# Deep Extrinsic Manifold Representation for Vision Tasks

arXiv: https://arxiv.org/abs/2404.00544 · HTML: https://mlsanity.com/paper/2404.00544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 31 Mar 2024.

## Builds on (most cited first, 15 of 15)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Understanding the Limitations of CNN-based Absolute Camera Pose Regression](https://mlsanity.com/paper/1903.07504/) (2019)
- [An Analysis of SVD for Deep Rotation Estimation](https://mlsanity.com/paper/2006.14616/) (2020)
- [SE3-Nets: Learning Rigid Body Motion using Deep Neural Networks](https://mlsanity.com/paper/1606.02378/) (2016)
- [Projective Manifold Gradient Layer for Deep Rotation Regression](https://mlsanity.com/paper/2110.11657/) (2021)
- [Learning Implicit Brain MRI Manifolds with Deep Learning](https://mlsanity.com/paper/1801.01847/) (2018)
- [Manifold Learning Benefits GANs](https://mlsanity.com/paper/2112.12618/) (2021)
- [Intrinsic and extrinsic deep learning on manifolds](https://mlsanity.com/paper/2302.08606/) (2023)
- [Robust Geodesic Regression](https://mlsanity.com/paper/2007.04518/) (2020)
- [Nested Grassmannians for Dimensionality Reduction with Applications](https://mlsanity.com/paper/2010.14589/) (2020)
- [Learning Invariant Riemannian Geometric Representations Using Deep Nets](https://mlsanity.com/paper/1708.09485/) (2017)
- [Bayesian Geodesic Regression on Riemannian Manifolds](https://mlsanity.com/paper/2009.05108/) (2020)
- [Robust Extrinsic Regression Analysis for Manifold Valued Data](https://mlsanity.com/paper/2101.11872/) (2021)

## Abstract (arXiv)

Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick named Deep Extrinsic Manifold Representation (DEMR) for visual tasks in this context. DEMR incorporates extrinsic manifold embedding into deep neural networks, which helps generate manifold representations. The DEMR approach does not directly optimize the complex geodesic loss. Instead, it focuses on optimizing the computation graph within the embedded Euclidean space, allowing for adaptability to various architectural requirements. We provide empirical evidence supporting the proposed concept on two types of manifolds, SE(3) and its associated quotient manifolds. This evidence offers theoretical assurances regarding feasibility, asymptotic properties, and generalization capability. The experimental results show that DEMR effectively adapts to point cloud alignment, producing outputs in  SE(3) , as well as in illumination subspace learning with outputs on the Grassmann manifold.