1,721,394 research outputs found
An image segmentation variational model with free discontinuities and contour curvature
No full textWe introduce a functional for image segmentation which takes into account the transparencies (or shadowing) and the occlusions between objects located at different depths in space. By minimizing the functional, we try to reconstruct a piecewise smooth approximation of the input image, the contours due to transparencies, and the contours of the objects together with their hidden portions. The functional includes a Mumford-Shah type energy and a term involving the curvature of the contours. The variational properties of the functional are studied, as well as its approximation by Gamma-convergence. The comparison with the Nitzberg-Mumford variational model for segmentation with depth is also discussed
Approximation by Gamma-convergence of a curvature-depending functional in visual reconstruction
No full textVariational properties of a model for image segmentation with overlapping regions
No full textWe introduce a functional for image segmentation which takes into account the occlusions between objects in the image which are located at different depths in space. By minimizing the functional, we try to reconstruct both a piecewise smooth approximation of the input image g and the contours of the objects together with their hidden portions. Some variational properties of the involved functionals are then studied
Asymptotic properties of the Nitzberg-Mumford variational model for segmentation with depth
No full textWe consider the Nitzberg-Mumford variational formulation of the segmentation with depth problem. This is an image segmentation model that allows regions to overlap in order to take into account occlusions between different objects. The model gives rise to a variational problem with free boundaries. We discuss some qualitative properties of the Nitzberg-Mumford functional within the framework of the relaxation methods of the Calculus of Variations. We try to characterize minimizing segmentations of images made up of smooth overlapping regions, when the weight of the fidelity term in the functional becomes large. This should give some theoretical information about the capability of the model to reconstruct both occluded boundaries and depth order. © Birkhäuser Verlag Basel/Switzerland 2006
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
One-Dimensional Failure Modes for Bodies with Non-convex Plastic Energies
Full text linkIn this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution. Here, an approximate analytical solution of the evolution problem is determined in the one-dimensional case of a tensile bar. Different solutions are found describing specific plastic strain processes, and correlations between the different evolution modes and the convexity/concavity properties of the plastic energy density are established. The variety of solutions demonstrates the large versatility of the model in describing many failure mechanisms, ranging from brittle to ductile. Indeed, for a convex plastic energy, the plastic strain diffuses in the body, while, for a concave plastic energy, it localizes in regions whose amplitude depends on the internal length parameter included into the non-local energy term, and, depending on the convexity properties of the first derivative of the plastic energy, the localization band expands or contracts. Complex failure processes combining different modes can be reproduced by assuming plastic energy functionals with specific convex and concave branches. The quasi-brittle failure of geomaterials in simple tension tests was reproduced by assuming a convex-concave plastic energy, and the accuracy of the analytical predictions was checked by comparing them with the numerical results of finite element simulations
Variational approximation of a second order free discontinuity problem in computer vision
Full text linkWe consider a functional, proposed by Blake and Zisserman for computer vision
problems, which depends on free discontinuities, free gradient discontinuities, and second order
derivatives. We show how this functional can be approximated by elliptic functionals defined on
Sobolev spaces. The approximation takes place in a variational sense, the De Giorgi Γ-convergence,
and extends to this second order model an approximation of the Mumford–Shah functional obtained
by Ambrosio and Tortorelli. For the purpose of illustration an algorithm based on the Γ-convergent
approximation is applied to the problem of computing depth from stereo images and some numerical
examples are presented
Variational approximation of a second order free discontinuity problem in computer vision
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