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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 128 (22 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.
The Dirichlet Problem for the Total Variation Flow
, 2001
"... We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov's method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L¹ for entropy solutions. To prove the existence we u ..."
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Cited by 27 (9 self)
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We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov's method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L¹ for entropy solutions. To prove the existence we use the nonlinear semigroup theory and we show that when the initial and boundary data are nonnegative the semigroup solutions are strong solutions.
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 12 (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.
Generalized stress concentration factors for equilibrated forces and stresses, accepted for publication
 Journal of Elasticity
"... Abstract. As a sequel to a recent work we consider the generalized stress concentration factor, a purely geometric property of a body that for the various loadings, indicates the ratio between the maximum of the optimal stress and maximum of the loading fields. The optimal stress concentration facto ..."
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Cited by 4 (3 self)
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Abstract. As a sequel to a recent work we consider the generalized stress concentration factor, a purely geometric property of a body that for the various loadings, indicates the ratio between the maximum of the optimal stress and maximum of the loading fields. The optimal stress concentration factor pertains to a stress field that satisfies the principle of virtual work and for which the stress concentration factor is minimal. Unlike the previous work, we require that the external loading be equilibrated and that the stress field be a symmetric tensor field.
BOUNDS ON THE TRACE MAPPING OF LDFIELDS
, 2005
"... Abstract. Bounds on the trace mappings defined on the Sobolev space W 1 1 (Ω) and the space LD(Ω) of integrable stains are obtained. Such bounds correspond to stress concentration—the ratio between the maximal stress in a body and the maximum of the traction applied to its boundary. The analysis lea ..."
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Cited by 1 (0 self)
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Abstract. Bounds on the trace mappings defined on the Sobolev space W 1 1 (Ω) and the space LD(Ω) of integrable stains are obtained. Such bounds correspond to stress concentration—the ratio between the maximal stress in a body and the maximum of the traction applied to its boundary. The analysis leading to the bounds may be described in the mechanical context of stress theory and stress concentration. 1.
STRESS OPTIMIZATION FOR SUPPORTED BODIES
, 1946
"... Abstract. For a surface traction t, acting on a region Γt of the boundary of a given body Ω supported on Γ0 ⊂ ∂Ω, we consider the infimum σ opt t = infσ {ess supx σ(x)} over all stress fields σ in equilibrium with t, i.e., the smallest essential bound on all conceivable stress fields. Using the sp ..."
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Abstract. For a surface traction t, acting on a region Γt of the boundary of a given body Ω supported on Γ0 ⊂ ∂Ω, we consider the infimum σ opt t = infσ {ess supx σ(x)} over all stress fields σ in equilibrium with t, i.e., the smallest essential bound on all conceivable stress fields. Using the space of LDvector fields on Ω, we show that σ opt t is attainable by some stress field ̂σ and that t · w dA∣
and
, 1999
"... We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov’s method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L1 for entropy solutions. To prove the existence we use t ..."
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We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov’s method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L1 for entropy solutions. To prove the existence we use the nonlinear semigroup theory and we show that when the initial and boundary data are nonnegative the semigroup solutions are strong solutions. 2001 Academic Press 1.
SES/RIVLIN/SPECIAL ISSUE LOAD CAPACITY OF BODIES
"... Abstract. For the stress analysis in a plastic body Ω, we prove that there exists a maximal positive number C, the load capacity ratio, such that the body will not collapse under any external traction field t bounded by CY0, where Y0 is the yield stress. The load capacity ratio depends only on the g ..."
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Abstract. For the stress analysis in a plastic body Ω, we prove that there exists a maximal positive number C, the load capacity ratio, such that the body will not collapse under any external traction field t bounded by CY0, where Y0 is the yield stress. The load capacity ratio depends only on the geometry of the body and is given by