This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric. In this SRV representation, the elastic metric simplifies to the IL(2) metric, the reparameterization group acts by isometries, and the space of unit length curves becomes the unit sphere. The shape space of closed curves is the quotient space of (a submanifold of) the unit sphere, modulo rotation, and reparameterization groups, and we find geodesics in that space using a path straightening approach. These geodesics and geodesic distances provide a framework for optimally matching, deforming, and comparing shapes. These ideas are demonstrated using: 1) shape analysis of cylindrical helices for studying protein structure, 2) shape analysis of facial curves for recognizing faces, 3) a wrapped probability distribution for capturing shapes of planar closed curves, and 4) parallel transport of deformations for predicting shapes from novel poses.
Applications in computer vision involve statistically analyzing an important class of constrained, nonnegative functions, including probability density functions (in texture analysis), dynamic time-warping functions (in activity analysis), and re-parametrization or non-rigid registration functions (in shape analysis of curves). For this one needs to impose a Riemannian
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) 'A study of Gaussian mixture models of color and texture features for image classi cation and segmentation.', Pattern recognition., 39 (4). pp. 695-706. Further information on publisher's website:http://dx.doi.org/10.1016/j.patcog.2005.10.028Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Pattern Recognition. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe aims of this paper are two-fold: to define Gaussian mixture models of colored texture on several feature spaces and to compare the performance of these models in various classification tasks, both with each other and with other models popular in the literature. We construct Gaussian mixtures models over a variety of different color and texture feature spaces, with a view to the retrieval of textured color images from databases. We compare supervised classification results for different choices of color and texture features using the Vistex database, and explore the best set of features and the best GMM configuration for this task. In addition we introduce several methods for combining the 'color' and 'structure' information in order to improve the classification performances. We then apply the resulting models to the classification of texture databases and to the classification of man-made and natural areas in aerial images. We compare the GMM model with other models in the literature, and show an overall improvement in performance.
Abstract. We introduce a new class of active contour models that hold great promise for region and shape modelling, and we apply a special case of these models to the extraction of road networks from satellite and aerial imagery. The new models are arbitrary polynomial functionals on the space of boundaries, and thus greatly generalize the linear functionals used in classical contour energies. While classical energies are expressed as single integrals over the contour, the new energies incorporate multiple integrals, and thus describe long-range interactions between different sets of contour points. As prior terms, they describe families of contours that share complex geometric properties, without making reference to any particular shape, and they require no pose estimation. As likelihood terms, they can describe multi-point interactions between the contour and the data. To optimize the energies, we use a level set approach. The forces derived from the new energies are non-local however, thus necessitating an extension of standard level set methods. Networks are a shape family of great importance in a number of applications, including remote sensing imagery. To model them, we make a particular choice of prior quadratic energy that describes reticulated structures, and augment it with a likelihood term that couples the data at pairs of contour points to their joint geometry. Promising experimental results are shown on real images.
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