Closed-Form Solution for Relative Rotations between Image Pairs Using Normal Vectors of Epipolar Planes

Abstract

Determining the spatial relations between image and object spaces is an essential concern in photogrammetric applications. One such routine practice is to find the relative orientations between image pairs so that images acquired at a series of exposure stations can be properly aligned in a predefined reference frame. In a classic approach, this is typically done by the iterative least-squares estimation based on the collinearity condition. In this study, an analytical solution for the relative rotations between multiple images is derived utilizing the normal vectors of epipolar planes, which can be easily constructed by the coordinate vectors measured in conjugate images. This novel approach not only provides an effective geometric constraint between images but also makes possible a direct determination of the relative rotations without the need to carry out a tedious iterative computation. From the numerical test results, it is illustrated that the proposed approach is capable of providing a rotation solution at the same level of quality as the classic collinearity-based least-squares approach, but with an improved computational efficiency. Consequently, the cost of a photogrammetric analysis can be substantially reduced when the proposed approach is implemented in a real field application.