Shape-from-intrinsic operator

by   Davide Boscaini, et al.

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).


page 1

page 6

page 7

page 8

page 9


Steklov Spectral Geometry for Extrinsic Shape Analysis

We propose using the Dirichlet-to-Neumann operator as an extrinsic alter...

OperatorNet: Recovering 3D Shapes From Difference Operators

This paper proposes a learning-based framework for reconstructing 3D sha...

Steklov Geometry Processing: An Extrinsic Approach to Spectral Shape Analysis

We propose Steklov geometry processing, an extrinsic approach to spectra...

SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator

Intrinsic graph convolution operators with differentiable kernel functio...

Hamiltonian operator for spectral shape analysis

Many shape analysis methods treat the geometry of an object as a metric ...

Intrinsic Neural Fields: Learning Functions on Manifolds

Neural fields have gained significant attention in the computer vision c...

An Intrinsic Geometrical Approach for Statistical Process Control of Surface and Manifold Data

This paper presents a new method for statistical process control (SPC) o...