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Computer Vision, IEEE International Conference on (2007)
Rio de Janeiro, Brazil
Oct. 14, 2007 to Oct. 21, 2007
ISBN: 978-1-4244-1630-1
pp: 1-7
B. C. Davis , University of North Carolina at Chapel Hill, Chapel Hill, NC, USA; Kitware, Inc., Clifton Park, NY, USA.
P. T. Fletcher , University of Utah, Salt Lake City, Utah, USA
E. Bullitt , University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
S. Joshi , University of Utah, Salt Lake City, Utah, USA
Regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable, and in particular it is applicable to the study of anatomical growth and shape change. When the underlying process can be modeled by parameters in a Euclidean space, classical regression techniques [13, 34] are applicable and have been studied extensively. However, recent work suggests that attempts to describe anatomical shapes using flat Euclidean spaces undermines our ability to represent natural biological variability [9, 11]. In this paper we develop a method for regression analysis of general, manifold-valued data. Specifically, we extend Nadaraya-Watson kernel regression by recasting the regression problem in terms of Fréchet expectation. Although this method is quite general, our driving problem is the study anatomical shape change as a function of age from random design image data. We demonstrate our method by analyzing shape change in the brain from a random design dataset of MR images of 89 healthy adults ranging in age from 22 to 79 years. To study the small scale changes in anatomy, we use the infinite dimensional manifold of diffeomorphic transformations, with an associated metric. We regress a representative anatomical shape, as a function of age, from this population.

E. Bullitt, P. T. Fletcher, B. C. Davis and S. Joshi, "Population Shape Regression From Random Design Data," 2007 11th IEEE International Conference on Computer Vision(ICCV), Rio de Janeiro, 2007, pp. 1-7.
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