Robust Stereo Matching by Risk Minimization

Ce Liu, Suryansh Kumar, Shuhang Gu, Radu Timofte, Yao Yao, Luc Van Gool

Primary Area: representation learning for computer vision, audio, language, and other modalities

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Keywords: Stereo Matching, Deep Stereo, Risk Minimization, Robust Estimation

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Abstract: This paper presents a novel formulation for capturing the continuous disparity in stereo matching networks. In contrast to previous approaches that regress the final output as the expectation of discretized disparity values, we derive a continuous modeling formulation by treating the predicted disparity as an optimal solution to the risk minimization problem. We demonstrate that the commonly used disparity expectation represents an $L^2$ special case within the proposed risk formulation, and transitioning to an $L^1$ formulation notably enhances stereo matching robustness, particularly for disparities with multi-modal probability distributions. Moreover, to enable the end-to-end network training with the non-differentiable $L^1$ risk optimization, we explored the well-known implicit function theorem and proposed a differentiable scheme for both network forward prediction and backward propagation. A comprehensive analysis of our proposed formulation demonstrates its theoretical soundness and superior performance over current state-of-the-art methods across various benchmarks, including KITTI 2012, KITTI 2015, ETH3D, SceneFlow, and Middlebury 2014. We believe our work not only advances the field of stereo matching but also holds promise for broader applications, spanning computer vision, robotics, and control engineering.

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Submission Number: 1847