Decomposition theory and transformations of visual directions

The author shows that there are two basic ways to eliminate rotation; either you eliminate actual (effective) rotation R˜ or abstract rotation R. The transformation of visual directions P is decomposed into pure deformation (pure strain) and abstract rotation. Methods can be grouped as to whether they eliminate actual or abstract rotation. An interesting elimination of R can be done for equatorial motion fields on the image hemisphere, using equator-normal flow, having a moving sensor in a fixed environment. Then rotation can be eliminated by detecting the phase and amplitude of a sine wave hidden in a 1-D signal (the signal is a function of longitudes). Both sparse velocities and normal flow for nearly equator-parallel image contours can be used (directly) as input data. This approach seems robust and can be used in conjunction with the algorithm by R.C. Nelson and J. Aloimonos (1988)