Results 1  10
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18
Fillingin by joint interpolation of vector fields and gray levels
 IEEE Trans. Image Processing
, 2001
"... Abstract—A variational approach for fillingin regions of missing data in digital images is introduced in this paper. The approach is based on joint interpolation of the image graylevels and gradient/isophotes directions, smoothly extending in an automatic fashion the isophote lines into the holes ..."
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Cited by 122 (20 self)
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Abstract—A variational approach for fillingin regions of missing data in digital images is introduced in this paper. The approach is based on joint interpolation of the image graylevels and gradient/isophotes directions, smoothly extending in an automatic fashion the isophote lines into the holes of missing data. This interpolation is computed by solving the variational problem via its gradient descent flow, which leads to a set of coupled second order partial differential equations, one for the graylevels and one for the gradient orientations. The process underlying this approach can be considered as an interpretation of the Gestaltist’s principle of good continuation. No limitations are imposed on the topology of the holes, and all regions of missing data can be simultaneously processed, even if they are surrounded by completely different structures. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity. Examples of these applications are given. We conclude the paper with a number of theoretical results on the proposed variational approach and its corresponding gradient descent flow. Index Terms—Fillingin, Gestalt principles, image gradients, image graylevels, interpolation, partial differential equations, variational approach. I.
M.G.: Quasistatic evolution problems for linearly elastic  perfectly plastic materials
"... Abstract. The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rateindependent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded d ..."
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Cited by 25 (5 self)
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Abstract. The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rateindependent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain. Keywords: quasistatic evolution, rateindependent processes, perfect plasticity, PrandtlReuss
Some Qualitative Properties for the Total Variational Flow
"... We prove the existence of a nite extinction time for the solutions of the Dirichlet problem for the total variational ow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in nite time. The asymptotic prole of the solutions of the Dirichlet problem is also s ..."
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Cited by 13 (0 self)
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We prove the existence of a nite extinction time for the solutions of the Dirichlet problem for the total variational ow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in nite time. The asymptotic prole of the solutions of the Dirichlet problem is also studied. It is shown that the proles are non zero solutions of an eigenvalue type problem which seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour enterely dierent to the case of the problem associated to the pLaplacian operator. Finally, the study of the radially symmetric case allows us to point out other qualitative properties which are peculiar of this special class of quasilinear equations. Key words: Total variation ow, nonlinear parabolic equations, asymptotic behaviour, eigenvalue type problem, propagation of the support. AMS (MOS) subject classication: 35K65, 35K55. 1 Introduction Let be a ...
Disocclusion By Joint Interpolation Of Vector Fields And Gray Levels
 SIAM Journal Multiscale Modelling and Simulation
, 2003
"... In this paper we study a variational approach for fillingin regions of missing data in 2D and 3D digital images. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity, or the zooming of images. The approach pre ..."
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Cited by 11 (0 self)
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In this paper we study a variational approach for fillingin regions of missing data in 2D and 3D digital images. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity, or the zooming of images. The approach presented here, initially introduced in [12], is based on a joint interpolation of the image graylevels and gradient/isophotes directions, smoothly extending the isophote lines into the holes of missing data. The process underlying this approach can be considered as an interpretation of the Gestaltist's principle of good continuation. We study the existence of minimizers of our functional and its approximation by smoother functionals. Then we present the numerical algorithm used to minimize it and display some numerical experiments. Key words. Disocclusion, Elastica, BV functions, Interpolation, Variational approach, # convergence AMS subject classifications. 68U10, 35A15, 65D05, 49J99, 47H06, 1.
A Parabolic Quasilinear Problem for Linear Growth Functionals
"... We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. A tipical example of energy functional we consider is the one given by the nonparametric area integrand f(x; ) = p 1 + kk ..."
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Cited by 7 (2 self)
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We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. A tipical example of energy functional we consider is the one given by the nonparametric area integrand f(x; ) = p 1 + kk 2 , which corresponds with the timedependent minimal surface equation. We also study the asymptotic behavoiur of the solutions.
REGULARITY OF STRESSES IN PRANDTLREUSS PERFECT PLASTICITY
"... Abstract. We study the differential properties of solutions of the PrandtlReuss model. We prove that the stress tensor has locally squareintegrable first derivatives: σ ∈ L ∞ ([0, T]; W 1,2 loc (Ω; Mn×n sym)). The result is based on discretization of time and uniform estimates of solutions of the ..."
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Cited by 3 (0 self)
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Abstract. We study the differential properties of solutions of the PrandtlReuss model. We prove that the stress tensor has locally squareintegrable first derivatives: σ ∈ L ∞ ([0, T]; W 1,2 loc (Ω; Mn×n sym)). The result is based on discretization of time and uniform estimates of solutions of the incremental problems, which generalize the estimates in the case of Hencky perfect plasticity. Counterexamples to the regularity of displacements and plastic strains in the quasistatic case are presented. Keywords: quasistatic evolution, rate independent processes, PrandtlReuss plasticity, regularity of solutions.
Existence and Uniqueness of Solution for a Parabolic Quasilinear Problem for Linear Growth Functionals with L¹ Data
, 2001
"... We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. A tipical example of energy functional we consider is the one given by the nonparametric area integrand f(x; ) = p 1 + kk ..."
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Cited by 2 (0 self)
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We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. A tipical example of energy functional we consider is the one given by the nonparametric area integrand f(x; ) = p 1 + kk 2 , which corresponds with the timedependent minimal surface equation. We also study the asimptotic behavoiur of the solutions.
QUASISTATIC EVOLUTION PROBLEMS FOR NONHOMOGENEOUS ELASTIC PLASTIC MATERIALS
"... Abstract. The paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant depen ..."
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Cited by 1 (0 self)
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Abstract. The paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration
Some ThreeDimensional Problems Related to Dielectric Breakdown and Polycrystal Plasticity
"... The wellknown Sachs and Taylor bounds provide easy inner and outer estimates for the e#ective yield set of a polycrystal. It is natural to ask whether they can be improved. We examine this question for two model problems, involving 3D gradients and divergencefree vector fields. For 3D gradients th ..."
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The wellknown Sachs and Taylor bounds provide easy inner and outer estimates for the e#ective yield set of a polycrystal. It is natural to ask whether they can be improved. We examine this question for two model problems, involving 3D gradients and divergencefree vector fields. For 3D gradients the Taylor bound is far from optimal: we derive an improved estimate which scales di#erently when the yield set of the basic crystal is highly eccentric. For 3D divergencefree vector fields the Taylor bound may not be optimal, but it has the optimal scaling law. In both settings the Sachs bound is optimal.