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In this paper, we present a local graph matching based method for tracking cells and cell divisions. This will allow us to estimate the lineages of the cells in a 4D spatio-temporal image stack obtained using fluorescence imaging techniques. We work with plant cells, where the cells are tightly clustered in space and computing correspondences in space and time can be very challenging. The local graph matching method is able to compute the lineages even when significant portions of the images are corrupted due to sensor noise in the imaging process or segmentation errors. The geometric structure and topology of the cells' relative positions are efficiently exploited to solve the tracking problem using the local graph matching technique. The process not only computes the correspondences of cells across spatial and temporal image slices, but is also able to find out where and when cells divide, identify new cells and detect missing ones. Using this method we show experimental results to track the properly segmented cells, and compute cell lineages from images captured over 72 hours, even when some of those images are highly noisy (e.g., missing cells).