Light field essentially represents rays in space. The epipolar geometry between two light fields is an important relationship that captures ray-ray correspondences and relative configuration of two views. Unfortunately, so far little work has been done in deriving a formal epipolar geometry model that is specifically tailored for light field cameras. This is primarily due to the high-dimensional nature of the ray sampling process with a light field camera. This paper fills in this gap by developing a novel ray-space epipolar geometry which intrinsically encapsulates the complete projective relationship between two light fields, while the generalized epipolar geometry which describes relationship of normalized light fields is the specialization of the proposed model to calibrated cameras. With Plücker parameterization, we propose the ray-space projection model involving a 6×66\!\times \!6 ray-space intrinsic matrix for ray sampling of light field camera. Ray-space fundamental matrix and its properties are then derived to constrain ray-ray correspondences for general and special motions. Finally, based on ray-space epipolar geometry, we present two novel algorithms, one for fundamental matrix estimation, and the other for calibration. Experiments on synthetic and real data have validated the effectiveness of ray-space epipolar geometry in solving 3D computer vision tasks with light field cameras.

中文翻译：

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光场相机的射线空间对极几何


光场本质上代表了空间中的光线。两个光场之间的对极几何是捕获射线-射线对应关系和两个视图的相对配置的重要关系。不幸的是，到目前为止，在推导专门为光场相机定制的正式对极几何模型方面还没有做多少工作。这主要是由于光场相机的射线采样过程的高维性质。本文通过开发一种新颖的光线空间对极几何来填补这一空白，该几何本质上封装了两个光场之间的完整投影关系，而描述归一化光场关系的广义对极几何是所提出的模型对校准相机的专业化。通过 Plücker 参数化，我们提出了用于光场相机光线采样的 6×66\!\times \!6 光线空间本征矩阵的光线空间投影模型。然后导出光线空间基本矩阵及其属性，以约束一般和特殊运动的光线-光线对应关系。最后，基于射线空间对极几何，我们提出了两种新颖的算法，一种用于基本矩阵估计，另一种用于校准。对合成数据和真实数据的实验验证了光线空间对极几何在使用光场相机解决 3D 计算机视觉任务方面的有效性。