IEEE Trans Image Process. 2018 Nov;27(11):5328-5337. doi: 10.1109/TIP.2018.2849866. Epub 2018 Jun 22.
We propose a method to estimate the essential matrix using two affine correspondences for a pair of calibrated perspective cameras. Two novel, linear constraints are derived between the essential matrix and a local affine transformation. The proposed method is also applicable to the over-determined case. We extend the normalization technique of Hartley to local affinities and show how the intrinsic camera matrices modify them. Even though perspective cameras are assumed, the constraints can straightforwardly be generalized to arbitrary camera models since they describe the relationship between local affinities and epipolar lines (or curves). Benefiting from the low number of exploited points, it can be used in robust estimators, e.g. RANSAC, as an engine, thus leading to significantly less iterations than the traditional point-based methods. The algorithm is validated both on synthetic and publicly available data sets and compared with the state-of-the-art. Its applicability is demonstrated on two-view multi-motion fitting, i.e., finding multiple fundamental matrices simultaneously, and outlier rejection.
我们提出了一种使用一对校准透视相机的两个仿射对应来估计本质矩阵的方法。推导出了本质矩阵和局部仿射变换之间的两个新颖的线性约束。所提出的方法也适用于过定情况。我们将 Hartley 的归一化技术扩展到局部仿射，并展示了内在相机矩阵如何修改它们。尽管假设使用透视相机，但由于约束描述了局部仿射与极线（或曲线）之间的关系，因此它们可以直接推广到任意相机模型。受益于所利用点的数量较少，它可以在鲁棒估计器（例如 RANSAC）中用作引擎，从而导致比传统基于点的方法少得多的迭代。该算法在合成和公开可用的数据集上进行了验证，并与最新技术进行了比较。它的适用性在两视图多运动拟合中得到了证明，即同时找到多个基本矩阵和异常值拒绝。
