Nonlinear Deformation Synthesis via Sparse Principal Geodesic Analysis

Josua Sassen, Klaus Hildebrandt, Martin Rumpf

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

This paper introduces the construction of a low-dimensional nonlinear space capturing the variability of a non-rigid shape from a data set of example poses. The core of the approach is a Sparse Principal Geodesic Analysis (SPGA) on the Riemannian manifold of discrete shells, in which a pose of a non-rigid shape is a point. The SPGA is invariant to rigid body motions of the poses and supports large deformation. Since the Riemannian metric measures the membrane and bending distortions of the shells, the sparsity term forces the modes to describe largely decoupled and localized deformations. This property facilitates the analysis of articulated shapes. The modes often represent characteristic articulations of the shape and usually come with a decomposing of the spanned subspace into low-dimensional widely decoupled subspaces. For example, for human models, one expects distinct, localized modes for the bending of elbow or knee whereas some more modes are required to represent shoulder articulation. The decoupling property can be used to construct useful starting points for the computation of the nonlinear deformations via a superposition of shape submanifolds resulting from the decoupling. In a preprocessing stage, samples of the individual subspaces are computed, and, in an online phase, these are interpolated multilinearly. This accelerates the construction of nonlinear deformations and makes the method applicable for interactive applications. The method is compared to alternative approaches and the benefits are demonstrated on different kinds of input data.

Original languageEnglish
Pages (from-to)119-132
Number of pages14
JournalComputer Graphics Forum
Volume39
Issue number5
DOIs
Publication statusPublished - 2020

Keywords

  • Computing methodologies
  • Shape modeling

Fingerprint

Dive into the research topics of 'Nonlinear Deformation Synthesis via Sparse Principal Geodesic Analysis'. Together they form a unique fingerprint.

Cite this