Dynamic Programming Algorithms for Efficiently Computing Cosegmentations between Biological Images

Algorithms for comparing trees have recently been found relevant in the context of bioimage analysis. While previously proposed algorithms deal with problems that are computationally hard in general, we propose efficient algorithms for restricted versions that are able to handle significantly larger instances in practice. We propose two dynamic programming algorithms for the so-called tree assignment problem, which generalizes bipartite matchings to trees. We formulate restricted versions that are tractable by a dynamic programming algorithm. Furthermore, we describe a second dynamic programming algorithm that deals with the efficient computation of certain weights between so-called component trees that can be applied to obtain certain cosegmentations in bioimaging applications. Our investigations indicate that our algorithms are both efficient and effective, supported by evaluating the influence of the restrictions imposed by the dynamic programming formulation on a collection of image data.