Tracking and motion estimation based on time-sequentially sampled imagery and a general theory of time-sequential sampling

We present two algorithms for estimating the instantaneous velocity field of the brightness pattern generated on the focal plane of an imaging device due to the 3-D motion of an object in front of it. The development of these algorithms is based on spatiotemporal analysis of the data collected time-sequentially from the field of view (FOV). The first algorithm to be discussed is a centroid-based one which estimates the velocity based on the distance traveled by the centroid of the time-sequential data during the observation period. Next, we introduce a Fourier-based velocity estimator. When the motion within a small portion of the FOV is assumed to be a constant speed translation, the spectral energy of the time-varying scene will be confined to a plane in the frequency domain. We will outline a strategy for estimating a set of candidate points on this plane. This utilizes the 1-D FFT of the weighted time-sequential data. Then, we take as our velocity estimate that orientation which gives a least squares fit between the candidate set and the plane. The solution is a set of linear equations which are updated recursively. We will show that this procedure can estimate motion over a larger range of velocities than any of the existing algorithms. Finally, we analyze the merits and limitations of these algorithms in a general setting where the underlying assumptions are relaxed and where the target is maneuvering in a cluttered and noisy environment. We introduce a powerful technique from number theory which permits the analysis of time-sequential technique sampling with arbitrary periodicities to be carried out in an orthogonal coordinate system where the signal is rectangularly periodic. This facilitates the design of anti-aliasing patterns on arbitrary geometries. These patterns have a congruential structure. Finally, we will show that most classic field-instantaneous strategies considered for sampling time-varying imagery can be formulated in the general framework of time-sequential sampling. This includes face-centered and body-centered orthorhombic cubic lattices as well as lexicographic and 2:1 line-interlaced ordering used in commercial broadcast TV. (Abstract shortened with permission of author.