Hypothesizing Structures in Edge-Focused Cerebral Magnetic Resonance Images Using Graph-Theoretic Cycle Enumeration

We present a novel method for the automatic generation of structure hypotheses (that is, educated guesses) suitable for recognition in medical images. The notion is that computer-based image analysis cannot be accomplished in a purely bottom-up fashion; the system should first organize the image structure into promising hypotheses, each of which is then compared to elements of the system modelbase for recognition or rejection. In this work, we tackle the hypothesis generation problem, for which computational efficiency is a major concern. We base our approach on segment-based edge-focusing to delineate significant boundaries precisely, and graph-theoretic cycle enumeration to produce natural closures and, therefore, plausible tissue structures of interest from incomplete boundary information. An efficient edge focusing algorithm selects significant fine scale boundaries as those natural descendants (in scale space) of prominent coarse scale edges. The fine scale representation provides the localization precision necessary, while the focusing ensures that only significant contours surviving over a range of scales are considered and so eliminates much of the "clutter" associated with a fine scale edge map. The spatial relationships among the edge segments are stored in the form of a directed graph. Possible extensions (closures) of broken edge segments are searched using time- and space-efficient voting methods. Cycle enumeration techniques for directed graphs then generate the structure hypotheses. The overall paradigm is fairly general and can be used in other problem domains, certainly for images of other parts of the anatomy. We demonstrate the effectiveness of the method with extensive experimental results on various magnetic resonance images of the human brain.