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Medial Profiles for Modeling Deformation and Statistical Analysis of Shape and their Use in Medical Image Segmentation

We present a novel medial-based, multi-scale approach to shape representation and controlled deformation. We use medial-based profiles for shape representation, which follow the geometry of the structure and describe general, intuitive, and independent shape measures (length, orientation, and thickness). Controlled shape deformations (stretch, bend, and bulge) are obtained either as a result of applying deformation operators at certain locations and scales on the medial profiles, or by varying the weights of the main variation modes obtained from a new hierarchical (multi-scale) and regional (multi-location) principal component analysis of the medial profiles. We demonstrate the ability to produce controlled shape deformations on a medial-based representation of the corpus callosum. We show how this control of shape deformations facilitates the design of a layered framework for image segmentation and present results of segmenting the corpus callosum from 2D mid-sagittal magnetic resonance images of the human brain. Furthermore we show how the medial-based representation facilitates hierarchical, deformation-specific statistical shape analysis of segmented corpora callosa.