Abstract

We present an approach for correcting the bias in 3D reconstruction of points imaged by a calibrated stereo rig. Our analysis is based on the observation that, due to quantization error, a 3D point reconstructed by triangulation essentially represents an entire region in space. The true location of the world point that generated the triangulated point could be anywhere in this region. We argue that the reconstructed point, if it is to represent this region in spacewithout bias, should be located at the centroid of this region, which is not what has been done in the literature. We derive the exact geometry of these regions in space, whichwe call 3D cells, and we show how they can be viewed asuniform distributions of possible pre-images of the pair ofcorresponding pixels. By assuming a uniform distributionof points in 3D, as opposed to a uniform distribution of theprojections of these 3D points on the images, we arrive at afast and exact computation of the triangulation bias in eachcell. In addition, we derive the exact covariance matricesof the 3D cells. We validate our approach in a variety ofsimulations ranging from 3D reconstruction to camera lo-calization and relative motion estimation. In all cases, weare able to demonstrate a marked improvement comparedto conventional techniques for small disparity values, for which bias is significant and the required corrections arelarge.