2,088 research outputs found

    A Unified Algebraic Framework for Fuzzy Image Compression and Mathematical Morphology

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    In this paper we show how certain techniques of image processing, having different scopes, can be joined together under a common "algebraic roof"

    The Interaction of Yer Deletion and Nasal Assimilation in Optimality Theory1

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    The problem of opacity presents a challenge for generative phonology. This paper examines the process of Nasal Assimilation in Polish rendered opaque by the process of Vowel Deletion in Optimality Theory (Prince & Smolensky, 1993), which currently is a dominating model for phonological analysis. The opaque interaction of the two processes exposes the inadequacy of standard Optimality Theory arising from the fact that standard OT is a non-derivational theory. It is argued that only by introducing intermediate levels can Optimality Theory deal with complex cases of opaque interactions

    On morphological hierarchical representations for image processing and spatial data clustering

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    Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

    Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms

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    We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate minimizer of the model function yields a descent direction, along which the next iterate is found. Complemented with an Armijo-like line search strategy, we obtain a flexible algorithm for which we prove (subsequential) convergence to a stationary point under weak assumptions on the growth of the model function error. Special instances of the algorithm with a Euclidean distance function are, for example, Gradient Descent, Forward--Backward Splitting, ProxDescent, without the common requirement of a "Lipschitz continuous gradient". In addition, we consider a broad class of Bregman distance functions (generated by Legendre functions) replacing the Euclidean distance. The algorithm has a wide range of applications including many linear and non-linear inverse problems in signal/image processing and machine learning

    Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

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    Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations U:RdSd1RU:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R} defined on the extended space of positions and orientations, which we relate to data on the roto-translation group SE(d)SE(d), d=2,3d=2,3. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in SE(d)SE(d). These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on SE(d)SE(d). We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation UU and we show their advantage compared to the standard left-invariant frame on SE(d)SE(d). Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores
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