Related papers: Smooth Non-Rigid Shape Matching via Effective Diri…

This paper presents smoothed combined field integral equations for the solution of Dirichlet and Neumann exterior Helmholtz problems. The integral equations introduced in this paper are smooth in the sense that they only involve…

To produce cartographic maps, simplification is typically used to reduce complexity of the map to a legible level. With schematic maps, however, this simplification is pushed far beyond the legibility threshold and is instead constrained by…

This paper is the first of a series in which we develop exact and approximate algorithms for mappings of systems of differential equations. Here we introduce the MapDE algorithm and its implementation in Maple, for mappings relating…

Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate the basis mismatch between the true support in the…

In this paper we aim to minimize the sum of two nonsmooth (possibly also nonconvex) functions in separate variables connected by a smooth coupling function. To tackle this problem we chose a continuous forward-backward approach and…

We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemannian manifolds from the image of symmetric stable processes…

Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…

We propose a definition of the Dirichlet energy (which is roughly speaking the integral of the square of the gradient) for mappings mu : Omega -> (P(D), W\_2) defined over a subset Omega of R^p and valued in the space P(D) of probability…

This paper studies the numerical approximation of solution of the Dirichlet problem for the fully nonlinear Monge-Ampere equation. In this approach, we take the advantage of reformulation the Monge-Ampere problem as an optimization problem,…

We propose a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal) operators associated with regular Dirichlet forms and with measure data. Using the theory of backward stochastic differential…

An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…

While dealing with matching shapes to their parts, we often apply a tool known as functional maps. The idea is to translate the shape matching problem into "convenient" spaces by which matching is performed algebraically by solving a least…

We introduce a combinatorial energy for maps of triangulated surfaces with simplicial metrics and analyze the existence and uniqueness properties of the corresponding harmonic maps. We show that some important applications of smooth…

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…

In this paper, we propose a learning-based framework for non-rigid shape registration without correspondence supervision. Traditional shape registration techniques typically rely on correspondences induced by extrinsic proximity, therefore…

Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach…

Deep functional map frameworks are widely employed for 3D shape matching. However, most existing deep functional map methods cannot adaptively capture important frequency information for functional map estimation in specific matching…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

We consider the approximation of minimal geodesics between two closed sets in $\mathbb{R}^D$ endowed with a smooth Riemannian metric. The continuous problem is formulated as the minimization of the energy functional over piecewise smooth…

Stabilization of an underactuated mechanical system may be accomplished by energy shaping. Interconnection and damping assignment passivity-based control is an approach based on total energy shaping by assigning desired kinetic and…