Direct Ground Surface Reconstruction from Stereo Images

Abstract

We propose a method for directly estimating a square grid ground surface from stereo images. We estimate the heights of all vertices in a square mesh, in which each square is divided into two triangular patches, drawn on a level plane of the ground, from a pair of images captured by nearly front-looking stereo cameras. We formulate a data term, representing the sum of the squared differences of photometrically transformed pixel values in homography-related projective triangular patches between the two stereo images, by the inverse compositional trick for both surface and photometric parameters for realizing an efficient estimation algorithm. The main difficulty of this problem formulation lies in the estimation instability for the heights of the distant vertices from the cameras, since the image projections of the distant triangular patches are crushed in the images. We effectively improve the stability by the combinational use of an additional smoothness term, update constraint term, and a hierarchical meshing approach. We demonstrate the validity of the proposed method through experiments using real images, and the usability for mobile robots by showing traversable area detection results on the ground surfaces estimated by the proposed method.