Abstract: To solve the problem that the traditional stereo matching model fails to consider the inaccuracy of epiplor-rectification. This paper proposes a two-dimensional model by entering the one-dimensional stereo matching model with another dimension function for disparity estimation, and theoretically analyzes the numerical algorithm for solving the improved model. Firstly, rewrite the proposed nonconvex variational problem as a variational problem in a higher dimension by using the theory of calibrations. Secondly, relax the lifted variational problem as a saddle-point problem by the biconjugate theory in convex optimization. Finally, compute this model fast and efficiently by using the first order primal-dual algorithm for solving the saddle-point problem. The experiment results show that the proposed two-dimensional model can solve the proposed problem effectively, improve the accuracy of disparity estimation, and the numerical algorithm can compute the optimization effectively.

Key words: stereo matching, primal-dual, biconjugate

摘要： 针对传统立体匹配模型中忽视的极线校准不精确的情况，提出一种二维立体匹配模型及其数值解法。该模型是在一维立体匹配模型的基础上，加入另一维度的视差估计函数得到的。首先利用笛卡尔理论，将提出的非凸模型表示为更高维空间中的变分问题，然后利用双共轭函数（共轭函数的共轭函数）将高维空间的变分问题凸松弛为鞍点问题，最后使用可以快速有效解决鞍点问题的一阶原始对偶算法进行求解。实验结果表明，二维模型可以解决极线校准不精确问题并获取更高精度的视差图像，采用的数值算法可以有效地收敛。

关键词: 立体匹配, 原始对偶, 双共轭