Nonlinear tube-fitting for the analysis of anatomical and functional structures. (English) Zbl 1220.62135

Goldsmith, Jeff; Caffo, Brian; Crainiceanu, Ciprian; Reich, Daniel; Du, Yong; Hendrix, Craig

Ann. Appl. Stat. 5, No. 1, 337-363 (2011).

Summary: We are concerned with the estimation of the exterior surface and interior summaries of tube-shaped anatomical structures. This interest is motivated by two distinct scientific goals, one dealing with the distribution of HIV microbicide in the colon and the other with measuring degradation in white-matter tracts in the brain. Our problem is posed as the estimation of the support of a distribution in three dimensions from a sample from that distribution, possibly measured with error. We propose a novel tube-fitting algorithm to construct such estimators. Further, we conduct a simulation study to aid in the choice of a key parameter of the algorithm, and we test our algorithm with validation study tailored to the motivating data sets. Finally, we apply the tube-fitting algorithm to a colon image produced by single photon emission computed tomography (SPECT) and to a white-matter tract image produced using diffusion tensor imaging (DTI).

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
92C50	Medical applications (general)
65C60	Computational problems in statistics (MSC2010)
92C55	Biomedical imaging and signal processing

Keywords:

medical imaging; support estimation; SPECT; DTI; principal curves; nonlinear curve estimation

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