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3. Modelling Dynamic Scenes by Registrating Multi-View Image Sequences

Author

Pons, Jean-Philippe, Keriven, Renaud, Faugeras, Olivier, Inria, Rapport De Recherche, Computer and biological vision (ODYSSEE), Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), INRIA, Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria Sophia Antipolis - Méditerranée (CRISAM)

Subjects
VARIATIONAL METHOD, NON-RIGID 3D MOTION, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], SCENE FLOW, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, MUTUAL INFORMATION, CROSS CORRELATION, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], REGISTRATION, NON-LAMBERTIAN, PREDICTION ERROR, LEVEL SETS, ComputingMethodologies_COMPUTERGRAPHICS, STEREOVISION
Abstract

We present a new variational method for multi-view stereovision and non-rigid three-dimensional motion estimation from multiple video sequences. Our method minimizes the prediction error of the estimated shape and motion. Both problems then translate into a generic image registration task. The latter is entrusted to a similarity measure chosen depending on imaging conditions and scene properties. In particular, our method can be made robust to appearance changes due to non-Lambertian materials and illumination changes. Our method results in a simpler, more flexible, and more efficient implementation than existing deformable surface approaches. The computation time on large datasets does not exceed thirty minutes. Moreover, our method is compliant with a hardware implementation with graphics processor units. Our stereovision algorithm yields very good results on a variety of datasets including specularities and translucency. We have successfully tested our scene flow algorithm on a very challenging multi-view video sequence of a non-rigid event.

Published
2004

4. How to deal with point correspondences and tangential velocities in the level set framework

Author

Pons, Jean-Philippe, Hermosillo, Gerardo, Keriven, Renaud, Faugeras, Olivier, Inria, Rapport De Recherche, Computer and biological vision (ODYSSEE), Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École des Ponts ParisTech (ENPC), INRIA, Département d'informatique - ENS Paris (DI-ENS), Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria Sophia Antipolis - Méditerranée (CRISAM), École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL)

Subjects
[INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], POINT CORRESPONDENCES, INTRINSIC HEAT FLOW, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], CORTEX UNFOLDING, DIFFEOMORPHISMS, MEAN CURVATURE FLOW, AREA PRESERVATION, LEVEL SETS, SURFACE DIFFUSION FLOW, LAPLACE-BELTRAMI OPERATOR
Abstract

In this report, we overcome a major drawback of the level set framework: the lack of point correspondences. We maintain explicit backward correspondences from the evolving interface to the initial one by advecting the initial point coordinates with the same velocity as the level set function. Our method leads to a system of coupled Eulerian partial differential equations. We show in a variety of numerical experiments that it can handle both normal and tangential velocities, large deformations, shocks, rarefactions and topological changes. Applications are many since our method can upgrade virtually any level set evolution. We complement our work with the design of non zero tangential velocities that preserve the relative area of interface patches; this feature may be crucial in such applications as computational geometry, grid generation or unfolding of the organs' surfaces, e.g. brain, in medical imaging. This report also tackles a diffeomorphic approach to level set evolution, a family of volume-preserving smoothing flows, and some numerical aspects of the intrinsic heat flow on implicit surfaces.

Published
2003

5. Variational, geometric, and statistical methods for modeling brain anatomy and function

Author

Faugeras, Olivier, Adde, Geoffray, Charpiat, Guillaume, Chefd'Hotel, Christophe, Clerc, Maureen, Deneux, Thomas, Deriche, Rachid, Hermosillo, Gerardo, Keriven, Renaud, Kornprobst, Pierre, Kybic, Jan, Lenglet, Christophe, Lopez-Perez, Lucero, Papadopoulo, Théo, Pons, Jean-Philippe, Segonne, Florent, Thirion, Bertrand, Tschumperlé, David, Viéville, Thierry, and Wotawa, Nicolas

Subjects
*BRAIN anatomy, *MAGNETIC resonance imaging, *MATHEMATICS, *DIAGNOSTIC imaging
Abstract

We survey the recent activities of the Odyssée Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases. [Copyright &y& Elsevier]

Published
2004
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