Optic flow: multiple instantaneous rigid motions

Abstract

In Zhuang et al. (1988), a linear algorithm was presented to estimate a single instantaneous rigid motion from optic flow image point data. In order to obtain reasonable answers, however, the data must be quite accurate. This was shown by a lot of simulated experiments. As was well recognized, all machine vision feature extractors, recognizers, and matchers explicitly or implicitly needed for computing optic flow are unavoidably error prone and seem to make occasional errors which indeed are blunders. The realistic assumption for errors in optic flow should be a contaminated Gaussian noise which is a regular white Gaussian noise with probability 1 - (epsilon) plus an outlier process with probability (epsilon) , Huber (1981). Either the linear algorithm or the least-squares estimator are very sensitive to minor deviations from the Gaussian noise model assumption. In Haralick et al. (1989), the classical M-estimator was successfully applied to solve a single pose estimation from corresponding point data. However, lots of experiments conducted in Haralick et al. (1989) showed that the M-estimator only allowed a low proportion of outliers. For multiple pose segmentation and estimation, an estimator of high robustness is needed. A highly robust estimator called by the MF-estimator for general regression is presented and is applied to an important problem in computer vision, i.e., segmenting and estimating multiple instantaneous rigid motions from optic flow data. To be realistic, the observed or processed optic flow data are contaminated by various noises including outliers. Notationally, `MF' represents an abbreviation of `Model Fitting.' The MF- estimator is a result of partially modeling the unknown log likelihood function.