English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper introduces a new mathematical and numerical framework for surfaceanalysis derived from the general setting of elastic Riemannian metrics onshape spaces. Traditionally, those metrics are defined over the infinitedimensional manifold of immersed surfaces and satisfy specific invarianceproperties enabling the comparison of surfaces modulo shape preservingtransformations such as reparametrizations. The specificity of the approach wedevelop is to restrict the space of allowable transformations to predefinedfinite dimensional bases of deformation fields. These are estimated in adata-driven way so as to emulate specific types of surface transformationsobserved in a training set. The use of such bases allows to simplify therepresentation of the corresponding shape space to a finite dimensional latentspace. However, in sharp contrast with methods involving e.g. meshautoencoders, the latent space is here equipped with a non-Euclidean Riemannianmetric precisely inherited from the family of aforementioned elastic metrics.We demonstrate how this basis restricted model can be then effectivelyimplemented to perform a variety of tasks on surface meshes which, importantly,does not assume these to be pre-registered (i.e. with given pointcorrespondences) or to even have a consistent mesh structure. We specificallyvalidate our approach on human body shape and pose data as well as human facescans, and show how it generally outperforms state-of-the-art methods onproblems such as shape registration, interpolation, motion transfer or randompose generation.

Basis restricted elastic shape analysis on the space of unregistered surfaces