On the Hessian of Shape Matching Energy

04/08/2016
by   Yun Fei, et al.
0

In this technical report we derive the analytic form of the Hessian matrix for shape matching energy. Shape matching is a useful technique for meshless deformation, which can be easily combined with multiple techniques in real-time dynamics. Nevertheless, it has been rarely applied in scenarios where implicit integrators are required, and hence strong viscous damping effect, though popular in simulation systems nowadays, is forbidden for shape matching. The reason lies in the difficulty to derive the Hessian matrix of the shape matching energy. Computing the Hessian matrix correctly, and stably, is the key to more broadly application of shape matching in implicitly-integrated systems.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/08/2020

Dissecting Hessian: Understanding Common Structure of Hessian in Neural Networks

Hessian captures important properties of the deep neural network loss la...
research
03/15/2021

Eigen Space of Mesh Distortion Energy Hessian

Mesh distortion optimization is a popular research topic and has wide ra...
research
12/30/2020

A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges

We present a second order numerical scheme to compute capillary bridges ...
research
07/19/2023

An Operator-Splitting Approach for Variational Optimal Control Formulations for Diffeomorphic Shape Matching

We present formulations and numerical algorithms for solving diffeomorph...
research
06/27/2012

Estimating the Hessian by Back-propagating Curvature

In this work we develop Curvature Propagation (CP), a general technique ...
research
05/17/2019

Sliced Score Matching: A Scalable Approach to Density and Score Estimation

Score matching is a popular method for estimating unnormalized statistic...
research
09/03/2020

Symmetry and scaling limits for matching of implicit surfaces based on thin shell energies

In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. ...

Please sign up or login with your details

Forgot password? Click here to reset