# Geometric Disentanglement for Generative Latent Shape Models

## TL;DR

This paper introduces an unsupervised geometric disentanglement method for 3D shape generative models, enabling interpretable and manipulable latent representations using spectral differential geometry.

## Contribution

It proposes a novel spectral geometry-based approach for unsupervised disentanglement of latent spaces in 3D shape models, including a new Jacobian penalty for improved interpretability.

## Key findings

- Enables pose transfer and shape retrieval with disentangled representations
- Uses spectral differential geometry to separate intrinsic and extrinsic shape features
- Demonstrates improved interpretability over entangled models

## Abstract

Representing 3D shape is a fundamental problem in artificial intelligence, which has numerous applications within computer vision and graphics. One avenue that has recently begun to be explored is the use of latent representations of generative models. However, it remains an open problem to learn a generative model of shape that is interpretable and easily manipulated, particularly in the absence of supervised labels. In this paper, we propose an unsupervised approach to partitioning the latent space of a variational autoencoder for 3D point clouds in a natural way, using only geometric information. Our method makes use of tools from spectral differential geometry to separate intrinsic and extrinsic shape information, and then considers several hierarchical disentanglement penalties for dividing the latent space in this manner, including a novel one that penalizes the Jacobian of the latent representation of the decoded output with respect to the latent encoding. We show that the resulting representation exhibits intuitive and interpretable behavior, enabling tasks such as pose transfer and pose-aware shape retrieval that cannot easily be performed by models with an entangled representation.