Optimal extended optical flow and statistical constraint

This work is motivated by the necessity to improve the Heart image tracking. This technique is related to the ability to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one, which are both supposed segmented. Given two images rho₀ and rho₁, we calculate an evolution process rho(t, middot) which transports rho₀ to <₁ by using the optimal extended optical flow. Such a strategy has been found well suited to Heart image tracking, provided the motion is controlled by a statistical model. In this paper we use viability theory to give sufficient conditions for handling the optimal extended optical flow subject to point-wise statistical constraint using Parzen´s approximation. The strategy is implemented in a 1D case and numerical results are presented showing the efficiency of the proposed strategy.