document: The remainder of our discussion proceeds as follows. In Section 2 we briefly describe the problem of cell tracking and introduce our approach to cell tracking, which may be regarded as fitting a mathematical model to experimental image data sets. We present the geometric evolution law model we seek to fit, which is a simplification of recently developed models in the literature that show good agreement with experiments [8,10–12,4,13,9]. We finish Section 2 by reformulating our model into the phase field framework, which appears more suitable for the problem in hand, and we formulate the cell tracking problem as a PDE constrained optimisation problem. In Section 3 we propose an algorithm for the resolution of the PDE constrained optimisation problem and we discuss some practical aspects related to the implementation. In particular we note that the theoretical and computational framework may be applied directly to multi-cell image data sets and raw image data sets (of sufficient quality) without segmentation. In Section 4 we present some numerical examples for the case of 2d single and multi-cell image data sets. Finally in Section 5 we present some conclusions of our study and discuss future extensions and applications of the work.
extractive_keyphrases: algorithm cell tracking problem experimental image data sets geometric evolution law model image data sets introduce our approach to cell tracking mathematical model our model pde constrained optimisation problem phase field framework problem of cell tracking segmentation theoretical and computational framework
abstractive_keyphrases: multi-cell image data sets raw image data sets