# Object Tracking via Non-Euclidean Geometry: A Grassmann Approach

arXiv: https://arxiv.org/abs/1403.0309 · HTML: https://mlsanity.com/paper/1403.0309/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2014.

## Built on by (most cited first, 2 of 2)

- [GraffMatch: Global Matching of 3D Lines and Planes for Wide Baseline LiDAR Registration](https://mlsanity.com/paper/2212.12745/) (2022)
- [Registration beyond Points: General Affine Subspace Alignment via Geodesic Distance on Grassmann Manifold](https://mlsanity.com/paper/2507.17998/) (2025)

## Abstract (arXiv)

A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single image. In this paper, we first propose a tracking approach based on affine subspaces (constructed from several images) which are able to accommodate the abovementioned variations. We use affine subspaces not only to represent the object, but also the candidate areas that the object may occupy. We furthermore propose a novel approach to measure affine subspace-to-subspace distance via the use of non-Euclidean geometry of Grassmann manifolds. The tracking problem is then considered as an inference task in a Markov Chain Monte Carlo framework via particle filtering. Quantitative evaluation on challenging video sequences indicates that the proposed approach obtains considerably better performance than several recent state-of-the-art methods such as Tracking-Learning-Detection and MILtrack.