Gauge Independence in Optimization Algorithms for 3D Vision

We attack the problem of coordinate frame dependence and gauge freedoms in structure-from-motion. We are able to formulate a bundle adjustment algorithm whose results are independent of both the coordinate frame chosen to represent the scene and the ordering of the images. This method is more efficient that existing approaches to the problem in photogrammetry. We demonstrate that to achieve coordinate frame independent results, (i) Rotations should be represented by quaternions or local rotation parameters, not angles, and (ii) the translation vector describing the camera/scene motion should be represented in scene 3D coordinates, not camera 3D coordinates, two representations which are normally treated as interchangeable. The algorithm allows 3D point and line features to be reconstructed. Implementation is via the efficient recursive partitioning algorithm common in photogrammetry. Results are presented demonstrating the advantages of the new method in terms of the stability of the bundle adjustment iterations.