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Dive into the research topics where Andres Fco. Solé is active.

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Featured researches published by Andres Fco. Solé.


Multiscale Modeling & Simulation | 2003

Image Decomposition and Restoration Using Total Variation Minimization and the H1

Stanley Osher; Andres Fco. Solé; Luminita A. Vese

In this paper, we propose a new model for image restoration and image decomposition into cartoon and texture, based on the total variation minimization of Rudin, Osher, and Fatemi [Phys. D, 60 (1992), pp. 259--268], and on oscillatory functions, which follows results of Meyer [Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, Univ. Lecture Ser. 22, AMS, Providence, RI, 2002]. This paper also continues the ideas introduced by the authors in a previous work on image decomposition models into cartoon and texture [L. Vese and S. Osher, J. Sci. Comput., to appear]. Indeed, by an alternative formulation, an initial image f is decomposed here into a cartoon part u and a texture or noise part v. The u component is modeled by a function of bounded variation, while the v component is modeled by an oscillatory function, bounded in the norm dual to


Journal of Scientific Computing | 2003

TV Based Image Restoration with Local Constraints

Marcelo Bertalmío; Vicent Caselles; Bernard Rougé; Andres Fco. Solé

|\cdot|_{H^1_0}


IEEE Transactions on Medical Imaging | 2001

Anisotropic 2-D and 3-D averaging of fMRI signals

Andres Fco. Solé; Shing-Chung Ngan; Guillermo Sapiro; Xiaoping Hu; Antonio M. López

. After some transformation, the resulting PDE is of fourth order, envolving the Laplacian of the curvature of level lines. Fina...


IEEE Transactions on Image Processing | 2004

Morse description and geometric encoding of digital elevation maps

Andres Fco. Solé; Vicent Caselles; Guillermo Sapiro; Francesc Aràndiga

The problem of recovering an image that has been blurred and corrupted with additive noise is ill-posed. Among the methods that have been proposed to solve this problem, one of the most successful ones is that of constrained Total Variation (TV) image restoration, proposed by L. Rudin, S. Osher, and E. Fatemi. In its original formulation, to ensure the satisfaction of constraints, TV restoration requires the estimation of a global parameter λ (a Lagrange multiplier). We observe that if λ is global, the constraints of the method are also satisfied globally, but not locally. The effect is that the restoration is better achieved in some regions of the image than in others. To avoid this, we propose a variant of the TV restoration model including, instead of a single constraint λ, a set of constraints λi, each one corresponding to a region Oi of the image. We discuss the existence and uniqueness of solutions of the proposed model and display some numerical experiments.


Computer Vision and Image Understanding | 2001

Crease Enhancement Diffusion

Andres Fco. Solé; Antonio M. López; Guillermo Sapiro

A novel method for denoising functional magnetic resonance imaging temporal signals is presented in this note. The method is based on progressively enhancing the temporal signal by means of adaptive anisotropic spatial averaging. This average is based on a new metric for comparing temporal signals corresponding to active fMRI regions. Examples are presented both for simulated and real two and three-dimensional data. The software implementing the proposed technique is publicly available for the research community.


international conference on image processing | 2003

Image decomposition, image restoration, and texture modeling using total variation minimization and the H/sup -1/ norm

Stanley Osher; Andres Fco. Solé; Luminita A. Vese

Two complementary geometric structures for the topographic representation of an image are developed in this work. The first one computes a description of the Morse-topological structure of the image, while the second one computes a simplified version of its drainage structure. The topographic significance of the Morse and drainage structures of digital elevation maps (DEMs) suggests that they can been used as the basis of an efficient encoding scheme. As an application, we combine this geometric representation with an interpolation algorithm and lossless data compression schemes to develop a compression scheme for DEMs. This algorithm achieves high compression while controlling the maximum error in the decoded elevation map, a property that is necessary for the majority of applications dealing with DEMs. We present the underlying theory and compression results for standard DEM data.


Journal of Mathematical Imaging and Vision | 2003

3D Curves Reconstruction Based on Deformable Models

Catalina Sbert; Andres Fco. Solé

Ridge and valley structures are important image features, especially in oriented textures. Usually, the extraction of these structures requires a prefiltering step to regularize the source image. In this paper, we show that classical diffusion-based filters are not always appropriate for this task and propose a new filtering process. This new filter can be interpreted as an example of introducing the intrinsic image structure in a diffusion process.


Multiscale Modeling & Simulation | 2004

Morse Description and Morphological Encoding of Continuous Data

Vicent Caselles; Guillermo Sapiro; Andres Fco. Solé; Coloma Ballester

We propose a new model for image restoration and decomposition, based on the total variation minimization of Rudin-Osher-Fatemi (1992), and on some new techniques by Y. Meyer (2002) for oscillatory functions. An initial image f is decomposed into a cartoon part u and a texture or noise part v. The u component is modeled by a function of bounded variation, while the v component by an oscillatory function, with bounded H/sup -1/ norm. After some transformation, the resulting PDE is of fourth order. The proposed model continues the ideas and techniques previously introduced by the authors in L Vese et al., (2002). Image decomposition and denoising numerical results will be shown by the proposed new fourth order nonlinear partial differential equation.


international conference on pattern recognition | 2000

Stereo reconstruction of 3D curves

Catalina Sbert; Andres Fco. Solé

We present a new method, based on curve evolution, for the reconstruction of a 3D curve from two different projections. It is based on the minimization of an energy functional. Following the work on geodesic active contours by Caselles et al. (in Int. Conf. on Pattern Recognition, 1996, Vol. 43, pp. 693–737), we then transform the problem of minimizing the functional into a problem of geodesic computation in a Riemann space. The Euler-Lagrange equation of this new functional is derived and its associated PDE is solved using the level set formulation, giving the existence and uniqueness results. We apply the model to the reconstruction of a vessel from a biplane angiography.


international conference on image processing | 2003

Morse description and geometric encoding of DEM data

Andres Fco. Solé; Vicent Caselles; Guillermo Sapiro; Francesc Aràndiga

A geometric representation for images is studied in this work. This is based on two complementary geometric structures for the topographic representation of an image. The first one computes a description of the Morse structure, while the second one computes a simplified version of drainage structures. The topographic significance of the Morse and drainage structures of digital elevation maps (DEMs) suggests that they can been used as the basis of an efficient encoding scheme. As an application we then combine this geometric representation with a consistent interpolation algorithm and lossless data compression schemes to develop an efficient compression algorithm for DEMs. This coding scheme controls the

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Antonio M. López

Autonomous University of Barcelona

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Bernard Rougé

Centre National D'Etudes Spatiales

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Stanley Osher

University of California

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