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A geometrical framework for low level vision
 IEEE Trans. on Image Processing
, 1998
"... Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, an ..."
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Cited by 176 (35 self)
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Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, and 2D surfaces in five dimensions for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms. Index Terms — Color image processing, image enhancement, image smoothing, nonlinear image diffusion, scalespace. I.
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.
Modified curvature motion for image smoothing and enhancement
 IEEE Trans. Image Processing
, 1998
"... Abstract—In this paper, we formulate a general modified mean curvature based equation for image smoothing and enhancement. The key idea is to consider the image as a graph in some Rn, and apply a mean curvature type motion to the graph. We will consider some special cases relevant to greyscale and ..."
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Cited by 28 (2 self)
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Abstract—In this paper, we formulate a general modified mean curvature based equation for image smoothing and enhancement. The key idea is to consider the image as a graph in some Rn, and apply a mean curvature type motion to the graph. We will consider some special cases relevant to greyscale and color images. Index Terms—Enhancement, smoothing, mean curvature, partial differential equations. 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 use th ..."
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Cited by 21 (7 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.
Uniqueness of the Cheeger set of a convex body
, 2007
"... We prove that if C ⊂ IR N is a an open bounded convex set, then there is only one Cheeger set inside C and it is convex. A Cheeger set of C is a set which minimizes the ratio perimeter over volume among all subsets of C. ..."
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Cited by 12 (2 self)
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We prove that if C ⊂ IR N is a an open bounded convex set, then there is only one Cheeger set inside C and it is convex. A Cheeger set of C is a set which minimizes the ratio perimeter over volume among all subsets of C.
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.
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.
Modified Curvature Motion for Image Smoothing and Enhancement
"... Abstract—In this paper, we formulate a general modified mean curvature based equation for image smoothing and enhancement. The key idea is to consider the image as a graph in some ‚ �, and apply a mean curvature type motion to the graph. We will consider some special cases relevant to greyscale an ..."
Abstract
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Abstract—In this paper, we formulate a general modified mean curvature based equation for image smoothing and enhancement. The key idea is to consider the image as a graph in some ‚ �, and apply a mean curvature type motion to the graph. We will consider some special cases relevant to greyscale and color images. Index Terms—Enhancement, smoothing, mean curvature, partial differential equations. I.