Bayesian estimation of templates in computational anatomy: Difference between revisions
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{{Main|Computational anatomy}}
[[Statistical shape analysis]] and [[Computational anatomy#Statistical shape theory in computational anatomy|statistical shape theory]] in [[computational anatomy]] (CA) is performed relative to templates, therefore it is a local theory of statistics on shape.[[Computational anatomy#Template Estimation from Populations|Template estimation]] in [[computational anatomy]] from populations of observations is a fundamental operation ubiquitous to the discipline. Several methods for template estimation based on [[Bayesian probability|Bayesian]] probability and statistics in the [[Computational anatomy#The random orbit model of computational anatomy|random orbit model of CA]] have emerged for submanifolds<ref>{{Cite journal|title = A Bayesian Generative Model for Surface Template Estimation|journal = International Journal of Biomedical Imaging|date = 2010-01-01|issn = 1687-4188|pmc = 2946602|pmid = 20885934|pages = 1–14|volume = 2010|doi = 10.1155/2010/974957|
== The deformable template model of shapes and forms via diffeomorphic group actions ==
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== The Bayes model of computational anatomy ==
The central statistical model of [[computational anatomy]] in the context of [[medical imaging]] is the source-channel model of [[Shannon theory]];<ref>{{Cite journal|title = Statistical methods in computational anatomy|journal = Statistical Methods in Medical Research|date = 1997-06-01|issn = 0962-2802|pmid = 9339500|pages = 267–299|volume = 6|issue = 3|doi = 10.1177/096228029700600305|language = en|
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\hat \theta \doteq \arg \max_{\theta \in \Theta} \log p(\theta \mid I^D). </math>
[[File:Xiaoying Tang ADNI template.png|thumb|Shown are shape templates of amygdala, hippocampus, and ventricle generated from 754 ADNI samples` Top panel denotes the localized surface area group differences between normal aging and Alzheimer disease (positive represents atrophy in Alzheimer whereas negative suggests expansion). Bottom panel denotes the group differences in the annualized rates of change in the localized surface areas (positive represents faster atrophy rates (or slower expansion rates) in Alzheimer whereas negative suggests faster expansion rates (or slower atrophy rates) in Alzheimer); taken from Tang et al.<ref name="Tang 599–611">{{Cite journal|
]]This requires computation of the conditional probabilities <math>p(\theta\mid I^D) = \frac{p(I^D,\theta)}{p(I^D)}</math>. The multiple atlas orbit model randomizes over the denumerable set of atlases <math>\{ I_a, a \in \mathcal{A} \}</math>. The model on images in the orbit take the form of a multi-modal mixture distribution
:<math>p(I^D, \theta) = \textstyle \sum_{a \in \mathcal{A}} p(I^D,\theta\mid I_a) \pi_{\mathcal A}(a) \ .</math>
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== Surface templates for computational neuroanatomy and subcortical structures ==
The study of sub-cortical neuroanatomy has been the focus of many studies. Since the original publications by Csernansky and colleagues of hippocampal change in Schizophrenia,<ref>{{Cite journal|
Shown in the accompanying Figure is an example of subcortical structure templates generated from T1-weighted [[Magnetic resonance imaging|magnetic resonance imagery]] by Tang et al.<ref name="Tang 599–611"/><ref name="Tang 2093–2117"/><ref name="Tang 645–660"/> for the study of Alzheimer's disease in the ADNI population of subjects.
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== Surface estimation in cardiac computational anatomy ==
[[File:Siamak atlas.tif|alt=Showing population heart atlases with superimposed hypertrophy.|thumb|Showing population atlases identifying regional differences in radial thickness at end-systolic cardiac phase between patients with hypertrophic cardiomyopathy (left) and hypertensive heart disease (right). Gray mesh shows the common surface template to the population, with the color map representing basilar septal and anterior epicardial wall with larger radial thickness in patients with hypertrophic cardiomyopathy vs. hypertensive heart disease.<ref name="Semantic Scholar">{{Cite web|url=https://www.semanticscholar.org/paper/Shape-analysis-of-hypertrophic-and-hypertensive-Ardekani-Jain/4073fc2af6ef7fb978d5203be3e84c999e1a0dbd|title=Semantic Scholar|website=www.semanticscholar.org|language=en-US|access-date=2016-04-05}}{{Dead link|date=October 2019 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>]]
Numerous studies have now been done on cardiac hypertrophy and the role of the structural integraties in the functional mechanics of the heart. Siamak Ardekani has been working on populations of Cardiac anatomies reconstructing atlas coordinate systems from populations.<ref>{{Cite journal|
== MAP Estimation of volume templates from populations and the EM algorithm ==
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