# Basis restricted elastic shape analysis on the space of unregistered surfaces Source: [Basis restricted elastic shape analysis on the space of unregistered surfaces]() Collection index: [llms.txt]() Data updated: 2025-10-25T16:51:38.409Z Authors: Emmanuel Hartman, Emery Pierson, Martin Bauer, Mohamed Daoudi, Nicolas Charon Published: 2023-11-07T23:06:22.000Z ## Abstract This paper introduces a new mathematical and numerical framework for surface analysis derived from the general setting of elastic Riemannian metrics on shape spaces. Traditionally, those metrics are defined over the infinite dimensional manifold of immersed surfaces and satisfy specific invariance properties enabling the comparison of surfaces modulo shape preserving transformations such as reparametrizations. The specificity of the approach we develop is to restrict the space of allowable transformations to predefined finite dimensional bases of deformation fields. These are estimated in a data-driven way so as to emulate specific types of surface transformations observed in a training set. The use of such bases allows to simplify the representation of the corresponding shape space to a finite dimensional latent space. However, in sharp contrast with methods involving e.g. mesh autoencoders, the latent space is here equipped with a non-Euclidean Riemannian metric precisely inherited from the family of aforementioned elastic metrics. We demonstrate how this basis restricted model can be then effectively implemented to perform a variety of tasks on surface meshes which, importantly, does not assume these to be pre-registered (i.e. with given point correspondences) or to even have a consistent mesh structure. We specifically validate our approach on human body shape and pose data as well as human face scans, and show how it generally outperforms state-of-the-art methods on problems such as shape registration, interpolation, motion transfer or random pose generation. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Unconditional Mesh Shape Generation on Human](): Unconditional mesh shape generation; Human; ER: 4.41. - [Unconditional mesh shape generation on Animal SMAL](): Unconditional mesh shape generation; Animal SMAL; Error Rate (ER): 6.12. ## Original sources and implementation [Original paper]() [PDF]()