Asymmetric Geodesic Distance Propagation for Active Contours

This is the final version. Available from British Machine Vision Association (BMVA) via the link in this record. The dual-front scheme is a powerful curve evolution tool for active contours and image segmentation, which has proven its capability in dealing with various segmentation tasks. In its basic formulation, a contour is represented by the interface of two adjacent Voronoi regions derived from the geodesic distance map which is the solution to an Eikonal equation. The original dual-front model [17] is based on isotropic metrics, and thus cannot take into account the asymmetric enhancements during curve evolution. In this paper, we propose a new asymmetric dual-front curve evolution model through an asymmetric Finsler geodesic metric, which is constructed in terms of the extended normal vector field of the current contour and the image data. The experimental results demonstrate the advantages of the proposed method in computational efficiency, robustness and accuracy when compared to the original isotropic dual-front model.Roche pharmaAgence Nationale de la Recherch

A stable and optimally convergent LaTIn-CutFEM algorithm for multiple unilateral contact problems

In this paper, we propose a novel unfitted finite element method for the simulation of multiple body contact. The computational mesh is generated independently of the geometry of the interacting solids, which can be arbitrarily complex. The key novelty of the approach is the combination of elements of the CutFEM technology, namely the enrichment of the solution field via the definition of overlapping fictitious domains with a dedicated penalty-type regularisation of discrete operators, and the LaTIn hybrid-mixed formulation of complex interface conditions. Furthermore, the novel P1-P1 discretisation scheme that we propose for the unfitted LaTIn solver is shown to be stable, robust and optimally convergent with mesh refinement. Finally, the paper introduces a high-performance 3D level-set/CutFEM framework for the versatile and robust solution of contact problems involving multiple bodies of complex geometries, with more than two bodies interacting at a single point

Multimaterial Mesh-Based Surface Tracking

© ACM, 2014. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Da, F., Batty, C., & Grinspun, E. (2014). Multimaterial Mesh-Based Surface Tracking. Acm Transactions on Graphics, 33(4), 112. https://doi.org/10.1145/2601097.2601146We present a triangle mesh-based technique for tracking the evolution of three-dimensional multimaterial interfaces undergoing complex deformations. It is the first non-manifold triangle mesh tracking method to simultaneously maintain intersection-free meshes and support the proposed broad set of multimaterial remeshing and topological operations. We represent the interface as a non-manifold triangle mesh with material labels assigned to each half-face to distinguish volumetric regions. Starting from proposed application-dependent vertex velocities, we deform the mesh, seeking a non-intersecting, watertight solution. This goal necessitates development of various collision-safe, label-aware non-manifold mesh operations: multimaterial mesh improvement; T1 and T2 processes, topological transitions arising in foam dynamics and multiphase flows; and multimaterial merging, in which a new interface is created between colliding materials. We demonstrate the robustness and effectiveness of our approach on a range of scenarios including geometric flows and multiphase fluid animation.This work was supported in part by the NSF (Grants IIS-1319483, CMMI-1331499, IIS-1217904, IIS-1117257, CMMI-1129917, IIS-0916129), the Israel-US Binational Science Founda-tion, the Natural Sciences and Engineering Research Council of Canada (NSERC), Intel, The Walt Disney Company, Autodesk, Side Effects Software, NVIDIA, and the Banting Postdoctoral Fel-lowships program

Geometric partial differential equations: Theory, numerics and applications

This workshop concentrated on partial differential equations involving stationary and evolving surfaces in which geometric quantities play a major role. Mutual interest in this emerging field stimulated the interaction between analysis, numerical solution, and applications