Optimal extended optical flow subject to a statistical constraint

This work is motivated by the necessity to improve heart image tracking. This technique is related to the ability of generating an apparent continuous motion, which is observable through the variation of intensity from a starting image to an ending one. Given two images @r"0 and @r"1, we calculate an evolution process @r(t,@?) which transports @r"0 to @r"1 by using the optimal extended optical flow. Such a strategy is found to be well suited for heart image tracking, provided the motion is controlled by a statistical model. In this paper we use viability theory to give sufficient conditions to handle the optimal extended optical flow subject to a point-wise statistical constraint by using Parzen's approximation. The strategy is implemented in a 1D case and the numerical results which are presented show the efficiency of the proposed strategy.