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Date of Award
Doctor of Philosophy (PhD)
With the tremendous amount of data generated by the latest imaging technologies, research efforts have shifted focus from rendering and reconstructing shapes from raw image data, to analyzing these shapes. This is especially true in biomedical applications with widespread availability of many non-invasive biological imaging modalities -- ultrasonography, computed tomography, magnetic resonance imaging, etcetera. The insights gained from the analysis of biomedical images can help us understand biological processes, diagnose diseases and take preventative or remedial action. Examples include the study of an organ that is normally in cyclical motion, or that of an organ undergoing transformation in the course of normal development, or deterioration as a result of disease.
Many biological studies depend on a reliable means to compare different images or shapes of a similar nature, and quantify changes in them. A key component in these studies is the accuracy and reliability of the correspondence between shapes. This task is often complicated by the lack of easily identifiable features underpinning the correspondence, in addition to the inherent difficulties of obtaining high resolution, low noise and real-time images.
In this dissertation, we address the problem of constructing a meaningful shape correspondence for biological surfaces that lack distinctive features. First, we describe a geodesic based correspondence for surfaces with bent cylindrical shape, using domain-specific characteristics to circumvent the lack of features. Second, we adapt mechanical strain -- a well-established physical measure for deformation -- to refine an initial correspondence and measure similarity between non-rigid shapes. We demonstrate how to calculate strain for a two-dimensional (2D) surface embedded in three-dimensions (3D). We then adjust the correspondence between two surfaces so that the strain varies smoothly across the deformed surface, by minimizing the difference in strain at neighboring locations. This provides us with not just a physics-based shape correspondence, but also a measure of shape similarity in the form of the final strain on the deformed surface. We demonstrate the effectiveness of our approach using three biomedical applications: growth of the human abdominal aortic aneurysm, motion of the embryonic chick heart, and development of the ferret brain.
Philip Bayly, Cindy Grimm, Robert Pless, Sandra Rugonyi, Kilian Weinberger