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Pattern Analysis and Machine Intelligence, IEEE Transactions on

Issue 1 • Date Jan. 1987

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  • [Front cover]

    Page(s): c1
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  • List of Contributors

    Page(s): nil1
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  • [Breaker page]

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  • Opinion

    Page(s): 1
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  • The Synthesis and Analysis of Color Images

    Page(s): 2 - 13
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    I describe a method for performing the synthesis and analysis of digital color images. The method is based on two principles. First, image data are represented with respect to the separate physical factors, surface reflectance and the spectral power distribution of the ambient light, that give rise to the perceived color of an object. Second, the encoding is made efficient by using a basis expansion for the surface spectral reflectance and spectral power distribution of the ambient light that takes advantage of the high degree of correlation across the visible wavelengths normally found in such functions. Within this framework, the same basic methods can be used to synthesize image data for color display monitors and printed materials, and to analyze image data into estimates of the spectral power distribution and surface spectral reflectances. The method can be applied to a variety of tasks. Examples of applications include the color balancing of color images and the identification of material surface spectral reflectance when the lighting cannot be completely controlled. View full abstract»

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  • Color-Encoded Structured Light for Rapid Active Ranging

    Page(s): 14 - 28
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    In this paper, we discuss a novel strategy for rapid acquisition of the range map of a scene employing color-encoded structured light. This technique offers several potential advantages including increased speed and improved accuracy. In this approach we illuminate the scene with a single encoded grid of colored light stripes. The indexing problem, that of matching a detected image plane stripe with its position in the projection grid, is solved from a knowledge of the color grid encoding. In fact, the possibility exists for the first time to acquire high-resolution range data in real time for modest cost, since only a single projection and single color image are required. Grid to grid alignment problems associated with previous multistripe techniques are eliminated, as is the requirement for dark interstices between grid stripes. Scene illumination is more uniform, simplifying the stripe detection problem, and mechanical difficulties associated with the equipment design are significantly reduced. View full abstract»

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  • Toward a Fundamental Theory of Optimal Feature Selection: Part II-Implementation and Computational Complexit

    Page(s): 29 - 38
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    Certain algorithms and their computational complexity are examined for use in a VLSI implementation of the real-time pattern classifier described in Part I of this work. The most computationally intensive processing is found in the classifier training mode wherein subsets of the largest and smallest eigenvalues and associated eigenvectors of the input data covariance pair must be computed. It is shown that if the matrix of interest is centrosymmetric and the method for eigensystem decomposition is operator-based, the problem architecture assumes a parallel form. Such a matrix structure is found in a wide variety of pattern recognition and speech and signal processing applications. Each of the parallel channels requires only two specialized matrix-arithmetic modules. These modules may be implemented as linear arrays of processing elements having at most O(N) elements where N is the input data vector dimension. The computations may be done in O(N) time steps. This compares favorably to O(N3) operations for a conventional, or general, rotation-based eigensystem solver and even the O(2N2) operations using an approach incorporating the fast Levinson algorithm for a matrix of Toeplitz structure since the underlying matrix in this work does not possess a Toeplitz structure. Some examples are provided on the convergence of a conventional iterative approach and a novel two-stage iterative method for eigensystem decomposition. View full abstract»

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  • Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields

    Page(s): 39 - 55
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    This paper presents a new approach to the use of Gibbs distributions (GD) for modeling and segmentation of noisy and textured images. Specifically, the paper presents random field models for noisy and textured image data based upon a hierarchy of GD. It then presents dynamic programming based segmentation algorithms for noisy and textured images, considering a statistical maximum a posteriori (MAP) criterion. Due to computational concerns, however, sub-optimal versions of the algorithms are devised through simplifying approximations in the model. Since model parameters are needed for the segmentation algorithms, a new parameter estimation technique is developed for estimating the parameters in a GD. Finally, a number of examples are presented which show the usefulness of the Gibbsian model and the effectiveness of the segmentation algorithms and the parameter estimation procedures. View full abstract»

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  • Finding Trajectories of Feature Points in a Monocular Image Sequence

    Page(s): 56 - 73
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    Identifying the same physical point in more than one image, the correspondence problem, is vital in motion analysis. Most research for establishing correspondence uses only two frames of a sequence to solve this problem. By using a sequence of frames, it is possible to exploit the fact that due to inertia the motion of an object cannot change instantaneously. By using smoothness of motion, it is possible to solve the correspondence problem for arbitrary motion of several nonrigid objects in a scene. We formulate the correspondence problem as an optimization problem and propose an iterative algorithm to find trajectories of points in a monocular image sequence. A modified form of this algorithm is useful in case of occlusion also. We demonstrate the efficacy of this approach considering synthetic, laboratory, and real scenes. View full abstract»

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  • A New Class of Detail-Preserving Filters for Image Processing

    Page(s): 74 - 90
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    A new class of median type filters for image processing is proposed. In the filters, linear FIR substructures are used in conjunction with the median operation. The root signals and noise attenuation properties of the FIR-median hybrid filters are analyzed and compared to representative edge preserving filtering operations. The concept of multilevel median operation is introduced to improve the detail preserving property of conventional median and the FIR-median hybrid filters. In the multilevel filters there exists a tradeoff between noise attenuation and detail preservation. The analysis and examples indicate that FIR-median hybrid filters preserve details better and are computationally much more efficient than the conventional median and the K-nearest neighbor averaging filters. View full abstract»

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  • Large Tree Classifier with Heuristic Search and Global Training

    Page(s): 91 - 102
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    In the tree classifier with top-down search, a global decision is made via a series of local decisions. Although this approach gains in classification efficiency, it also gives rise to error accumulation which can be very harmful when the number of classes is very large. To overcome this difficulty, a new tree classifier with the following characteristics is proposed: 1) fuzzy logic search is used to find all ``possible correct classes,'' and some similarity measures are used to determine the ``most probable class''; 2) global training is applied to generate extended terminals in order to enhance the recognition rate; 3) both the training and search algorithms have been given a lot of flexibility, to provide tradeoffs between error and rejection rates, and between the recognition rate and speed. A computer simulation of the decision trees for the recognition of 3200 Chinese character categories yielded a very high recognition rate of 99.93 percent and a very high speed of 861 samples/s, when the program was written in a high level language and run on a large multiuser time-sharing computer. View full abstract»

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  • Bias of Nearest Neighbor Error Estimates

    Page(s): 103 - 112
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    The bias of the finite-sample nearest neighbor (NN) error from its asymptotic value is examined. Expressions are obtained which relate the bias of the NN and 2-NN errors to sample size, dimensionality, metric, and distributions. These expressions isolate the effect of sample size from that of the distributions, giving an explicit relation showing how the bias changes as the sample size is increased. Experimental results are given which suggest that the expressions accurately predict the bias. It is shown that when the dimensionality of the data is high, it may not be possible to estimate the asymptotic error simply by increasing the sample size. A new procedure is suggested to alleviate this problem. This procedure involves measuring the mean NN errors at several sample sizes and using our derived relationship between the bias and the sample size to extrapolate an estimate of the asymptotic NN error. The results are extended to the multiclass problem. The choice of an optimal metric to minimize the bias is also discussed. View full abstract»

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  • Multiple Resolution Representation and Probabilistic Matching of 2-D Gray-Scale Shape

    Page(s): 113 - 121
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    One approach to pattern classification is to match a structural description of a pattern to models which describe the structural properties of pattern classes. The central problem in structural pattern matching is to determine the correspondence between the symbols which comprise a model and symbols which describe a pattern. The difficulty of determining this correspondence depends critically on the representation that is used to describe patterns. This correspondence presents a probabilistic representation for structural models of pattern classes. Both pattern descriptions and models for pattern classes are based on symbols which represent grayscale information at multiple resolutions. A pattern description is given by a tree of symbols with attribute values. Structural models are represented by a tree of symbols with probabilistic attributes. The position and scale (resolution) of the symbols, as well as other ``features,'' are represented by these attributes. An algorithm is presented for determining the correspondence between symbols in a description of a pattern and symbols in a model of a pattern class. This algorithm uses the connectivity between symbols at different scales to constrain the search for correspondence. An interactive training program for learning models of pattern classes is described, and some conclusions from the work are presented. View full abstract»

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  • Histogram Analysis Using a Scale-Space Approach

    Page(s): 121 - 129
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    A new application of scale-space filtering to the classical problem of estimating the parameters of a normal mixture distribution is described. The technique involves generating a multiscale description of a histogram by convolving it with a series of Gaussians of gradually increasing width (standard deviation), and marking the location and direction of the sign change of zero-crossings in the second derivative. The resulting description, or fingerprint, is interpreted by relating pairs of zero-crossings to modes in the histogram where each mode or component is modeled by a normal distribution. Zero-crossings provide information from which estimates of the mixture parameters are computed. These initial estimates are subsequently refined using an iterative maximum likelihood estimation technique. Varying the scale or resolution of the analysis allows the number of components used in approximating the histogram to be controlled. View full abstract»

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  • Computation of Surface Orientation and Structure of Objects Using Grid Coding

    Page(s): 129 - 137
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    In this correspondence, algorithms are introduced to infer surface orientation and structure of visible object surfaces using grid coding. We adopt the active lighting technique to spatially ``encode'' the scene for analysis. The observed objects, which can have surfaces of arbitrary shape, are assumed to rest on a plane (base plane) in a scene which is ``encoded'' with light cast through a grid plane. Two orthogonal grid patterns are used, where each pattern is obtained with a set of equally spaced stripes marked on a glass pane. The scene is observed through a camera and the object surface orientation is determined using the projected patterns on the object surface. If the surfaces under consideration obey certain smoothness constraints, a dense orientation map can be obtained through proper interpolation. The surface structure can then be recovered given this dense orientation map. Both planar and curved surfaces can be handled in a uniform manner. The algorithms we propose yield reasonably accurate results and are relatively tolerant to noise, especially when compared to shape-from-shading techniques. In contrast to other grid coding techniques reported which match the grid junctions for depth reconstruction under the stereopsis principle, our techniques use the direction of the projected stripes to infer local surface orientation and do not require any correspondence relationship between either the grid lines or the grid junctions to be specified. The algorithm has the ability to register images and can therefore be embedded in a system which integrates knowledge from multiple views. View full abstract»

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  • Gradient-Type Algorithms for Partial Singular Value Decomposition

    Page(s): 137 - 142
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    It is often desirable to calculate only a few terms of the SVD expansion of a matrix, corresponding to the largest or smallest singular values. Two algorithms, based on gradient and conjugate gradient search, are proposed for this purpose. SVD is computed term by term in a decreasing or increasing order of singular values. The algorithms are simple to implement and are especially advantageous with large matrices. View full abstract»

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  • Estimating Components of Univariate Gaussian Mixtures Using Prony's Method

    Page(s): 142 - 148
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    A new technique for estimating the component parameters of a mixture of univariate Gaussian distributions using the method of moments is presented. The method of moments basically involves equating the sample moments to the corresponding mixture moments expressed in terms of component parameters and solving these equations for the unknown parameters. These moment equations, however, are nonlinear in the unknown parameters, and heretofore, an analytic solution of these equations has been obtained only for two-component mixtures [2]. Numerical solutions also tend to be unreliable for more than two components, due to the large number of nonlinear equations and parameters to be solved for. In this correspondence, under the condition that the component distributions have equal variances or equal means, the nonlinear moment equations are transformed into a set of linear equations using Prony's method. The solution of these equations for the unknown parameters is analytically feasible and numerically reliable for mixtures with several components. Numerous examples using the proposed technique for two-, three-, and four-component mixtures are presented. View full abstract»

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  • Modified Quadratic Discriminant Functions and the Application to Chinese Character Recognition

    Page(s): 149 - 153
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    Issues in the quadratic discriminant functions (QDF) are discussed and two types of modified quadratic disriminant functions (MQDF1, MQDF2) which are less sensitive to the estimation error of the covariance matrices are proposed. The MQDF1 is a function which employs a kind of a (pseudo) Bayesian estimate of the covariance matrix instead of the maximum likelihood estimate ordinarily used in the QDF. The MQDF2 is a variation of the MQDF1 to save the required computation time and storage. Two discriminant functions were applied to Chinese character recognition to evaluate their effectiveness, and remarkable improvement was observed in their performance. View full abstract»

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  • Semantic Network Array Processor and Its Applications to Image Understanding

    Page(s): 153 - 160
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    The problems in computer vision range from edge detection and segmentation at the lowest level to the problem of cognition at the highest level. This correspondence describes the organization and operation of a semantic network array processor (SNAP) as applicable to high level computer vision problems. The architecture consists of an array of identical cells each containing a content addressable memory, microprogram control, and a communication unit. The applications discussed in this correspondence are the two general techniques, discrete relaxation and dynamic programming. While the discrete relaxation is discussed with reference to scene labeling and edge interpretation, the dynamic programming is tuned for stereo. View full abstract»

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  • Projection-Based Geometrical Feature Extraction for Computer Vision: Algorithms in Pipeline Architectures

    Page(s): 160 - 168
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    In this correspondence, some image transforms and features such as projections along linear patterns, convex hull approximations, Hough transform for line detection, diameter, moments, and principal components will be considered. Specifically, we present algorithms for computing these features which are suitable for implementation in image analysis pipeline architectures. In particular, random access memories and other dedicated hardware components which may be found in the implementation of classical techniques are not longer needed in our algorithms. The effectiveness of our approach is demonstrated by running some of the new algorithms in conventional short-pipelines for image analysis. In related papers, we have shown a pipeline architecture organization called PPPE (Parallel Pipeline Projection Engine), which unleashes the power of projection-based computer vision, image processing, and computer graphics. In the present correspondence, we deal with just a few of the many algorithms which can be supported in PPPE. These algorithms illustrate the use of the Radon transform as a tool for image analysis. View full abstract»

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  • Direct Passive Navigation

    Page(s): 168 - 176
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    In this correspondence, we show how to recover the motion of an observer relative to a planar surface from image brightness derivatives. We do not compute the optical flow as an intermediate step, only the spatial and temporal brightness gradients (at a minimum of eight points). We first present two iterative schemes for solving nine nonlinear equations in terms of the motion and surface parameters that are derived from a least-squares fomulation. An initial pass over the relevant image region is used to accumulate a number of moments of the image brightness derivatives. All of the quantities used in the iteration are efficiently computed from these totals without the need to refer back to the image. We then show that either of two possible solutions can be obtained in closed form. We first solve a linear matrix equation for the elements of a 3 × 3 matrix. The eigenvalue decomposition of the symmetric part of the matrix is then used to compute the motion parameters and the plane orientation. A new compact notation allows us to show easily that there are at most two planar solutions. View full abstract»

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  • [Breaker page]

    Page(s): 177 - 178
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  • Information for authors

    Page(s): 179
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  • [Advertisement]

    Page(s): 180
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  • List of Contributors

    Page(s): nil2
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Aims & Scope

The IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) is published monthly. Its editorial board strives to present most important research results in areas within TPAMI's scope.

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Editor-in-Chief
David A. Forsyth
University of Illinois