Omnidirectional depth estimation is an emerging research topic and has received significant attention in recent years. However, the existing methods were developed based on the theory of planar stereo matching; and introduce the nonlinear epipolar constraint and significant distortions of re-projections. In this paper, we propose a novel approach that use spherical CNNs and the epipolar constraint on sphere for omnidirectional depth estimation. We discuss the epipolar constraint for spherical stereo imaging and convert the nonlinear constraint on a planar projection to the linear constraint on a sphere. We then propose a Spherical Convolution Residual Network (SCRN) for omnidirectional depth estimation via the spherical linear epipolar constraint. The input equirectangular projection (ERP) images are sampled to spherical meshes and fed into SCRN to calculate spherical depth maps. For 2D visualization, we design a Planar Refinement Network (PRN) and adopt the cascade learning scheme to improve the accuracy of depth maps. This scheme reduces the errors caused by projection, interpolation, and the limitation of spherical representation. The experiment shows that our full scheme Cascade Spherical Depth Network (CSDNet) results in more accurate and detailed depth maps with lower errors, as compared to recent seminal works. Our approach yields the comparable performance to the other state-of-the-art works on the omnidirectional stereo datasets with less number of parameters. The effectiveness of the spherical network and the cascade learning scheme is validated, and the influence of spherical sampling density is also discussed.

全向深度估计是一个新兴的研究课题，近年来受到了极大的关注。然而，现有的方法是基于平面立体匹配理论发展起来的；并引入非线性对极约束和重投影的显着失真。在本文中，我们提出了一种使用球形 CNN 和对球体的对极约束进行全方位深度估计的新方法。我们讨论球面立体成像的对极约束，并将平面投影上的非线性约束转换为球体上的线性约束。然后，我们提出了一个球形卷积残差网络（SCRN），用于通过球形线性对极约束进行全向深度估计。输入的等距柱状投影 (ERP) 图像被采样为球面网格并输入 SCRN 以计算球面深度图。对于 2D 可视化，我们设计了平面细化网络 (PRN) 并采用级联学习方案来提高深度图的准确性。该方案减少了由投影、插值和球面表示的限制引起的误差。实验表明，与最近的开创性工作相比，我们的完整方案级联球面深度网络 (CSDNet) 可生成更准确、更详细的深度图，并且误差更低。我们的方法在参数数量较少的全向立体数据集上产生了与其他最先进的工作相当的性能。验证了球形网络和级联学习方案的有效性，