Cell Mapping: Tracking Cell Splits and Merges
in Large-Scale Evolving Structures

The main contribution of this thesis is the development of a new method of detecting object splits and merges in image sequences. The overlap-distance ratio provides the basis for efficiently tracking cells that split and merge over long periods of time. As long as the movement of cells from one image to the next does not extend beyond a threshold related to cell diameter, the methodology selects the appropriate ancestry. If the movement exceeds the limits of validity for the distance computation, a projection of motion must be included or the images must be captured at a faster rate. Because the inputs into the mapping equation are not domain-specific, this mapping technique can easily be expanded to other problem domains.

This mapping methodology has several advantages in applications involving extensive data sets. First, there are no complex computations needed to perform the mapping. This introduces minimal overhead in the tracking process. Second, the actual images are not required to perform the mapping, and therefore mapping can be done after the segmentation of all of the images in the tracking sequence is complete. The method only requires information on the cell center coordinates, direction vectors of the cell's principal axes and their lengths, and the coordinates the corners of the cell's bounding box oriented to the X-Y axes. This information can easily be held in main memory during the entire tracking process.

When animating cell interactions detected during the mapping procedure, one must determine which underlying processes need to be analyzed. The method detailed in this thesis provides an historical perspective into a cell's ancestry, and gives insight into the time dimension. This type of visualization can be expanded into other domains in which similar interactions take place. However, because the animations provide a two-dimensional representation, only two tracking features can be visualized together at one time. Obviously, the split/merge activity must be included, but a trade-off has to be made in determining the other feature. If cell orientation is selected, the time dimension and all information about dissipated cells is lost. On the other hand, if cell orientation is not present, representations like the one presented in this thesis may lose valuable insight on how the location of cells at the time of a split or merge affect the overall pattern equation.

During the design of visualizations of cell interactions, limitations to the Polka parallel processing environment were discovered. Until a means is available to smoothly group objects and reposition the groups as one unit, more complex visualizations such as the dividing squares representation cannot be developed.

Several questions arose as a result of this research and may be worth pursuing. First, because of the potential for large movement of cells between images in some of the experiments, integrating a projection of that motion may provide a more accurate placement of cells between frames, so the overlap-distance ratio can still be utilized. Second, other potential indicators of cell evolution could perhaps replace or supplement the overlap-distance ratio in correctly mapping cells between images. This could be used as a predictor of activity and may be useful in providing insight into how, when, and where a cell evolves. In addition, these indicators may be able to pinpoint unstable cells within an image. Information collected about unstable cells may also be key inputs into the overall pattern equations. Third, there needs to be a means of providing an integrated visualization of cell histories and the underlying movement and position of the cells over time. This added dimension would give a more complete description of the underlying processes and cell interactions involved in the combustion domain.