Shape-from-intrinsic operator

TL;DR

This paper introduces shape-from-operator (SfO), a novel approach to recover mesh embeddings from intrinsic differential operators, enabling applications like shape synthesis, reconstruction, and exaggeration through an alternating optimization scheme.

Contribution

It formulates the shape-from-operator problem and proposes a numerical method using alternating optimization to recover shape embeddings from intrinsic operators.

Findings

Effective reconstruction of mesh embeddings from intrinsic operators.

Application to shape synthesis, exaggeration, and reconstruction tasks.

Demonstrated the viability of the SfO framework in geometry processing.

Abstract

Shape-from-X is an important class of problems in the fields of geometry processing, computer graphics, and vision, attempting to recover the structure of a shape from some observations. In this paper, we formulate the problem of shape-from-operator (SfO), recovering an embedding of a mesh from intrinsic differential operators defined on the mesh. Particularly interesting instances of our SfO problem include synthesis of shape analogies, shape-from-Laplacian reconstruction, and shape exaggeration. Numerically, we approach the SfO problem by splitting it into two optimization sub-problems that are applied in an alternating scheme: metric-from-operator (reconstruction of the discrete metric from the intrinsic operator) and embedding-from-metric (finding a shape embedding that would realize a given metric, a setting of the multidimensional scaling problem).