We have presented a framework for multiscale analysis of the second-order local structures in medical volume data based on the analysis of the Hessian matrix. Multiscale filtering methods for enhancement of sheet, line, and blob structures were formulated. The guidelines for the filter design were clarified based on detailed analyses of single- and multiscale filter responses using mathematical local structure models. Further, formal approaches to description and quantification of sheet and line structures were presented. The accuracy of width quantification of sheet structures were theoretically analyzed and its inherent limits due to imaging resolution and postprocessing parameters were derived. In this chapter, we purely focus on local structures. Future work will include grouping these local structures to obtain higher-level descriptions incorporating global structures.
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