Joint direct estimation of 3D geometry and 3D motion using spatio temporal gradients

Abstract

Conventional image-motion based methods for structure from motion first compute optical flow, then solve for the 3D motion parameters based on the epipolar constraint, and finally recover the 3D geometry of the scene. However, errors in optical flow due to regularization can lead to large errors in 3D motion and structure. This paper investigates whether performance and consistency can be improved by avoiding optical flow estimation in the early stages of the structure-from-motion pipeline, and it proposes a new direct method based on image gradients (normal flow) only. Our main idea lies in a reformulation of the positive-depth constraint – the basis for estimating egomotion from normal flow – as a continuous piecewise differentiable function, which allows the use of well-known minimization techniques to solve for 3D motion.