Finding the motion, position and orientation of a planar patch in 3D space from scaled-orthographic projection

Abstract

For the time being, many methods about how to solve the motion and structure of a rigid object in 3D space by using point or line correspondences have been widely researched. In this paper, the projected 2D image shapes of planar patches in 3D space are used as our basic image features. We try to determine the motion parameters and plane equations of planar patches in 3D space from the relationships among their observed image shapes. Besides, scaled-orthographic projection is used instead of the original perspective projection because of its simpler and tractable mathematical formulas. Not only a closely-approximate model to perspective projection, it further solves the inherent depth indeterminacy which exists in orthographic projection. Moreover, after applying a pre-processing of rotation correction to the original image data, our estimation result can achieve a better numerical solution than that without this pre-processing. Simulation experiments show the excellence of our algorithms in estimating the motion parameters. Ambiguities, indeterminacy, and data degeneracy are also carefully discussed in this paper, which provides some important insights to the problems.