Deformation Recovery: Localized Learning for Detail-Preserving Deformations

TL;DR

This paper presents a localized, data-driven neural network approach for detail-preserving shape deformations that does not rely on global shape encodings, enabling better generalization and lightweight supervision.

Contribution

The method introduces a Jacobian-based local representation for deformations, removing the need for global shape encoding, and demonstrates strong generalization across shape classes.

Findings

Effective shape deformation refinement without global context

High generalization across different object categories

Successful application to shape editing and correspondence tasks

Abstract

We introduce a novel data-driven approach aimed at designing high-quality shape deformations based on a coarse localized input signal. Unlike previous data-driven methods that require a global shape encoding, we observe that detail-preserving deformations can be estimated reliably without any global context in certain scenarios. Building on this intuition, we leverage Jacobians defined in a one-ring neighborhood as a coarse representation of the deformation. Using this as the input to our neural network, we apply a series of MLPs combined with feature smoothing to learn the Jacobian corresponding to the detail-preserving deformation, from which the embedding is recovered by the standard Poisson solve. Crucially, by removing the dependence on a global encoding, every \textit{point} becomes a training example, making the supervision particularly lightweight. Moreover, when trained on a class of shapes, our approach demonstrates remarkable generalization across different object categories. Equipped with this novel network, we explore three main tasks: refining an approximate shape correspondence, unsupervised deformation and mapping, and shape editing. Our code is made available at https://github.com/sentient07/LJN