Fuzzy Object Skeletonization: Theory, Algorithms, and Applications

• Published in: IEEE transactions on visualization and computer graphics Vol. 24; no. 8; pp. 2298 - 2314
• Main Authors: Saha, Punam K., Jin, Dakai, Liu, Yinxiao, Christensen, Gary E., Chen, Cheng
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Animals; Bone and Bones - diagnostic imaging; Bone and Bones - physiology; collision-impact; Computational modeling; Computed tomography; Computer Graphics - statistics & numerical data; Computer Simulation; digital topology and geometry; distance transform; Filtration; Fuzzy Logic; fuzzy set; Fuzzy sets; Geodesy; grassfire propagation; Humans; Image resolution; Models, Anatomic; Models, Statistical; Phantoms, Imaging - statistics & numerical data; Pruning; Shape; Skeleton; Skeletonization; Tomography, X-Ray Computed - statistics & numerical data; Topology; Transforms; X-Ray Microtomography - statistics & numerical data
• ISSN: 1077-2626; 1941-0506; 1941-0506
• DOI: 10.1109/TVCG.2017.2738023

Skeletonization offers a compact representation of an object while preserving important topological and geometrical features. Literature on skeletonization of binary objects is quite mature. However, challenges involved with skeletonization of fuzzy objects are mostly unanswered. This paper presents a new theory and algorithm of skeletonization for fuzzy objects, evaluates its performance, and demonstrates its applications. A formulation of fuzzy grassfire propagation is introduced; its relationships with fuzzy distance functions, level sets, and geodesics are discussed; and several new theoretical results are presented in the continuous space. A notion of collision-impact of fire-fronts at skeletal points is introduced, and its role in filtering noisy skeletal points is demonstrated. A fuzzy object skeletonization algorithm is developed using new notions of surface- and curve-skeletal voxels, digital collision-impact, filtering of noisy skeletal voxels, and continuity of skeletal surfaces. A skeletal noise pruning algorithm is presented using branch-level significance. Accuracy and robustness of the new algorithm are examined on computer-generated phantoms and micro- and conventional CT imaging of trabecular bone specimens. An application of fuzzy object skeletonization to compute structure-width at a low image resolution is demonstrated, and its ability to predict bone strength is examined. Finally, the performance of the new fuzzy object skeletonization algorithm is compared with two binary object skeletonization methods.