# LSM: Learning Subspace Minimization for Low-level Vision

arXiv: https://arxiv.org/abs/2004.09197 · HTML: https://mlsanity.com/paper/2004.09197/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

## Built on by (most cited first, 6 of 6)

- [Many-to-many Splatting for Efficient Video Frame Interpolation](https://mlsanity.com/paper/2204.03513/) (2022)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Motion Basis Learning for Unsupervised Deep Homography Estimation with Subspace Projection](https://mlsanity.com/paper/2103.15346/) (2021)
- [Multi-Object Discovery by Low-Dimensional Object Motion](https://mlsanity.com/paper/2307.08027/) (2023)
- [Temporal-MPI: Enabling Multi-Plane Images for Dynamic Scene Modelling via Temporal Basis Learning](https://mlsanity.com/paper/2111.10533/) (2021)
- [Video Frame Interpolation with Many-to-many Splatting and Spatial Selective Refinement](https://mlsanity.com/paper/2310.18946/) (2023)

## Abstract (arXiv)

We study the energy minimization problem in low-level vision tasks from a novel perspective. We replace the heuristic regularization term with a learnable subspace constraint, and preserve the data term to exploit domain knowledge derived from the first principle of a task. This learning subspace minimization (LSM) framework unifies the network structures and the parameters for many low-level vision tasks, which allows us to train a single network for multiple tasks simultaneously with completely shared parameters, and even generalizes the trained network to an unseen task as long as its data term can be formulated. We demonstrate our LSM framework on four low-level tasks including interactive image segmentation, video segmentation, stereo matching, and optical flow, and validate the network on various datasets. The experiments show that the proposed LSM generates state-of-the-art results with smaller model size, faster training convergence, and real-time inference.