. Finally applications of the adjacency graphs induced from the above neighbor relations to texture analysis are described with the results of experiments.

Abstract: The analysis of images has traditionally been confined to the domain of the minicomputer (and larger). With the advent of technology such as the MC-680×0 it is now possible to analyse complex images on personal computers in reasonable time. The Acuity software package provides such a possibility for the measurement of the properties of objects in an image. The package, written entirely in C, consists of approximately 120 kB of code and provides image segmentation into the individual objects (automatic and/or interactive), measurement of object features, and measurement statistics. Automatic image segmentation is generally based upon histogram analysis with the possibility of pre-filtering. Interactive segmentation makes use of a mouse interface. After the image has been split into the individual objects, measurements are performed. The features fall into several categories: Position (2 measures), Size (2 measures), Shape (6 measures), Intensity (2 measures), and Texture (4 measures). The formulas used to compute the measures are based upon recent developments in digital-image measurement theory. A number of utilities are available to define an experiment (e.g., to choose which features need to be measured), to print a summary of the measured data, to print a limited set of descriptive statistics, or to format the output data (feature vectors) in a manner that is compatible with commercially available data analysis software (e.g., StatWorks™, MacSpin™, Excel™). The complete analysis of a 256 2 image that contains approximately 60 objects each with an approximate diameter of 25 pixels takes about 35 seconds. This is on a personal computer that uses a MC-68020 with a clock frequency of 16 MHz and a MC-68881 floating point co-processor.

Abstract: This note investigates the computational complexity of a special kind of decomposition of polygons into convex, star-shaped, and spiral components. In these polygon decompositions, the boundary of the resulting component is composed of edges which are segments of lines passing through any two vertices of the polygon and the resulting components are allowed to overlap each other. We point out that for certain kinds of components (such as star-shaped), the problem of finding the minimum number of, possibly, overlapping pieces remains NP-hard even under this restriction and we provide an approximate algorithm that yields a solution that is guaranteed to be at most O (log n ) times the optimal. We also provide an application of our approximate algorithm to guarding art galleries with almost the minimum number of watchmen. Index Terms: pattern recognition, polygon decompositions, art gallery problem, convex, star-shaped, spiral-shaped, covers, NP-complete, approximation algorithms.

Abstract: A stereo correspondence method designed to reconstruct a threedimensional image of the cerebral blood vessels is described. Unlike most other systems, the technique is based on a separate delineation of the vessels in both images. These high level primitives are subsequently used to guide the stereoscopic matching process. We will see that this threedimensional reconstruction is not considered as an independant process, separated from the delineation or interpretation process. Instead, we integrate both processes and exploit the knowledge obtained from the delineation to improve the reconstruction and vice versa. The approach makes extensive use of domain specific knowledge such as the orientation, diameter and intensity of blood vessels. Results on clinical images are presented.

Abstract: Recent developments in quantitative coronary angiography have been directed towards providing objective and reproducible measures about coronary anatomy during the catheterization procedure. The X-ray images of contrast-filled coronary arteries are converted into video format at the output screen of the image intensifier, digitized on-line and in real time in 512 × 512 × 8 bits matrices and stored in a large memory for subsequent retrieval and processing. To assess the morphology of a coronary segment (size and degree of obstructions) on the basis of automatically detected boundaries, a global centerline must be defined first. Goal of this investigation, therefore, has been the development of a technique for the automated detection of the global centerline of a coronary segment in a nonmagnified image (5122 pixels) with only the starting and endpoint manually defined by the user. Two methods have been implemented and evaluated: the beam algorithm and the minimal cost method. An evaluation of both approaches was performed on a series of 90 arterial segments digitized in nonmagnified mode from cinefilm, resulting in the same spatial resolution as by the on-line approach. Subsets were defined on the basis of the mean arterial diameter, curvature and the degree of an arterial obstruction if present. The beam method appeared to perform best in all subsets. The overall success score of the beam method in this evaluation procedure was 94%, suggesting that it may be the method of choice in a routine online catheterization environment. However, the success score for the on-line application still needs to be confirmed.

Abstract: We describe a versatile collection of mapping methods for computer-aided pattern analysis, and we report the results of two experiments: one for cluster analysis and the second for classifier design. The first experiment involved sixteen human subjects and the second involved fourteen. The collection of mapping methods includes our innovation — the least squares mapping, which combines a squared error criterion with agglomerative hierarchical clustering. In both of these experiments untrained humans aided by the generalized declustering mapping and our least squares mapping outperformed or equaled automatic clustering and classifier design techniques.

Abstract: Given a set of line segments in the plane it is not always possible to form a simple circuit (simple polygon) by connecting the endpoints of the segments. In general, it is NP-complete to decide whether a set of line segments admits a simple circuit We give polynomial algorithms to decide whether a set of line segments admits a monotone simple circuit. We also give polynomial algorithms for optimizing the perimeter or the area bounded by the simple circuit. The algorithms presented are based on a dynamic programming approach for solving a special case of the travelling salesman problem.

Abstract: Described is a coupled expert system for signal understanding. This system maintains two separate, collaborating knowledge bases, one for the signal analysis knowledge and one for the domain specific knowldege. Both kinds of knowledge are represented in the form of objects. The objects describing the domain knowledge contain the morphological and spatio-temporal description of each event to detect. The signal analysis knowledge is captured in frame-like objects referred to as specialists, capable of detection and evaluation tasks, respectively. A pattern matcher, operating on the event descriptions, is employed to identify what features need to be extracted from the signal and to trigger the appropriate specialists. The system has been implemented on KEE tm (IntelliCorp, Inc.) with links to LISP and Fortran routines and runs on a Symbolics 3640 Lisp machine. Tests with electroencephalograms (EEGs —brainwaves—) recorded during sleep demonstrated that the system could correctly identify specific waveforms (i.e., spindles and K-complexes).

Abstract: In this paper, a line is any one-dimensional structure having a cross-section profile in the form of an even function. To detect both magnitude and direction of lines we propose the employment of Rotation-Invariant Operators of order 0 and 2: h 0 (r) and (h 2 (r) cos 2ϕ, h 2 (r) sin 2ϕ), respectively. To obtain maximum sensitivity to pure 1D lines, we use a quadratic combination of the responses of these operators. For the fingerprint application, we employ a strategy borrowed from Granlund/ Knutsson: Suppress line responses having an orientation that is not matching the locally dominant direction.

Abstract: In this paper we will present LILY, a software package for image processing. LILY stands for Leuven Image processing LibrarY and has been developed with funding from a large number of Belgian industrial companies who are all interested in visual inspection problems. Therefore, the algorithms in the package are mainly concerned with this application field, although also other algorithms are incorporated. All procedures have been written in Pascal and Fortran on a VAX running VMS, with current work being done to convert the package to the C-language. Along with the programmed algorithms come a large number of support functions and procedures to facilitate the development of image processing programs. The package thus presents itself to the user as a large toolbox from which the appropriate tools must be taken to accomplish a certain task. The available procedures fall in one of the following categories: segmentation, coding, filtering, feature extraction, classification, texture analysis, relaxation, and pyramidal structures. In the first part of the paper, an overview will be given of the algorithms that are present in all these different classes. Syntactical conventions, documentation, maintenance and development tools will be discussed also. The second part of the paper is devoted to some specific problems that have been solved as a testcase for the algorithms. First Laws' procedure for texture segmentation is implemented and applied to the detection of defects in textiles. The procedure involves filtering the image with one or more suitably chosen masks, squaring the obtained values, computing the energy as a texture feature and classifying the resulting values. Each of these steps corresponds more or less to a different module of the package. A second industrial problem of defect inspection in unexposed radiographic film has been approached using three alternative techniques: one dimensional convolution filtering, Fourier domain filtering and polynomial regression.

Abstract: The fields of Information theory, In particular, the area of rate-distortion theory, and pattern recognition stand as well developed disciplines. While the areas of Interest to researchers In the two fields have overlapped In the past, up to now no comprehensive effort has been made to relate the philosophy, goals, and analytical techniques of these two disciplines. This paper Is motivated by the belief that such an examination of the two fields would uncover a number of Interesting new research questions; would add to the understanding of the fields, both separately and together; and would provide a basis for Increased collaboration among researchers.

Abstract: In computational geometry one may be interested in decomposing a polygon into simpler components, monotone polygons for example, in order to solve the geometric problem at hand more efficiently. However, in pattern recognition , where the motivation is morphological , one is interested in decomposing a polygon into perceptually meaningful parts. Therefore we can relax the strict requirement that the components be of a certain form such as convex or monotone and we can investigate decompositions which are procedure oriented rather than component oriented . In this paper we study the properties of a procedure oriented decomposition, termed the relative neighbour decomposition , and present different algorithms for performing such a decomposition.

Abstract: In many pattern recognition problems the objects of interest are represented as polygons. For some applications such as pattern matching the shape of the polygons is successfully measured in terms of the visibility relations between the edges. In this paper we survey some recent results in computational geometry that allow efficient computation of visibility properties between edges of a simple polygon as well as more general visibility relations. In particular, four natural definitions of edge-to-edge visibility are considered and a linear-time, and thus optimal, algorithm is discussed to determine edge-to-edge visibility under any of the four definitions. Furthermore, an O(n log log n) time algorithm is reviewed for determining that region of an n-gon P that is weakly visible from a specified edge of P (the strong hidden-line problem). The algorithm combines results from visibility and geodesic paths with the recent polygon triangulation algorithm of Tarjan and Van Wyk [42]. We also discuss the problem of determining whether a polygon is visible from a specified edge. In particular three natural definitions of edge-visibility of polygons are considered and new optimal algorithms are proposed for testing visibility from a specified edge under any of the three definitions.

Abstract: This paper deals with incomplete data sets. This subject is analyzed and some methods for estimating missing values are presented. Furthermore, the results of a simulation experiment are presented.

Abstract: Boundaries, edges and contours in image processing with the aim to measure parameters such as length and curvature, have almost exclusively been treated with common ID-signal processing techniques. The spacing of contour points along the path s is not equidistant however, but is depending on the tangent θ(s). In effect the apparent spacing is h' = h/ cosθ (h grid constant). So, any contour operation (implicitly) using h'=h will introduce directionally dependent inaccuracies in the analysis. For example, the frequency response of a linear filter may shift up to 41% to lower frequencies, depending on θ(s). As a remedy one may fit a curve, resample the digital curve, or match a curve as has been reported, but none of these methods solved the anisotropy of the grid fundamentally. We propose a solution where the set of original (i.e. predigitized) curves for each configuration of M contour points is reconstructed. The set is different for each different configuration. As we now have the set of originals, we have achieved two goals in one blow: The anisotropy of the grid has become irrelevant, and any parameter value of the curve can be estimated directly from the set of originals. For the noise-free situation the method produces results with the highest possible accuracy and the least possible sensitivity to the orientation of the object relative to the measurement grid. For any (local) parameter or specific shape clue, e.g. curvature, length, or rectangular corner detection, the method can be implemented efficiently by a table search operation of 2.3M-2 entries, requiring no contour tracing. It is concluded that the method is pre-eminently apt for low resolution, noise free measurement of shape as the method has the smallest possible measurement error.

Abstract: The paper gives a tutorial survey of the realizability problem of polyhedrons from line drawings. The realizability problem is to judge whether a given line drawing represents a polyhedron. The problem includes many variations depending on assumptions about the object worlds, on the view point or the view direction, on the drawing rules, etc. These variations are classified, and main results in each class of problems are summarized.

Abstract: Astronomers have used classification methods as tools in examining the nature of the universe for more than a century. Classification remains a very heavily used tool in many subfields of astronomy. The development of new and very powerful classification technologies, the development of enormously increased computing capacity, and the development of a new generation of areal and multi-object digital detectors are creating a substantially changed situation. For the first time since the invention of the photographic plate technological change is forcing a major revision in the methods used to reduce data. The need to create order from the nearly unthinkably huge streams of data which are beginning to appear presents the greatest challenge and opportunity for astronomical classification in more than a generation.

Abstract: Discriminant analysis based on a set of learning objects that is not an aselective random sample of the universe of objects is discussed. The use of fuzzy labels is argued. Possibilities for evaluation and feature selection are investigated.

Abstract: In reasoning systems, uncertainty plays a crucial part, especially for those fields where judgements are essential, as in pathology. Uncertainty has several aspects, such as prevalence of diseases, occurrence of findings and the predictive value of findings. For the functioning of a reasoning system two aspects are crucial: first, the internal representation of the uncertainty and second, the way in which the uncertainty is propagated in the reasoning process when combining formal statements. Five well known reasoning strategies are compared: probability theory, MYCIN'S certainty factor model, fuzzy set theory, the theory of Dempster-Shafer and the scoring scheme of Internist. The comparison addresses, among others, the following questions: - Can the different aspects of uncertainty be dealt with as separate entities? - How are unknown uncertainties dealt with? - How is evidence in favor of a hypothesis combined with evidence against it? - How does the model treat the simultanuous occurrence of more than one disorder, that is, how does the model support reasoning with compound hypotheses? It is preliminarly concluded, that only in Internist and probability theory, the different aspects of uncertainty are expressed as separate entities. Hence, the other models do not accurately represent uncertain knowledge. Also, theoretically attractive models such as Bayes, MYCIN and the theory of Dempster-Shafer can only function properly under the tight condition of mutual exclusiveness of hypotheses, not always suited for broader parts of pathology. They may, however, be suited for smaller parts with a limited number of defined diseases and a limited number of features. All models but Bayes lack a predictable performance as there is no or only a partial underlying theory to guarantee minimization of the overall error.