Mathematical methods and algorithms for identification, tracking, and quantitative analysis in cellular Bioimaging
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Abstract
Automated cell segmentation and tracking enables the quantification of static and dynamic cell characteristics and is significant for disease diagnosis, treatment, drug development and several other domains in health and life sciences.
The topic of this dissertation is the development of techniques for fully automated cell segmentation, tracking, lineage construction, and quantification. This work concentrates on two areas; cell segmentation and cell tracking.
We pursue a solution of the cell segmentation problem in the joint spatio-temporal domain to overcome weaknesses of previous works that operate only on the spatial domain of each frame. Here we propose a PDE-based formulation of spatio-temporal motion diffusion to detect the cell motion. In addition, we introduce an intensity standardization technique to address intensity variability complicating frame-to-frame analysis in differential techniques. To refine cell delineation accuracy produced by motion diffusion-based segmentation, we propose to use energy minimizing geometric active contours that assume a piece-wise constant image region model as a special case of the Mumford-Shah segmentation framework. Furthermore, we introduce temporal linking of the region-based level sets to allow for faster convergence and to resolve non-convexity that affects energy-based minimization that is typical in image analysis inverse problems.
In the cell tracking part of this work we first propose a variational method for joint local-global optical flow computation to estimate the cell motion. We utilize the predicted cell motion along with cell areas in a probabilistic Maximum Likelihood decision strategy assuming Markov dependency to find cell correspondences between consecutive frames. To perform track linking and to identify the cell states in the time-lapse sequence we find the solution that minimizes a global cost function defined over the set of all cell tracks by a heuristic approach. We represent cell tracks by an acyclic graph that we use to visualize the lineage tree. We use the region centroids to display the cell trajectories. Finally, we compute morphological, motility, diffusivity, and velocity measures using the time-lapse images, the cell label maps, and the tracking data.
We validate the cell segmentation and tracking stages both individually and as a joint system against reference standards that were manually generated. The image sequences and reference standards were obtained from a public database used for international cell tracking competitions. The validation measures quantify the region delineation accuracy by comparing levels of region overlapping and they calculate the cell tracking accuracy by comparison of acyclic graphs constructed from the cell tracks. The proposed techniques produce promising accuracy rates in comparison to the state-of-the-art. The ST-Diff-TCV segmentation technique yields an average DICE score of 89% over all 12 time-lapse image sequences. The automated tracking method using reference masks as input produces an average TRA score of 99%, which validates the tracking stage, and the fully automated system using both the proposed ST-Diff-TCV segmentation and tracking techniques produces an average of 89% with the 8 out of 12 sequences producing TRA > 91%.