We propose Steklov geometry processing, an extrinsic approach to spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace–Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, while many previous extrinsic methods lack theoretical justi cation. Instead, we propose a systematic approach by considering the Steklov eigenva...

We develop an operator splitting approach to solve diffeomorphic matching problems for sequences of surfaces in three-dimensional space. The goal is smoothly match, at a very fast rate, finite observed 3D-snapshots extracted from movies recording the smooth dynamic deformations "soft" surfaces. have implemented our algorithms proprietary software installed Methodist Hospital (Cardiology) monito...

In this note we consider a simple shape operator discretization for general meshes, based on computing an interpolating quadratic function passing through vertices of a triangle and its edge-adjacent neighbors. This approximation is computationally simple and consistent for a broad class of meshes. However, its convergence properties in the context of mesh optimization problems are not as good ...

1. Abstract The main purpose of this paper is to describe a numerical method of an inverse problem for two– dimensional flow of fluid around a profile. The principle of the method is based on construction of a contractive operator. The practical use is getting the possibility of constructing or modifying the shape of a profile by the velocity distribution on the profile surface. We formulate an...

Many problems in image analysis, digital processing and shape optimization are expressed as variational problems and involve the discritization of laplacians. Indeed, PDEs containing Laplace-Beltrami operator arise in surface fairing, mesh smoothing, mesh parametrization, remeshing, feature extraction, shape matching, etc. The discretization of the laplace-Beltrami operator has been widely stud...

We study some properties of a half-lightlike submanifoldM , of a semi-Riemannianmanifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distribution S(TM) of M is integrable and the geometry of M has a close relation with the nondegenerate geometry of a leaf of S(TM). We prove some results on symmetric induced Ricci tensor and null s...

We provide exact shape reconstruction formulas in the spirit of the Linear Sampling method for a class of inverse problems in shape determination in the context of timeindependent partial differential equations. To this end, we prove a general theorem how, and under which assumptions, domain characterizations based on the range of the square root of an operator transform into domain characteriz...