Results 1  10
of
127
Stereoscopic Segmentation
, 2001
"... We cast the problem of multiframe stereo reconstruction of a smooth shape as the global region segmentation of a collection of images of the scene. Dually, the problem of segmenting multiple calibrated images of an object becomes that of estimating the solid shape that gives rise to such images. We ..."
Abstract

Cited by 78 (18 self)
 Add to MetaCart
We cast the problem of multiframe stereo reconstruction of a smooth shape as the global region segmentation of a collection of images of the scene. Dually, the problem of segmenting multiple calibrated images of an object becomes that of estimating the solid shape that gives rise to such images. We assume that the radiance has smooth statistics. This assumption covers Lambertian scenes with smooth or constant albedo as well as fine homogeneous textures, which are known challenges to stereo algorithms based on local correspondence. We pose the segmentation problem within a variational framework, and use fast level set methods to approximate the optimal solution numerically. Our algorithm does not work in the presence of strong textures, where traditional reconstruction algorithms do. It enjoys significant robustness to noise under the assumptions it is designed for. 1
Anisotropic Diffusion of Surfaces and Functions on Surfaces
, 2002
"... We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated 2manifold surface meshes in IR 3 and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combi ..."
Abstract

Cited by 75 (8 self)
 Add to MetaCart
We present a unified anisotropic geometric diffusion PDE model for smoothing (fairing) out noise both in triangulated 2manifold surface meshes in IR 3 and functions defined on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic diffusion tensor. We combine the C 1 limit representation of Loop’s subdivision for triangular surface meshes and vector functions on the surface mesh with the established diffusion model to arrive at a discretized version of the diffusion problem in the spatial direction. The time direction discretization then leads to a sparse linear system of equations. Iteratively, solving the sparse linear system, yields a sequence of faired (smoothed) meshes as well as faired functions.
Fast computation of weighted distance functions and geodesics on implicit hypersurfaces
 J. Comput. Phys
"... An algorithm for the computationally optimal construction of intrinsic weighted distance functions on implicit hypersurfaces is introduced in this paper. The basic idea is to approximate the intrinsic weighted distance by the Euclidean weighted distance computed in a band surrounding the implicit h ..."
Abstract

Cited by 63 (8 self)
 Add to MetaCart
(Show Context)
An algorithm for the computationally optimal construction of intrinsic weighted distance functions on implicit hypersurfaces is introduced in this paper. The basic idea is to approximate the intrinsic weighted distance by the Euclidean weighted distance computed in a band surrounding the implicit hypersurface in the embedding space, thereby performing all the computations in a Cartesian grid with classical and efficient numerics. Based on work on geodesics on Riemannian manifolds with boundaries, we bound the error between the two distance functions. We show that this error is of the same order as the theoretical numerical error in computationally optimal, Hamilton–Jacobibased, algorithms for computing distance functions in Cartesian grids. Therefore, we can use these algorithms, modified to deal with spaces with boundaries, and obtain also for the case of intrinsic distance functions on implicit hypersurfaces a computationally efficient technique. The approach can be extended to solve a more general class of Hamilton–Jacobi equations defined on the implicit surface, following the same idea of approximating their solutions by the solutions in the embedding Euclidean space. The framework here introduced thereby allows for the computations to be performed on a Cartesian grid with computationally optimal algorithms, in spite of the fact that the distance and Hamilton–Jacobi equations are intrinsic to the implicit hypersurface. c ○ 2001 Academic Press Key Words: implicit hypersurfaces; distance functions; geodesics; Hamilton– Jacobi equations; fast computations.
Rapid and Accurate Computation of the Distance Function Using Grids
 J. Comput. Phys
, 2002
"... We present two fast and simple algorithms for approximating the distance function for given isolated points on uniform grids. The algorithms are then generalized to compute the distance to piecewise linear objects. By incorporating the geometry of Huygens ’ principle in the reverse order with the cl ..."
Abstract

Cited by 53 (3 self)
 Add to MetaCart
(Show Context)
We present two fast and simple algorithms for approximating the distance function for given isolated points on uniform grids. The algorithms are then generalized to compute the distance to piecewise linear objects. By incorporating the geometry of Huygens ’ principle in the reverse order with the classical viscosity solution theory for the eikonal equation ∇u=1, the algorithms become almost purely algebraic and yield very accurate approximations. The generalized closest point formulation used in the second algorithm provides a framework for further extension to compute the distance accurately to smooth geometric objects on different grid geometries, without the construction of the Voronoi diagrams. This method provides a fast and simple translator of data commonly given in computational geometry to the volumetric representation used in level set methods. c ○ 2002 Elsevier Science (USA) 1.
An Eulerian formulation for solving partial differential equations along a moving interface
 Jardin Botanique  BP 101  54602 VillerslsNancy Cedex (France) Unit de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu  35042 Rennes Cedex (France) Unit de recherche INRIA RhneAlpes : 655, avenue de l'Europe  38334 Montbonnot Saint
, 2002
"... ..."
(Show Context)
Diffusion tensor regularization with constraints preservation
 IN IEEE COMPUTER SOCIETY CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION, KAUAI MARRIOTT
"... This paper deals with the problem of regularizing noisy fields of diffusion tensors, considered as symmetric and semipositive definite n n matrices (as for instance 2D structure tensors or DTMRI medical images). We first propose a simple anisotropic PDEbased scheme that acts directly on the matr ..."
Abstract

Cited by 43 (12 self)
 Add to MetaCart
(Show Context)
This paper deals with the problem of regularizing noisy fields of diffusion tensors, considered as symmetric and semipositive definite n n matrices (as for instance 2D structure tensors or DTMRI medical images). We first propose a simple anisotropic PDEbased scheme that acts directly on the matrix coefficients and preserve the semipositive constraint thanks to a specific reprojection step. The limitations of this algorithm lead us to introduce a more effective approach based on constrained spectral regularizations acting on the tensor orientations (eigenvectors) and diffusivities (eigenvalues), while explicitely taking the tensor constraints into account. The regularization of the orientation part uses orthogonal matrices diffusion PDE’s and local vector alignment procedures and will be particularly developed. For the interesting 3D case, a special implementation scheme designed to numerically fit the tensor constraints is also proposed. Experimental results on synthetic and real DTMRI data sets finally illustrates the proposed tensor regularization framework.
Numerical Methods for pHarmonic Flows and Applications to Image Processing
 SIAM J. NUMER. ANAL
, 2002
"... We propose in this paper an alternative approach for computing pharmonic maps and flows: instead of solving a constrained minimization problem on S N i, we solve an unconstrained minimization problem on the entire space of functions. This is possible, using the projection on the sphere of any arbi ..."
Abstract

Cited by 43 (6 self)
 Add to MetaCart
We propose in this paper an alternative approach for computing pharmonic maps and flows: instead of solving a constrained minimization problem on S N i, we solve an unconstrained minimization problem on the entire space of functions. This is possible, using the projection on the sphere of any arbitrary function. Then we show how this formulation can be used in practice, for problems with both isotropic and anisotropic diffusion, with applications to image processing, using a new finite difference scheme.
Solving variational problems and partial differential equations mapping into general target manifolds
 J. Comput. Phys
, 2004
"... ..."
(Show Context)