Showing papers in "IEEE Transactions on Pattern Analysis and Machine Intelligence in 1982"

A Model for Radar Images and Its Application to Adaptive Digital Filtering of Multiplicative Noise

Abstract: Standard image processing techniques which are used to enhance noncoherent optically produced images are not applicable to radar images due to the coherent nature of the radar imaging process. A model for the radar imaging process is derived in this paper and a method for smoothing noisy radar images is also presented. The imaging model shows that the radar image is corrupted by multiplicative noise. The model leads to the functional form of an optimum (minimum MSE) filter for smoothing radar images. By using locally estimated parameter values the filter is made adaptive so that it provides minimum MSE estimates inside homogeneous areas of an image while preserving the edge structure. It is shown that the filter can be easily implemented in the spatial domain and is computationally efficient. The performance of the adaptive filter is compared (qualitatively and quantitatively) with several standard filters using real and simulated radar images.

Medial Axis Transformation of a Planar Shape

Abstract: The medial axis transformation is a means first proposed by Blum to describe a shape. In this paper we present a 0(n log n) algorithm for computing the medial axis of a planar shape represented by an n-edge simple polygon. The algorithm is an improvement over most previously known results interms of both efficiency and exactness and has been implemented in Fortran. Some computer-plotted output of the program are also shown in the paper.

Automated Visual Inspection: A Survey

Abstract: This paper surveys publications, reports, and articles dealing with automated visual inspection for industry The references are organized according to their contents: overview and discussions, rationales, components and design considerations, commercially available systems, applications A number of applications and their inspection methodologies are discussed in detail: the inspection of printed circuit boards, photomasks, integrated circuit chips Other inspection applications are listed as a bibliography A list of selectively annotated references in commercially available visual inspection tools is also included

Optimal Choice of AR and MA Parts in Autoregressive Moving Average Models

Abstract: This paper deals with the Bayesian method of choosing the best model for a given one-dimensional series among a finite number of candidates belonging to autoregressive (AR), moving average (MA), ARMA, and other families. The series could be either a sequence of observations in time as in speech applications, or a sequence of pixel intensities of a two-dimensional image. The observation set is not restricted to be Gaussian. We first derive an optimum decision rule for assigning the given observation set to one of the candidate models so as to minimize the average probability of error in the decision. We also derive an optimal decision rule so as to minimize the average value of the loss function. Then we simplify the decision rule when the candidate models are different Gaussian ARMA models of different orders. We discuss the consistency of the optimal decision rule and compare it with the other decision rules in the literature for comparing dynamical models.

Matching Images to Models for Registration and Object Detection via Clustering

Abstract: A new technique is presented for matching image features to maps or models. The technique forms all possible pairs of image features and model features which match on the basis of local evidence alone. For each possible pair of matching features the parameters of an RST (rotation, scaling, and translation) transformation are derived. Clustering in the space of all possible RST parameter sets reveals a good global transformation which matches many image features to many model features. Results with a variety of data sets are presented which demonstrate that the technique does not require sophisticated feature detection and is robust with respect to changes of image orientation and content. Examples in both cartography and object detection are given.

Cluster Validity for the Fuzzy c-Means Clustering Algorithrm

Abstract: The uniform data function is a function which assigns to the output of the fuzzy c-means (Fc-M) or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm. For the preselected number of cluster c, the Fc-M algorithm produces c vectors in the space in which the data lie, called cluster centers, which represent points about which the data are concentrated. It also produces for each data point c-membership values, numbers between zero and one which measure the similarity of the data points to each of the cluster centers. It is these membership values which indicate how the point is classified. They also indicate how well the point has been classified, in that values close to one indicate that the point is close to a particular center, but uniformly low memberships indicate that the point has not been classified clearly. The uniform data functional (UDF) combines the memberships in such a way as to indicate how well the data have been classified and is computed as follows. For each data point compute the ratio of its smallest membership to its largest and then compute the probability that one could obtain a smaller ratio (indicating better classification) from a clustering of a standard data set in which there is no cluster structure. These probabilities are then averaged over the data set to obtain the values of the UDF.

Efficient Calculation of Primary Images from a Set of Images

Abstract: A set of images is modeled as a stochastic process and Karhunen-Loeve expansion is applied to extract the feature images. Although the size of the correlation matrix for such a stochastic process is very large, we show the way to calculate the eigenvectors when the rank of the correlation matrix is not large. We also propose an iterative algorithm to calculate the eigenvectors which save computation time andc omputer storage requirements. This iterative algorithm gains its efficiency from the fact that only a significant set of eigenvectors are retained at any stage of iteration. Simulation results are also presented to verify these methods.

Hierarchical Classifier Design Using Mutual Information

Abstract: A nonparametric algorithm is presented for the hierarchical partitioning of the feature space. The algorithm is based on the concept of average mutual information, and is suitable for multifeature multicategory pattern recognition problems. The algorithm generates an efficient partitioning tree for specified probability of error by maximizing the amount of average mutual information gain at each partitioning step. A confidence bound expression is presented for the resulting classifier. Three examples, including one of handprinted numeral recognition, are presented to demonstrate the effectiveness of the algorithm.

Studies in Semi-Admissible Heuristics

Abstract: The paper introduces three extensions of the A* search algorithm which improve the search efficiency by relaxing the admissibility condition. 1) A* employs an admissible heuristic function but invokes quicker termination conditions while still guaranteeing that the cost of the solution found will not exceed the optimal cost by a factor greater than 1 + . 2) R?* may employ heuristic functions which occasionally violate the admissibility condition, but guarantees that at termination the risk of missing the opportunity for further cost reduction is at most ?. 3) R?*,* is a speedup version of R?*, combining the termination condition of A* with the risk-admissibility condition of R?*. The Traveling Salesman problem was used as a test vehicle to examine the performances of the algorithms A* and R?*. The advantages of A* are shown to be significant in difficult problems, i.e., problems requiring a large number of expansions due to the presence of many subtours of roughly equal costs. The use of R?* is shown to produce a 4:1 reduction in search time with only a minor increase in final solution cost.

Dot Pattern Processing Using Voronoi Neighborhoods

Abstract: A sound notion of the neighborhood of a point is essential for analyzing dot patterns. The past work in this direction has concentrated on identifying pairs of points that are neighbors. Examples of such methods include those based on a fixed radius, k-nearest neighbors, minimal spanning tree, relative neighborhood graph, and the Gabriel graph. This correspondence considers the use of the region enclosed by a point's Voronoi polygon as its neighborhood. It is argued that the Voronoi polygons possess intuitively appealing characteristics, as would be expected from the neighborhood of a point. Geometrical characteristics of the Voronoi neighborhood are used as features in dot pattern processing. Procedures for segmentation, matching, and perceptual border extraction using the Voronoi neighborhood are outlined. Extensions of the Voronoi definition to other domains are discussed.

Attributed Programmed Graph Grammars and Their Application to Schematic Diagram Interpretation

Abstract: Attributed programmed graph grammars are introduced in this paper and their application to the interpretation of schematic diagrams is proposed. In contrast with most of the approaches to syntactic pattern recognition, where the grammar controls a parser, the grammar in our system is used as a generative tool. Two classes of diagrams are studied, namely circuit diagrams and flowcharts. The task is in either case to extract a description from an input diagram.

Mathematical Structures of Line Drawings of Polyhedrons-Toward Man-Machine Communication by Means of Line Drawings

Abstract: Mathematical structures of line drawings of polyhedrons are studied and practical as well as theoretical solutions are obtained for several fundamental problems aroused in scene analysis and in man-machine communication. First, a necessary and sufficient condition for a line drawing to correctly represent a polyhedron is obtained in terms of linear algebra. Next, combinatorial structures are investigated and practical solutions are obtained to such problems as how to discriminate between correct and incorrect line drawings and how to correct vertex-position errors in incorrect line drawings. Lastly, distribution of the degree of freedom of a line drawing is elucidated and a method is proposed for interactive reconstruction of a polyhedron from a line drawing. The results obtained here enable us to make manmachine communication more ``flexible'' in the sense that a machine can reconstruct three-dimensional objects from hand-drawn pictures even if the pictures are not perfect.

Digital Straight Lines and Convexity of Digital Regions

Abstract: It is shown that a digital region is convex if and only if every pair of points in the region is connected by a digital straight line segment contained in the region. The midpoint property is shown to be a necessary but not a sufficient condition for the convexity of digital regions. However, it is shown that a digital region is convex if and only if it has the median-point property.

Organization of Relational Models for Scene Analysis

Abstract: Relational models are commonly used in scene analysis systems. Most such systems are experimental and deal with only a small number of models. Unknown objects to be analyzed are usually sequentially compared to each model. In this paper, we present some ideas for organizing a large database of relational models. We define a simple relational distance measure, prove it is a metric, and using this measure, describe two organizational/access methods: clustering and binary search trees. We illustrate these methods with a set of randomly generated graphs.

Minimum Cross-Entropy Pattern Classification and Cluster Analysis

Abstract: This paper considers the problem of classifying an input vector of measurements by a nearest neighbor rule applied to a fixed set of vectors. The fixed vectors are sometimes called characteristic feature vectors, codewords, cluster centers, models, reproductions, etc. The nearest neighbor rule considered uses a non-Euclidean information-theoretic distortion measure that is not a metric, but that nevertheless leads to a classification method that is optimal in a well-defined sense and is also computationally attractive. Furthermore, the distortion measure results in a simple method of computing cluster centroids. Our approach is based on the minimization of cross-entropy (also called discrimination information, directed divergence, K-L number), and can be viewed as a refinement of a general classification method due to Kullback. The refinement exploits special properties of cross-entropy that hold when the probability densities involved happen to be minimum cross-entropy densities. The approach is a generalization of a recently developed speech coding technique called speech coding by vector quantization.

Boundary Detection in Multidimensions

Abstract: The development of image processing algorithms for time-varying imagery and computerized tomography data calls for generalization of the concepts of adjacency, connectivity, boundary, etc., to three and four-dimensional discrete spaces. This paper defines these basic concepts in unified terminology and presents algorithms for a boundary detection task in multidimensional space. The performance of these algorithms is discussed with respect to theoretical maximum complexity, and is illustrated with simulated computerized tomography data.

A Model and Tracking Algorithm for a Class of Video Targets

Abstract: Algorithms are developed for a real-time, automatic system capable of tracking two-dimensional (2-D) targets in complex scenes. A mathematical model of 2-D image spatial and temporal evolution applicable to certain classes of targets and target perturbations is developed. It is shown that for small target perturbations the 2-D tracking problem may be approximated as a 1-D time-varying parameter estimation problem. A CCD-implementable solution is developed which is particularly useful when considering target rotation and dilation and target/background separation. Results of system simulation and suggestions for future research are presented.

Distance Transform for Images Represented by Quadtrees

Abstract: The concept of distance used in binary array representations of images is adapted to a quadtree representation. The chessboard distance metric is shown to be particularly suitable for the quadtree. A chessboard distance transform for a quadtree is defined as the minimum distance in the plane from each BLACK node to the border of a WHiTE node. An algorithm is presented which computes this transform by only examining the BLACK node's adjacent and abutting neighbors and their progeny. However, unlike prior work with quadtrees, computation of the distance transform requires a capability of finding neighbors in the diagonal direction rather than merely in the horizontal and vertical directions. The algorithm's average execution time is proportional to the number of leaf nodes in the quadtree.

Description of Textures by a Structural Analysis

Abstract: A structural analysis system for describing natural textures is introduced. The analyzer automatically extracts the texture elements in an input image, measures their properties, classifies them into some distinctive classes (one ``ground'' class and some ``figure'' classes), and computes the distributions of the gray level, the shape, and the placement of the texture elements in each class. These descriptions are used for classification of texture images. An analysis-by-synthesis method for evaluating texture analyzers is also presented. We propose a synthesizer which generates a texture image based on the descriptions. By comparing the reconstructed image with the original one, we can see what information is preserved and what is lost in the descriptions.

Experiments in Text Recognition with Binary n-Gram and Viterbi Algorithms

Abstract: The binary n-gram and Viterbi algorithms have been suggested as alternative approaches to contextual postprocessing for text produced by a noisy channel such as an optical character recognizer. This correspondence describes the underlying theory of each approach in unified terminology, and presents new implementation algorithms for each approach. In particular, a storage efficient data structure is proposed for the binary n-gram algorithm and a recursive formulation is given for the Viterbi algorithm. Results of extensive experiments with each algorithm are described.

Shape Measurement of Curved Objects Using Multiple Slit-Ray Projections

Abstract: A method for the shape measurement of curved objects has been developed using multiple slit-ray projections and a turntable The object is placed on a computer-controlled turntable and irradiated by two directed slit-ray projectors An ITV camera takes a line image of the reflection from the object, and a computer calculates the space coordinates of the object surface By using multiple projections, the total shape measurement of the object surface is attained accurately

Nonlinear Restoration of Noisy Images

Abstract: The restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image. The standard Wiener approach to this problem is modified to take into account the edge information of the image. Various filters of increasing complexity are derived. Experimental results are shown and compared to the standard Wiener filter results and other earlier attempts involving nonstationary filters.

A Note on the Quantitative Measure of Image Enhancement Through Fuzziness

Abstract: The ``index of fuzziness'' and ``entropy'' of an image reflect a kind of quantitative measure of its enhancement quality. Their values are found to decrease with enhancement of an image when different sets of S-type membership functions with appropriate crossover points were considered for extracting the fuzzy property plane from the spatial domain of the image.

On the Chain Code of a Line

Abstract: In 1970 Freeman suggested the following criteria which the chain code of a line must meet [1], [2]: 1) at most two basic directions are present and these can differ only by unity, modulo eight, 2) one of these values always occurs singly, 3) successive occurrences of the principal direction occurring singly are as uniformly spaced as possible. In this correspondence we give the following: 1) an algorithm presentation of Freeman's three properties about the chain code of a line and the proof that it is also the algorithm recognizing whether a chain code is the chain code of a line, 2) the proof of the equivalence of the above presentation and Rosenfeld's chord property [3].

Any Discrimination Rule Can Have an Arbitrarily Bad Probability of Error for Finite Sample Size

Abstract: Consider the basic discrimination problem based on a sample of size n drawn from the distribution of (X, Y) on the Borel sets of Rdx {0, 1}. If 0 ?. Thus, any attempt to find a nontrivial distribution-free upper bound for Rn will fail, and any results on the rate of convergence of Rn to R* must use assumptions about the distribution of (X, Y).

A Maximum Likelihood Approach to Texture Classification

Abstract: A new approach to texture classification is described which is based on measurements of the spatial gray-level co-occurrence probability matrix. This approach can make use of assumed stochastic models for texture in imagery and is an approximation to the statistically optimum maximum likelihood classifier. The efficacy of the approach is demonstrated through experimental results obtained with real-world texture data.

Threshold Selection Using Quadtrees

Abstract: A simple class of piecewise constant approximations to an image is constructed as follows: start with the entire image, subdivide it into quadrants if its gray level standard deviation is high, and repeat the process for each quadrant. This yields a decomposition of the image into blocks, each having low standard deviation, so that each of them can be approximated by a constant value, namely, its mean. The histogram of this approximated image tends to have sharper peaks than that of the original image since the block averaging reduces the variability of the gray levels within homogeneous regions. A possible way of further improving the histogram is based on the fact that small blocks tend to occur near region borders; thus, suppressing these blocks should tend to deepen the valleys on the histogram, making threshold selection (to separate regions of different types) easier. Conversely, the histogram of the small blocks only represents a population of pixels near region borders, and if there are only two types of regions (e.g., objects and background), the mean of this histogram should be a useful threshold for separating them; but in practice, this method is not very reliable since background fluctuations also give rise to border pixels.

An Automated Approach to the Design of Decision Tree Classifiers

Abstract: The classification of large dimensional data sets arising from the merging of remote sensing data with more traditional forms of ancillary data causes a significant computational problem. Decision tree classification is a popular approach to the problem. This type of classifier is characterized by the property that samples are subjected to a sequence of decision rules before they are assigned to a unique class. If a decision tree classifier is well designed, the result in many cases is a classification scheme which is accurate, flexible, and computationally efficient. This correspondence provides an automated technique for effective decision tree design which relies only on a priori statistics. This procedure utilizes canonical transforms and Bayes table look-up decision rules. An optimal design at each node is derived based on the associated decision table. A procedure for computing the global probability of correct classification is also provided. An example is given in which class statistics obtained from an actual Landsat scene are used as input to the program. The resulting decision tree design has an associated probability of correct classification of 0.75 compared to the theoretically optimum 0.79 probability of correct classification associated with a full dimensional Bayes classifier. Recommendations for future research are included.

Digital Convexity, Straightness, and Convex Polygons

Abstract: New schemes for digitizing regions and arcs are introduced. It is then shown that under these schemes, Sklansky's definition of digital convexity is equivalent to other definitions. Digital convex polygons of n vertices are defined and characterized in terms of geometric properties of digital line segments. Also, a linear time algorithm is presented that, given a digital convex region, determines the smallest integer n such that the region is a digital convex n-gon.

A Mathematical Model for Computer Image Tracking

Abstract: A mathematical model using an operator formulation for a moving object in a sequence of images is presented. Time-varying translation and rotation operators are derived to describe the motion. A variational estimation algorithm is developed to track the dynamic parameters of the operators. The occlusion problem is alleviated by using a predictive Kalman filter to keep the tracking on course during severe occlusion. The tracking algorithm (variational estimation in conjunction with Kalman filter) is implemented to track moving objects with occasional occlusion in computer-simulated binary images.