Globally optimal 3D image reconstruction and segmentation via energy minimisation techniques

This paper provides an overview of a number of techniques developed within our group to perform 3D reconstruction and image segmentation based of the application of energy minimisation concepts. We begin with classical snake techniques and show how similar energy minimisation concepts can be extended to derive globally optimal segmentation methods. Then we discuss more recent work based on geodesic active contours that can lead to globally optimal segmentations and reconstructions in 2D. Finally we extend the work to 3D by introducing continuous flow globally minimal surfaces. Several applications are discussed to show the wide applicability and suitability of these techniques to several difficult image analysis problems

Levelset and B-spline deformable model techniques for image segmentation: a pragmatic comparative study

International audienceDeformable contours are now widely used in image segmentation, using different models, criteria and numerical schemes. Some theoretical comparisons between some deformable model methods have already been published. Yet, very few experimental comparative studies on real data have been reported. In this paper,we compare a levelset with a B-spline based deformable model approach in order to understand the mechanisms involved in these widely used methods and to compare both evolution and results on various kinds of image segmentation problems. In general, both methods yield similar results. However, specific differences appear when considering particular problems

Precision Tests of the Standard Model

30 páginas, 11 figuras, 11 tablas.-- Comunicación presentada al 25º Winter Meeting on Fundamental Physics celebrado del 3 al 8 de MArzo de 1997 en Formigal (España).Precision measurements of electroweak observables provide stringent tests of the Standard Model structure and an accurate determination of its parameters. An overview of the present experimental status is presented.This work has been supported in part by CICYT (Spain) under grant No. AEN-96-1718.Peer reviewe

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Globally optimal geodesic active contours

An approach to optimal object segmentation in the geodesic active contour framework is presented with application to automated image segmentation. The new segmentation scheme seeks the geodesic active contour of globally minimal energy under the sole restriction that it contains a specified internal point p_int. This internal point selects the object of interest and may be used as the only input parameter to yield a highly automated segmentation scheme. The image to be segmented is represented as a Riemannian space S with an associated metric induced by the image. The metric is an isotropic and decreasing function of the local image gradient at each point in the image, encoding the local homogeneity of image features. Optimal segmentations are then the closed geodesics which partition the object from the background with minimal similarity across the partitioning. An efficient algorithm is presented for the computation of globally optimal segmentations and applied to cell microscopy, x-ray, magnetic resonance and cDNA microarray images

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Fast Marching Method for Generic Shape from Shading

International audienceWe develop a fast numerical method to approximate the solutions of a wide class of equations associated to the Shape From Shading problem. Our method, which is based on the control theory and the interfaces propagation, is an extension of the ?Fast Marching Method? (FMM) [30,25]. In particular our method extends the FMM to some equations for which the solution is not systematically decreasing along the optimal trajectories. We apply with success our one-pass method to the Shape From Shading equations which are involved by the most relevant and recent modelings [22,21] and which cannot be handled by the most recent extensions of the FMM [26,8]