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Pattern Analysis and Machine Intelligence, IEEE Transactions on

Issue 6 • Date Jun 2000

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Displaying Results 1 - 9 of 9
  • Exploring texture ensembles by efficient Markov chain Monte Carlo-Toward a “trichromacy” theory of texture

    Page(s): 554 - 569
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4700 KB)  

    Presents a mathematical definition of texture, the Julesz ensemble Ω(h), which is the set of all images (defined on Z2) that share identical statistics h. Then texture modeling is posed as an inverse problem: Given a set of images sampled from an unknown Ω(h *), we search for the statistics h* which define the ensemble. A Ω(h) has an associated probability distribution q(I; h), which is uniform over the images in Ω(h) and has zero probability outside. The authors previously (1999) showed q(I; h) to be the limit distribution of the FRAME (filter, random field, and minimax entropy) model, as the image lattice Λ→Z2. This conclusion establishes the intrinsic link between the scientific definition of texture on Z2 and the mathematical models of texture on finite lattices. It brings two advantages: the practice of texture image synthesis by matching statistics is put on a mathematical foundation; and we need not learn the expensive FRAME model in feature pursuit, model selection and texture synthesis. An efficient Markov chain Monte Carte algorithm is proposed for sampling Julesz ensembles. It generates random texture images by moving along the directions of filter coefficients and, thus, extends the traditional single site Gibbs sampler. We compare four popular statistical measures in the literature, in terms of their descriptive abilities. Our experiments suggest that a small number of bins in marginal histograms are sufficient for capturing a variety of texture patterns View full abstract»

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  • Bayesian graph edit distance

    Page(s): 628 - 635
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (572 KB)  

    This paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of edit-distance originally introduced for graph-matching by Sanfeliu and Fu (1983). We show how the Levenshtein distance (1966) can be used to model the probability distribution for structural errors in the graph-matching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graph-matching algorithm with that recently reported by Wilson and Hancock. The use of edit-distance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worst-case complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match View full abstract»

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  • Precise candidate selection for large character set recognition by confidence evaluation

    Page(s): 636 - 641
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (220 KB)  

    This paper proposes a precise candidate selection method for large character set recognition by confidence evaluation of distance-based classifiers. The proposed method is applicable to a wide variety of distance metrics and experiments on Euclidean distance and city block distance have achieved promising results. By confidence evaluation, the distribution of distances is analyzed to derive the probabilities of classes in two steps: output probability evaluation and input probability inference. Using the input probabilities as confidences, several selection rules have been tested and the rule that selects the classes with high confidence ratio to the first rank class produced best results. The experiments were implemented on the ETL9B database and the results show that the proposed method selects about one-fourth as many candidates with accuracy preserved compared to the conventional method that selects a fixed number of candidates View full abstract»

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  • Ordering and parameterizing scattered 3D data for B-spline surface approximation

    Page(s): 642 - 648
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (712 KB)  

    Surface representation is intrinsic to many applications in medical imaging, computer vision, and computer graphics. We present a method that is based on surface modeling by B-spline. The B-spline constructs a smooth surface that best fits a set of scattered unordered 3D range data points obtained from either a structured light system (a range finder), or from point coordinates on the external contours of a set of surface sections, as for example in histological coronal brain sections. B-spline stands as of one the most efficient surface representations. It possesses many properties such as boundedness, continuity, local shape controllability, and invariance to affine transformations that makes it very suitable and attractive for surface representation. Despite its attractive properties, however, B-spline has not been widely applied for representing a 3D scattered nonordered data set. This may be due to the problem in finding an ordering and a choice for the topological parameters of the B-spline that lead to a physically meaningful surface parameterization based on the scattered data set. The parameters needed for the B-spline surface construction, as well as finding the ordering of the data points, are calculated based on the geodesics of the surface extended Gaussian map. The set of control points is analytically calculated by solving a minimum mean square error problem for best surface fitting. For a noise immune modeling, we elect to use an approximating rather than an interpolating B-spline. We also examine ways of making the B-spline fitting technique robust to local deformation and noise View full abstract»

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  • Finding curvilinear features in spatial point patterns: principal curve clustering with noise

    Page(s): 601 - 609
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    Clustering about principal curves combines parametric modeling of noise with nonparametric modeling of feature shape. This is useful for detecting curvilinear features in spatial point patterns, with or without background noise. Applications include the detection of curvilinear minefields from reconnaissance images, some of the points in which represent false detections, and the detection of seismic faults from earthquake catalogs. Our algorithm for principal curve clustering is in two steps: The first is hierarchical and agglomerative (HPCC) and the second consists of iterative relocation based on the classification EM algorithm (CEM-PCC). HPCC is used to combine potential feature clusters, while CEM-PCC refines the results and deals with background noise. It is important to have a good starting point for the algorithm: This can be found manually or automatically using, for example, nearest neighbor clutter removal or model-based clustering. We choose the number of features and the amount of smoothing simultaneously, using approximate Bayes factors View full abstract»

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  • Classification with nonmetric distances: image retrieval and class representation

    Page(s): 583 - 600
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1188 KB)  

    A key problem in appearance-based vision is understanding how to use a set of labeled images to classify new images. Systems that model human performance, or that use robust image matching methods, often use nonmetric similarity judgments; but when the triangle inequality is not obeyed, most pattern recognition techniques are not applicable. Exemplar-based (nearest-neighbor) methods can be applied to a wide class of nonmetric similarity functions. The key issue, however, is to find methods for choosing good representatives of a class that accurately characterize it. We show that existing condensing techniques are ill-suited to deal with nonmetric dataspaces. We develop techniques for solving this problem, emphasizing two points: First, we show that the distance between images is not a good measure of how well one image can represent another in nonmetric spaces. Instead, we use the vector correlation between the distances from each image to other previously seen images. Second, we show that in nonmetric spaces, boundary points are less significant for capturing the structure of a class than in Euclidean spaces. We suggest that atypical points may be more important in describing classes. We demonstrate the importance of these ideas to learning that generalizes from experience by improving performance. We also suggest ways of applying parametric techniques to supervised learning problems that involve a specific nonmetric distance functions, showing how to generalize the idea of linear discriminant functions in a way that may be more useful in nonmetric spaces View full abstract»

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  • Evolutionary pursuit and its application to face recognition

    Page(s): 570 - 582
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1296 KB)  

    Introduces evolutionary pursuit (EP) as an adaptive representation method for image encoding and classification. In analogy to projection pursuit, EP seeks to learn an optimal basis for the dual purpose of data compression and pattern classification. It should increase the generalization ability of the learning machine as a result of seeking the trade-off between minimizing the empirical risk encountered during training and narrowing the confidence interval for reducing the guaranteed risk during testing. It therefore implements strategies characteristic of GA for searching the space of possible solutions to determine the optimal basis. It projects the original data into a lower dimensional whitened principal component analysis (PCA) space. Directed random rotations of the basis vectors in this space are searched by GA where evolution is driven by a fitness function defined by performance accuracy (empirical risk) and class separation (confidence interval). Accuracy indicates the extent to which learning has been successful, while separation gives an indication of expected fitness. The method has been tested on face recognition using a greedy search algorithm. To assess both accuracy and generalization capability, the data includes for each subject images acquired at different times or under different illumination conditions. EP has better recognition performance than PCA (eigenfaces) and better generalization abilities than the Fisher linear discriminant (Fisherfaces) View full abstract»

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  • Fractional-step dimensionality reduction

    Page(s): 623 - 627
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (192 KB)  

    Linear projections for dimensionality reduction, computed using linear discriminant analysis (LDA), are commonly based on optimization of certain separability criteria in the output space. The resulting optimization problem is linear, but these separability criteria are not directly related to the classification accuracy in the output space. Consequently, a trial and error procedure has to be invoked, experimenting with different separability criteria that differ in the weighting function used and selecting the one that performed best on the training set. Often, even the best weighting function among the trial choices results in poor classification of data in the subspace. In this short paper, we introduce the concept of fractional dimensionality and develop an incremental procedure, called the fractional-step LDA (F-LDA) to reduce the dimensionality in fractional steps. The F-LDA algorithm is more robust to the selection of weighting function and for any given weighting function, it finds a subspace in which the classification accuracy is higher than that obtained using LDA View full abstract»

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  • Fast and globally convergent pose estimation from video images

    Page(s): 610 - 622
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (332 KB)  

    Determining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effectively account for the orthonormal structure of rotation matrices. We show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object (as opposed to image) space. Using object space collinearity error, we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent. Experimentally, we show that the method is computationally efficient, that it is no less accurate than the best currently employed optimization methods, and that it outperforms all tested methods in robustness to outliers View full abstract»

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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