Dynamic Time Warping and Cross Correlation for the estimation of cell movements in conjunctival capillaries: a comparison through simulation

We wish to assess the performance of an automatic analysis of video sequences of conjunctival vessels, digitally imaged with high enough magnification to resolve movement of the blood within the vessel. With a previously developed algorithm, from each vessel and from each frame we extract a one dimensional signal representing the longitudinal variation of gray level along the vessel, which is related to the presence of red blood cells. Then we estimate the local shift of the signals of a vessel between different frames, using a modified dynamic-time-warping approach. Since manual tracking of cells on a large batch of real video is unfeasible, we assess the performance of the algorithm on set of simulated vessels, where the mean cell velocity is known. By this means, we are also able to vary the mean blood cells velocity and the frequency of their velocity variation in time, so as to study the error variation with regard to these variables. We show the effectiveness of our method comparing it with a cross correlation approach. Moreover, along with the estimation error and robustness toward changes in the mean cells velocity, we show that at variance with the cross correlation method, the proposed algorithm is able to provide estimates on instantaneous velocity with an acceptable error, even if suffering from an overestimation bias that increases with the cells mean velocity.