Image based modeling of complex boundaries

One outstanding challenge to understanding the behaviors of organisms and other complexities found in nature through the use of computational fluid dynamics simulations lies in the ability to accurately model the highly tortuous geometries and motions they generally exhibit. Descriptions must be created in a manner that is amenable to definition within some operative computational domain, while at the same time remaining fidelitous to the essence of what is desired to be understood. Typically models are created using functional approximations, so that complex objects are reduced to mathematically tractable representations. Such reductions can certainly lead to a great deal of insight, revealing trends by assigning parameterized motions and tracking their influence on a virtual surrounding environment. However, simplicity sometimes comes at the expense of fidelity; pared down to such a degree, simplified geometries evolving in prescribed fashions may fail to identify some of the essential physical mechanisms that make studying a system interesting to begin with. In this thesis, and alternative route to modeling complex geometries and behaviors is offered, basing its methodology on the coupling of image analysis and level set treatments. First a semi-Lagrangian method is explored, whereby images are utilized as a means for creating a set of surface points that describe a moving object. Later, points are dispensed with altogether, giving in the end a fully Eulerian representation of complex moving geometries that requires no surface meshing and that translates imaged objects directly to level sets without unnecessary tedium. The final framework outlined here represents a completely novel approach to modeling that combines image denoising, segmentation, optical flow, and morphing with level set- based embedded sharp interface methods to produce models that would be difficult to generate any other way.