# Learnable Cost Volume Using the Cayley Representation

arXiv: https://arxiv.org/abs/2007.11431 · HTML: https://mlsanity.com/paper/2007.11431/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2020.

## Built on by (most cited first, 7 of 7)

- [Disentangling Architecture and Training for Optical Flow](https://mlsanity.com/paper/2203.10712/) (2022)
- [CSFlow: Learning Optical Flow via Cross Strip Correlation for Autonomous Driving](https://mlsanity.com/paper/2202.00909/) (2022)
- [Self-supervised AutoFlow](https://mlsanity.com/paper/2212.01762/) (2022)
- [Sensor-Guided Optical Flow](https://mlsanity.com/paper/2109.15321/) (2021)
- [DCVNet: Dilated Cost Volume Networks for Fast Optical Flow](https://mlsanity.com/paper/2103.17271/) (2021)
- [Accurate Visual-Inertial SLAM by Feature Re-identification](https://mlsanity.com/paper/2102.13438/) (2021)
- [FlowNAS: Neural Architecture Search for Optical Flow Estimation](https://mlsanity.com/paper/2207.01271/) (2022)

## Abstract (arXiv)

Cost volume is an essential component of recent deep models for optical flow estimation and is usually constructed by calculating the inner product between two feature vectors. However, the standard inner product in the commonly-used cost volume may limit the representation capacity of flow models because it neglects the correlation among different channel dimensions and weighs each dimension equally. To address this issue, we propose a learnable cost volume (LCV) using an elliptical inner product, which generalizes the standard inner product by a positive definite kernel matrix. To guarantee its positive definiteness, we perform spectral decomposition on the kernel matrix and re-parameterize it via the Cayley representation. The proposed LCV is a lightweight module and can be easily plugged into existing models to replace the vanilla cost volume. Experimental results show that the LCV module not only improves the accuracy of state-of-the-art models on standard benchmarks, but also promotes their robustness against illumination change, noises, and adversarial perturbations of the input signals.