# Learning Pose Image Manifolds Using Geometry-Preserving GANs and Elasticae

arXiv: https://arxiv.org/abs/2305.10513 · HTML: https://mlsanity.com/paper/2305.10513/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 18 of 18)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [Few-View Object Reconstruction with Unknown Categories and Camera Poses](https://mlsanity.com/paper/2212.04492/) (2022)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)
- [Geometry-aware Deep Network for Single-Image Novel View Synthesis](https://mlsanity.com/paper/1804.06008/) (2018)
- [RGBD-Net: Predicting color and depth images for novel views synthesis](https://mlsanity.com/paper/2011.14398/) (2020)
- [Geometry of Deep Generative Models for Disentangled Representations](https://mlsanity.com/paper/1902.06964/) (2019)
- [AE-StyleGAN: Improved Training of Style-Based Auto-Encoders](https://mlsanity.com/paper/2110.08718/) (2021)

## Abstract (arXiv)

This paper investigates the challenge of learning image manifolds, specifically pose manifolds, of 3D objects using limited training data. It proposes a DNN approach to manifold learning and for predicting images of objects for novel, continuous 3D rotations. The approach uses two distinct concepts: (1) Geometric Style-GAN (Geom-SGAN), which maps images to low-dimensional latent representations and maintains the (first-order) manifold geometry. That is, it seeks to preserve the pairwise distances between base points and their tangent spaces, and (2) uses Euler's elastica to smoothly interpolate between directed points (points + tangent directions) in the low-dimensional latent space. When mapped back to the larger image space, the resulting interpolations resemble videos of rotating objects. Extensive experiments establish the superiority of this framework in learning paths on rotation manifolds, both visually and quantitatively, relative to state-of-the-art GANs and VAEs.