# Investigating Image Manifolds of 3D Objects: Learning, Shape Analysis, and Comparisons

arXiv: https://arxiv.org/abs/2503.06773 · HTML: https://mlsanity.com/paper/2503.06773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 55 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [Geometry Score: A Method For Comparing Generative Adversarial Networks](https://mlsanity.com/paper/1802.02664/) (2018)
- [Learning Flat Latent Manifolds with VAEs](https://mlsanity.com/paper/2002.04881/) (2020)
- [Geometric Autoencoders -- What You See is What You Decode](https://mlsanity.com/paper/2306.17638/) (2023)
- [DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling](https://mlsanity.com/paper/1711.06011/) (2017)
- [Shape Analysis of Surfaces Using General Elastic Metrics](https://mlsanity.com/paper/1910.02045/) (2019)
- [Geometry of Deep Generative Models for Disentangled Representations](https://mlsanity.com/paper/1902.06964/) (2019)
- [Statistical Shape Analysis of Brain Arterial Networks (BAN)](https://mlsanity.com/paper/2007.04793/) (2020)
- [Shape-Graph Matching Network (SGM-net): Registration for Statistical Shape Analysis](https://mlsanity.com/paper/2308.06869/) (2023)

## Abstract (arXiv)

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering these questions can provide key insights in explaining and advancing success of machine learning algorithms in computer vision. This paper investigates dual tasks -- learning and analyzing shapes of image manifolds -- by revisiting a classical problem of manifold learning but from a novel geometrical perspective. It uses geometry-preserving transformations to map the pose image manifolds, sets of images formed by rotating 3D objects, to low-dimensional latent spaces. The pose manifolds of different objects in latent spaces are found to be nonlinear, smooth manifolds. The paper then compares shapes of these manifolds for different objects using Kendall's shape analysis, modulo rigid motions and global scaling, and clusters objects according to these shape metrics. Interestingly, pose manifolds for objects from the same classes are frequently clustered together. The geometries of image manifolds can be exploited to simplify vision and image processing tasks, to predict performances, and to provide insights into learning methods.