Algorithmic Information Theory (AIT), also known as Kolmogorov complexity, is a quantitative approach to defining information. AIT is mainly used to measure the amount of information present in the observations of a given phenomenon. In this dissertation we explore the applications of AIT in two case studies. The first examines bright field cell image segmentation and the second examines the information complexity of multicellular patterns. In the first study we demonstrate that our proposed AIT-based algorithm provides an accurate and robust bright field cell segmentation. Cell segmentation is the process of detecting cells in microscopy images, which is usually a challenging task for bright field microscopy due to the low contrast of the images. In the second study, which is the primary contribution of this dissertation, we employ an AIT-based algorithm to quantify the complexity of information content that arises during the development of multicellular organisms. We simulate multicellular organism development by coupling the Gene Regulatory Networks (GRN) within an epithelial field. Our results show that the configuration of GRNs influences the information complexity in the resultant multicellular patterns.

Understanding complex interactions in cellular systems requires accurate tracking of individual cells observed in microscopic image sequence and acquired from multi-day in vitro experiments. To be effective, methods must follow each cell through the whole experimental sequence to recognize significant phenotypic transitions, such as mitosis, chemotaxis, apoptosis, and cell/cell interactions, and to detect the effect of cell treatments. However, high accuracy long-range cell tracking is difficult because the collection and detection of cells in images is error-prone, and single error in a one frame can cause a tracked cell to be lost. Detection of cells is especially difficult when using bright field microscopy images wherein the contrast difference between the cells and the background is very low. This work introduces a new method that automatically identifies and then corrects tracking errors using a combination of combinatorial registration, flow constraints, and image segmentation repair.