Spherical stereo matching on a geodesic grid using equal-epiline subdivision

Abstract

Spherical cameras with multiple fisheye lenses have been broadly used to capture an omnidirectional field of view of scenes. Since fisheye lenses' optical characteristics are significantly different, the traditional pinhole-based epipolar geometry is not directly applicable to spherical stereo matching. Current spherical stereo matching methods calculate stereo correspondences across \emph{strongly distorted} spherical images, suffering from the inefficiency of memory usage and computational cost and inaccuracy of estimated distance, particularly near the baseline poles of the stereo pair. In this paper, in order to increase the efficiency of computation and memory, we propose an spherical stereo matching algorithm by devising a novel \emph{equal-epiline subdivision} on a spherical geodesic grid. First, input spherical images are mapped to the icosahedral geodesic polyhedron divided into five sets of four principal polyhedral triangles. The spherical geodesic grid is transversely rotated to make two antipodal poles from north-south to west-east. The spherical geodesic grid is then tessellated with equal-arc subdivision, making the cell sizes and in-between distances virtually uniform, i.e., the arc length of the spherical grid cell's edges is consistent. Our novel equal-epiline subdivision scheme takes the advantages of the uniform equal-arcs geodesic grid on a spherical surface and an equal-chords geodesic grid on a planar plane simultaneously. In addition, our uniformly tessellated coordinates can be transformed into spherical coordinates via one-to-one mapping, allowing for analytical forward/backward transformation. It enables efficient and accurate stereo correspondence search from spherical images using epipolar geometry. We evaluate the efficiency and accuracy of our stereo matching method using ground-truth simulation. Our uniform tessellation scheme allows us to achieve higher accuracy of stereo matching than the traditional cylindrical and cubemap-based approaches. At the same time, it reduces the memory footage required for stereo matching by 20%.