Motion from point matches using affine epipolar geometry - Shapiro, LS; Zisserman, A; Brady, M (Springer, 2005)
Algorithms to perform point-based motion estimation under orthographic and scaled orthographic projection abound in the literature. A key limitation of many existing algorithms is that they rely on the selection of a minimal point set to define a “local coordinate frame”. This approach is extremely sensitive to errors and noise, and forfeits the advantages of using the full data set. Furthermore, attention is seldom paid to the statistical performance of the algorithms. We present a new framework that caters for errors and noise, and allows all available features to be used, without the need to select a frame explicitly. This theory is derived in the context of the affine camera, which generalises the orthographic, scaled orthographic and para-perspective models. We define the affine epipolar geometry for two such cameras, giving the fundamental matrix in this case and discussing its noise resistant computation. The two-view rigid motion parameters (the scale factor between views, projection of the 3D axis of rotation and cyclotorsion angle) are then determined directly from the epipolar geometry. Optimal estimates are obtained over time by means of a linear Kalman filter, and results are presented on real data.