  In the field of bioimaging, an important part of analyzing the motion of
objects is tracking. We propose a method that applies the Sinkhorn distance for
solving the optimal transport problem to track objects. The advantage of this
method is that it can flexibly incorporate various assumptions in tracking as a
cost matrix. First, we extend the Sinkhorn distance from two dimensions to
three dimensions. Using this three-dimensional distance, we compare the
performance of two types of tracking technique, namely tracking that associates
objects that are close to each other, which conventionally uses the
nearest-neighbor method, and tracking that assumes that the object is moving at
constant velocity, using three types of simulation data. The results suggest
that when tracking objects moving at constant velocity, our method is superior
to conventional nearest-neighbor tracking as long as the added noise is not
excessively large. We show that the Sinkhorn method can be applied effectively
to object tracking. Our simulation data analysis suggests that when objects are
moving at constant velocity, our method, which sets acceleration as a cost,
outperforms the traditional nearest-neighbor method in terms of tracking
objects. To apply the proposed method to real bioimaging data, it is necessary
to set an appropriate cost indicator based on the movement features.
