Showing papers in "IEEE Transactions on Pattern Analysis and Machine Intelligence in 1979"
TL;DR: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster which can be used to infer the appropriateness of data partitions.
Abstract: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster. The measure can be used to infer the appropriateness of data partitions and can therefore be used to compare relative appropriateness of various divisions of the data. The measure does not depend on either the number of clusters analyzed nor the method of partitioning of the data and can be used to guide a cluster seeking algorithm.
6,757 citations
TL;DR: Warnock-type algorithms are presented for building the quad tree for the picture of the boundary of apolygon, and for coloring the interior of such a polygon.
Abstract: A quad tree for representing a picture is a tree in which successively deeper levels represent successively finer subdivisions of picture area. An algorithm is given for superposing N quad trees in time proportional to the total number of nodes in the trees. Warnock-type algorithms are then presented for building the quad tree for the picture of the boundary of a polygon, and for coloring the interior of such a polygon. These algorithms take O(v + p + q) time, where v is the number of polygon vertices, p is the polygon perimeter, and q is a resolution parameter. When the resolution q is fixed, these algorithms are asymptotically optimal.
420 citations
TL;DR: Analysis of a first-order difference picture (FODP) provides a separate estimate for images of moving objects and of stationary scene components that represents the stationary scene component in a TV-image sequence.
Abstract: The count of events where sample areas from the second and subsequent frames of a TV-image sequence are incompatible with the corresponding sample area of the first frame are accumulated in a first-order difference picture (FODP). Analysis of this FODP provides a separate estimate for images of moving objects and of stationary scene components. We start from the hypothesis that the first frame represents the stationary scene component. Once it has been recognized that a subarea of this initial estimate corresponds to the image of a moving object, the grey values in this subarea are replaced by later estimates of the stationary background at this position. No knowledge specific to a particular scene is utilized in the algorithm. The results for two scene sequences are presented.
384 citations
TL;DR: In pattern recognition problems it has been noted that beyond a certain point the inclusion of additional parameters (that have been estimated) leads to higher probabilities of error, so the probability of error approaches one-half as the dimensionality increases and parameters are estimated.
Abstract: In pattern recognition problems it has been noted that beyond a certain point the inclusion of additional parameters (that have been estimated) leads to higher probabilities of error. A simple problem has been formulated where the probability of error approaches zero as the dimensionality increases and all the parameters are known; on the other hand, the probability of error approaches one-half as the dimensionality increases and parameters are estimated.
366 citations
TL;DR: In this article, a new approach to texture analysis based on the spatial distribution of local features in unsegmented textures is presented, where textures are described using features derived from generalized co-occurrence matrices (GCM).
Abstract: We present a new approach to texture analysis based on the spatial distribution of local features in unsegmented textures. The textures are described using features derived from generalized co-occurrence matrices (GCM). A GCM is determined by a spatial constraint predicate F and a set of local features P = {(Xi, Yi, di), i = 1,..., m} where (Xi, Yi) is the location of the ith feature, and di is a description of the ith feature. The GCM of P under F, GF, is defined by GF(i, j) = number of pairs, pk, pl such that F(pk, pl) is true and di and dj are the descriptions of pk and pl, respectively. We discuss features derived from GCM's and present an experimental study using natural textures.
326 citations
TL;DR: A new family of unitary transforms is introduced and it is shown that the well-known discrete Fourier, cosine, sine, and the Karhunen-Loeve (KL) (for first-order stationary Markov processes) transforms are members of this family.
Abstract: A new family of unitary transforms is introduced. It is shown that the well-known discrete Fourier, cosine, sine, and the Karhunen-Loeve (KL) (for first-order stationary Markov processes) transforms are members of this family. All the member transforms of this family are sinusoidal sequences that are asymptotically equivalent. For finite-length data, these transforms provide different approximations to the KL transform of the said data. From the theory of these transforms some well-known facts about orthogonal transforms are easily explained and some widely misunderstood concepts are brought to light. For example, the near-optimal behavior of the even discrete cosine transform to the KL transform of first-order Markov processes is explained and, at the same time, it is shown that this transform is not always such a good (or near-optimal) approximation to the above-mentioned KL transform. It is also shown that each member of the sinusoidal family is the KL transform of a unique, first-order, non-stationary (in general), Markov process. Asymptotic equivalence and other interesting properties of these transforms can be studied by analyzing the underlying Markov processes.
314 citations
TL;DR: This approach was tested on a data base consisting of digitized coastlines in various map projections and found that in nearly all cases, all matches except the correct one were eliminated by the relaxation processes.
Abstract: The problem of finding approximate matches of pieces of shapes to parts of larger shapes is investigated. The shapes are represented by polygonal approximations. Initially, figures of merit are assigned to the matches between pairs of angles on the two shapes. Relaxation methods are then used to find acceptable combinations of these matches. This approach was tested on a data base consisting of digitized coastlines in various map projections. In nearly all cases, all matches except the correct one were eliminated by the relaxation processes.
289 citations
TL;DR: It is shown that Latin square puzzles, finding N-ary relations, graph or auto-mata homomorphisms, graph colorings, as well as determining satisfiability of propositional logic statements and solving scene and edge labeling problems, are all special cases of the general consistent labeling problem.
Abstract: In this second part of a two-part paper, we explore the power and complexity of the g=fKP and g=vKP class of look-ahead operators which can be used to speed up the tree search in the consistent labeling problem. For a specified K and P we show that the fixedpoint power of g=fKP and g=vKP is the same, that g=fKP+1 is at least as powerful as g=fKP, and that g=vK+1p is at least as powerful at g=fKP. Finally, we define a minimal compatibility relation and show how the standard tree search procedure for finding all the consistent labelings is quicker for a minimal relation. This leads to the concept of grading the complexity of compatibility relations according to how much look-ahead work it requires to reduce them to minimal relations and suggests that the reason look-ahead operators, such as Waltz filtering, work so well is that the compatibility relations used in practice are not very complex and are reducible to minimal or near minimal relations by a g=fKP or g=vKP look-ahead operator with small value for parameter P.
286 citations
TL;DR: The positional distributions of n-grams obtained in the present study are discussed and statistical studies on word length and trends ofn-gram frequencies versus vocabulary are presented.
Abstract: n-gram (n = 1 to 5) statistics and other properties of the English language were derived for applications in natural language understanding and text processing. They were computed from a well-known corpus composed of 1 million word samples. Similar properties were also derived from the most frequent 1000 words of three other corpuses. The positional distributions of n-grams obtained in the present study are discussed. Statistical studies on word length and trends of n-gram frequencies versus vocabulary are presented. In addition to a survey of n-gram statistics found in the literature, a collection of n-gram statistics obtained by other researchers is reviewed and compared.
237 citations
TL;DR: An intuitively appealing, noniterative estimator for intrinsic dimensionality which is based on nearneighbor information is proposed which works well in identifying the true dimensionality for a variety of artificial data sets and is fairly insensitive to the number of samples and to the algorithmic parameters.
Abstract: The intrinsic dimensionality of a set of patterns is important in determining an appropriate number of features for representing the data and whether a reasonable two- or three-dimensional representation of the data exists. We propose an intuitively appealing, noniterative estimator for intrinsic dimensionality which is based on nearneighbor information. We give plausible arguments supporting the consistency of this estimator. The method works well in identifying the true dimensionality for a variety of artificial data sets and is fairly insensitive to the number of samples and to the algorithmic parameters. Comparisons between this new method and the global eigenvalue approach demonstrate the utility of our estimator.
230 citations
TL;DR: This paper considers the problem of optimizing spatial frequency domain filters for detecting edges in digital pictures and shows that the optimum filter is very effective for detecting blufred and noisy edges.
Abstract: Edge detection and enhancement are widely used in image processing applications. In this paper we consider the problem of optimizing spatial frequency domain filters for detecting edges in digital pictures. The filter is optimum in that it produces maximum energy within a resolution interval of specified width in the vicinity of the edge. We show that, in the continuous case, the filter transfer function is specified in terms of the prolate spheroidal wave function. In the discrete case, the filter transfer function is specified in terms of the sampled values of the first-order prolate spheroidal wave function or in terms of the sampled values of an asymptotic approximation of the wave function. Both versions can be implemented via the fast Fourier transform (FFT). We show that the optimum filter is very effective for detecting blufred and noisy edges. Finally, we compare the performance of the optimum edge detection filter with other edge detection filters using a variety of input images.
TL;DR: Using this procedure on handdrawn colon shapes copied from an X-ray and on handprinted characters, the parts determined by the clustering often correspond well to decompositions that a human might make.
Abstract: This paper describes a technique for transforming a twodimensional shape into a binary relation whose clusters represent the intuitively pleasing simple parts of the shape. The binary relation can be defined on the set of boundary points of the shape or on the set of line segments of a piecewise linear approximation to the boundary. The relation includes all pairs of vertices (or segments) such that the line segment joining the pair lies entirely interior to the boundary of the shape. The graph-theoretic clustering method first determines dense regions, which are local regions of high compactness, and then forms clusters by merging together those dense regions having high enough overlap. Using this procedure on handdrawn colon shapes copied from an X-ray and on handprinted characters, the parts determined by the clustering often correspond well to decompositions that a human might make.
TL;DR: This paper describes a sequential procedure for processing registered range and intensity data to detect and extract regions that correspond to planar surfaces in a scene.
Abstract: This paper describes a sequential procedure for processing registered range and intensity data to detect and extract regions that correspond to planar surfaces in a scene.
TL;DR: The spherical decomposition permits the computation of points on the symmetric surface of an object, the three-dimensional analog of Blum's symmetric axis, and can be useful for graphical display.
Abstract: Algorithms are presented for converting between different three-dimensional object representations: from a collection of cross section outlines to surface points, and from surface points to a collection of overlapping spheres. The algorithms effect a conversion from surface representations (outlines or surface points) to a volume representation (spheres). The spherical representation can be useful for graphical display, and perhaps as an intermediate representation for conversions to representations with other primitives. The spherical decomposition also permits the computation of points on the symmetric surface of an object, the three-dimensional analog of Blum's symmetric axis. The algorithms work in real coordinates rather than in a discrete space, and so avoid error introduced by the quantization of the space.
TL;DR: An algorithm that generates the distance for any two trees is presented and cluster analysis for patterns represented by tree structures is discussed, using a tree-to-tree distance to measure the similarity between patterns.
Abstract: A distance measure between two trees is proposed. Using the idea of language transformation, a tree can be derived from another by a series of transformations. The distance between the two trees is the minimum-cost sequence of transformations. Based on this definition, an algorithm that generates the distance for any two trees is presented. Cluster analysis for patterns represented by tree structures is discussed. Using a tree-to-tree distance, the similarity between patterns is measured in terms of distance between their tree representations. An illustrative example on clustering of character patterns is presented.
TL;DR: This paper describes a parser whose input is a piecewise linear encoding of a contour and whose output is a string of high-level descriptions: arcs, corners, protrusions, intrusions, etc.
Abstract: In many cases a picture is described in terms of various plane objects and their shape. This paper describes a parser whose input is a piecewise linear encoding of a contour and whose output is a string of high-level descriptions: arcs, corners, protrusions, intrusions, etc. Such a representation can be used not only for description but also for recognition. Previous syntactic techniques for contour description have often used high-level languages for the description of contours. This has been necessary in order to guarantee contour closure and eliminate the noise. In the present approach the numerical preprocessing of the contour removes most of the noise and also produces the answers to certain simple questions about its shape. Therefore, simpler grammars can be used for the contour description. Examples of descriptions of contours are given for handwritten numerals, white blood cells, and printed wiring circuit boards.
TL;DR: A method is developed to represent movement of convex blocks in three-dimensional space from a sequence of two-dimensional camera images to determine the objects' movement toward or away from the camera as well as left/right and up/down movement in the image plane.
Abstract: A method is developed to represent movement of convex blocks in three-dimensional space from a sequence of two-dimensional camera images. The goals are to determine the objects' movement toward or away from the camera as well as left/right and up/down movement in the image plane and to build models of the blocks. The movement information is used as part of a hierarchical matching process that determines the correspondence of blocks between scenes.
TL;DR: Elongated black objects in black-and-white pictures can be ``thinned'' to arcs and curves, without changing their connectedness, by (repeatedly) deleting black border points whose deletion does not locally disconnect the black points in their neighborhoods.
Abstract: Elongated black objects in black-and-white pictures can be ``thinned'' to arcs and curves, without changing their connectedness, by (repeatedly) deleting black border points whose deletion does not locally disconnect the black points in their neighborhoods This technique generalizes to gray-scale pictures if we use a weighted definition of connectedness: two points are ``connected'' if there is a path joining them on which no point is lighter than either of them We can then ``thin'' dark objects by changing each point's gray level to the minimum of its neighbors' gray levels, provided this does not disconnect any pair of points in its neighborhood Examples illustrating the performance of this technique are given
TL;DR: The results empirically answer the long-standing question of what is the benefit, if any, of using transition probabilities that depend on the length of a word and their position in it.
Abstract: In this paper a modification of the Viterbi algorithm is formally described, and a measure of its complexity is derived. The modified algorithm uses aheuristic to limit the search through a directed graph or trellis. The effectiveness of the algorithm is investigated via exhaustive experimentation on an input of machine-printed text. The algorithm assumes language to be a Markov chain and uses transition probabilities between characters. The results empirically answer the long-standing question of what is the benefit, if any, of using transition probabilities that depend on the length of a word and their position in it.
TL;DR: Algorithms enabling efficient retrieval of subpicture areas from sequential and direct access files are presented, and examples show that improved retrieval response is possible from using NUMERIC to sort lists of areas to be recalled.
Abstract: This paper concerns methods for indexing areas in twodimensional array data. A method for naming subpictures from rasterscan image data is presented with notation that eases their subsequent storage access. Equations are given for converting each subpicture name into a storage-location pointer. A function ``NUMERIC'' is described that aids this task. Algorithms enabling efficient retrieval of subpicture areas from sequential and direct access files are presented. Examples are given that show that improved retrieval response is possible from using NUMERIC to sort lists of areas to be recalled. The paper includes an overview of tree data structures, the subject implemented by these techniques. An overlapping picture subareas storage scheme is discussed.
TL;DR: The valid junction transitions provide a new set of edge semantics for line labeling and an ability to verify whether a given sequence of junctions forms a realizable configuration.
Abstract: A line and junction labeling scheme is introduced that is valid for both planar and curved-surface bodies. Seven generalized junction types are defined and shown to cover all valid projections for a wide class of planar and curved-surface bodies. It is further shown that there are limitations on the permissible junction types as one moves from one end of a line segment to the other. The valid junction transitions provide 1) a new set of edge semantics for line labeling and 2) an ability to verify whether a given sequence of junctions forms a realizable configuration.
TL;DR: An overview of some recent work using alternate representations for multistage and nearest neighbor multiclass classification, and for structural analysis and feature extraction, based on generalizations of state-space and AND/OR graph models and search strategies developed in artificial intelligence.
Abstract: Noting the major limitations of multivariate statistical classification and syntactic pattern recognition models, this paper presents an overview of some recent work using alternate representations for multistage and nearest neighbor multiclass classification, and for structural analysis and feature extraction. These alternate representations are based on generalizations of state-space and AND/OR graph models and search strategies developed in artificial intelligence (AI). The paper also briefly touches on other current interactions and differences between artificial intelligence and pattern recognition.
TL;DR: This paper presents a method of cluster analysis based on a pseudo F-statistic (PFS) criterion function, designed to subdivide an ensemble into an optimal set of groups, where the number of groups is not specified and no ad hoc parameters are employed.
Abstract: This paper presents a method of cluster analysis based on a pseudo F-statistic (PFS) criterion function. It is designed to subdivide an ensemble into an optimal set of groups, where the number of groups is not specified and no ad hoc parameters are employed. Univariate and multivariate F-statistic and pseudo F-statistic consistency is displayed. Algorithms for feasible application of PFS are given. Results from simulations are utilized to demonstrate the capabilities of the PFS clustering method and to provide a comparative guide for other users.
TL;DR: The likelihood maximization approach provides a unified view for seemingly different approaches to boundary estimation, such as sequential boundary finding and region growing, and bounds on the accuracy of boundary estimation are readily derived with this formulation.
Abstract: Effective and elegant procedures have recently appeared in the published literature for determining by computer a highly variable blob boundary in a noisy image [1]-[3]. In this paper we point out that if the blob boundary is modeled as a Markov process and the additive noise is modeled as a white Gaussian noise field, then maximization of the joint likelihood of the hypothesized blob boundary and all of the image data results in roughly the same blob boundary determination as does one of the aforementioned deterministic formulations [2]. However, the formulation in this paper provides insights into and optimal parameter values for the functions involved and reveals suboptimalities in some of the formulations appearing in the literature. More generally, we agree that maximization of the joint likelihood of the hypothesized blob boundary and of the entire picture function is a fundamental approach to boundary estimation or the estimation of linear features (roads, rivers, etc.) in images, and provides a powerful mechanism for designing sequential, parallel, or other boundary estimation algorithms. The ripple filter, an advanced form of region growing, is briefly introduced and illustrates one of a number of alternative algorithms for maximizing the likelihood function. Hence, this likelihood maximization approach provides a unified view for seemingly different approaches, such as sequential boundary finding and region growing. Bounds on the accuracy of boundary estimation are readily derived with this formulation and are presented.
TL;DR: This correspondence describes research in the development of symbolic registration techniques directed toward the comparison of pairs of images of the same scene to ultimately generate descriptions of the changes in the scene.
Abstract: This correspondence describes research in the development of symbolic registration techniques directed toward the comparison of pairs of images of the same scene to ultimately generate descriptions of the changes in the scene. Unlike most earlier work in image registration, all the matching and analysis will be performed at a symbolic level rather than a signal level. We have applied this registration procedure on several different types of scenes and the system appears to work well both on pairs of images which may be analyzed in part by signal based systems and those which cannot be so analyzed.
TL;DR: The query language XQL is introduced, and the XQL translator is described in some detail, which can be translated and disambiguated by analyzing the queries using the conceptual graphs of a database skeleton.
Abstract: The concept of a database skeleton which reflects both the user's conception of the real world and the system's understanding of the interrelationships among database entities is described. It consists of a conceptual schema (conceptual graphs) and a relational schema (information graph). With the aid of the database skeleton, fuzzy queries can be translated and disambiguated by analyzing the queries using the conceptual graphs of a database skeleton. The query language XQL is introduced, and the XQL translator is described in some detail.
TL;DR: Graphical techniques are presented for estimating Hough transform performance for detecting straight lines in noisy digital pictures showing explicitly the influence of noise due, for example, to quantizing errors on the accuracy of estimating the underlying sets of collinear points.
Abstract: Graphical techniques are presented for estimating Hough transform performance for detecting straight lines in noisy digital pictures. The methods show explicitly the influence of noise due, for example, to quantizing errors on the accuracy of estimating the underlying sets of collinear points. Exact bounds are obtained for sets of collinear points showing that under quite general conditions only the endpoints are of significance. Theorems governing grid size for the accumulator method are given.
TL;DR: The random walk procedure is intended mainly for the texture discrimination problem, and its possible application to the edge detection problem (as shown in this paper) is just a by-product.
Abstract: We consider the problem of texture discrimination Random walks are performed in a plain domain D bounded by an absorbing boundary ? and the absorption distribution is calculated Measurements derived from such distributions are the features used for discrimination Both problems of texture discrimination and edge segment detection can be solved using the same random walk approach The border distributions and their differences with respect to a homogeneous image can classify two different images as having similar or dissimilar textures The existence of an edge segment is concluded if the boundary distribution for a given window (subimage) differs significantly from the boundary distribution for a homogeneous (uniform grey level) window The random walk procedure has been implemented and results of texture discrimination are shown A comparison is made between results obtained using the random walk approach and the first-or second-order statistics, respectively The random walk procedure is intended mainly for the texture discrimination problem, and its possible application to the edge detection problem (as shown in this paper) is just a by-product
TL;DR: A method for studying the asymptotic behavior of discrete transformations is developed using numerical quadrature theory and it is shown that the discrete cosine transform is asymptonically optimal for all finite-order Markov signals.
Abstract: A method for studying the asymptotic behavior of discrete transformations is developed using numerical quadrature theory. This method allows a more convenient examination of the correlation properties of common unitary transforms for large block sizes. As a practical result of this method it is shown that the discrete cosine transform is asymptotically optimal for all finite-order Markov signals.
TL;DR: This paper presents a new clustering algorithm for analyzing unordered discrete-valued data that consists of a cluster initiation phase and a sample regrouping phase based on a data-directed valley detection process utilizing the optimal second-order product approximation of high-order discrete probability distribution.
Abstract: This paper presents a new clustering algorithm for analyzing unordered discrete-valued data. This algorithm consists of a cluster initiation phase and a sample regrouping phase. The first phase is based on a data-directed valley detection process utilizing the optimal second-order product approximation of high-order discrete probability distribution, together with a distance measure for discrete-valued data. As for the second phase, it involves the iterative application of the Bayes' decision rule based on subgroup discrete distributions. Since probability is used as its major decision criterion, the proposed method minimizes the disadvantages of yielding solutions sensitive to the arbitrary distance measure adopted. The performance of the proposed algorithm is evaluated by applying it to four different sets of simulated data and a set of clinical data. For performance comparison, the decision-directed algorithm [11] is also applied to the same set of data. These evaluation experiments fully demonstrate the validity and the operational feasibility of the proposed algorithm and its superiority as compared to the decision-directed algorithm.