Analytical studies of low-level motion estimators in space-time images using a unified filter concept

Low-level motion estimators based on differential, tensor and phase methods are reformulated in a unified way as filter methods in the continuous space-time domain. This approach allows inherent conceptual deficits to be distinguished from those related to the implementation in discrete space. A detailed analytical error analysis is performed. All techniques yield unbiased motion estimates for areas of constant velocity with any type of gray value structure in continuous space. Errors are only introduced by an inadequate discrete implementation. Further investigated are the influence of zero-mean normal distributed noise, spatially and temporally (accelerated) varying motion, motion discontinuities, and illumination changes. The main results of the paper are also illustrated with real-world image sequences