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Pattern TheoryFrom representation to inference$
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Ulf Grenander and Michael I. Miller

Print publication date: 2006

Print ISBN-13: 9780198505709

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780198505709.001.0001

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Computational Anatomy: Hypothesis Testing on Disease

Computational Anatomy: Hypothesis Testing on Disease

(p.494) 17 Computational Anatomy: Hypothesis Testing on Disease
Pattern Theory

Ulf Grenander

Michael I. Miller

Oxford University Press

Computational Anatomy (CA) is the study of human anatomy I ∈ I = Iα ◦G, an orbit under groups of diffeomorphisms of anatomical exemplars Iα ∈ I. The observable images I<D ∈ ID are the output of Medical imaging devices. This chapter focuses on the third of the three components of CA: (iii) generation of probability laws of anatomical variation P(·) on the images I within the anatomical orbits and inference of disease models. The basic random objects studied are the diffeomorphic transformations encoding the anatomical objects in the orbit; Gaussian random fields are constructed based on empirical observations of the transformations. Hypothesis testing on various neuromorphometric changes are studied.

Keywords:   Banach spaces, acceptance probability, birth-death processes, conservative jump processes

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