A General Approach to Model Biomedical Data from 3D Unorganised Point Clouds with Medial Scaffolds

Abstract

We present the latest developments in modeling 3D biomedical data via the Medial Scaffold (MS), a 3D acyclic oriented graph representation of the Medial Axis (MA) [LK07, SP08]. TheMS (and associated 3DMA) can be computed as the result of the singularities of a geometric wave propagation simulation. We consider here some of the potential applications of this shape model in the realm of biomedical imaging. We can reconstruct complex object surfaces and make explicit the coarse-scale structures, which are ready-to-use in a number of practical applications, including: morphological measurement for cortex or bone thickness, centerline extraction (curve skeleton) for tracheotomy or colonoscopy, surface partitioning for cortical or anatomical surface classification, as well as registration and matching of shapes of tumors or carpal bones. TheMS permits to automatically and efficiently map an unorganised point cloud, i.e., simple 3D coordinates of point samples, to a coherent surface set and associated approximate MA. The derivedMS is used to further recover significant medium and large scale features, such as surface ridges and main axial symmetries. The radius field of theMS provides an intuitive definition for morphological measurements, while the graph structure made explicit by theMS is useful for shape registration and matching applications.