N-dimensional zonal algorithms. The future of block based motion estimation?

The popularity of zonal based algorithms for block based motion estimation has been increasing due to their superior performance in both terms of reduced complexity and superior quality versus other preexisting algorithms. In our previous work we mainly focused on generalizing the different parameters used in these algorithms and finding the possibly most efficient implementation. In this paper a further generalization of these algorithms is presented, where instead we mainly consider the way zones can be designed and what should be the ultimate goal of such an algorithm. As a result we present a framework of algorithms which can have applications not only in video coding, but also in other video signal processing areas, such as computer vision, video analysis, salient stills etc. We do so by initially considering the dimensionality of video data and how it can be most efficiently analyzed and exploited in the context of zonal algorithms. A formulization of these algorithms is then presented, according to which different implementations for different applications can be selected. Simulation results, for the simple 3-D case using the predictive diamond search (PDS) algorithm, a low complexity zonal algorithm, demonstrate the efficacy of the proposed techniques while still having low complexity. Higher order implementations using more dimensions and more efficient zonal algorithms can also be considered