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|first1 = Michael|last1 = Miller|first2 = Ayananshu|last2 = Banerjee|first3 = Gary|last3 = Christensen|first4 = Sarang|last4 = Joshi|first5 = Navin|last5 = Khaneja|first6 = Ulf|last6 = Grenander|first7 = Larissa|last7 = Matejic|s2cid = 35247542}}</ref><ref>{{Cite book|title = Pattern Theory: From Representation to Inference|author = U. Grenander and M. I. Miller |publisher = Oxford University Press|date = 2007-02-08|isbn = {{Format ISBN|9780199297061}}978-0-19-929706-1|language = English}}</ref><ref>{{Cite book|title = Bayesian Multiple Atlas Deformable Templates|author = M. I. Miller and S. Mori and X. Tang and D. Tward and Y. Zhang | series = Brain Mapping: An Encyclopedic Reference|url = https://books.google.com/books?id=ysucBAAAQBAJ|publisher = Academic Press|date = 2015-02-14|isbn = {{Format ISBN|9780123973160}}978-0-12-397316-0|language = en}}</ref> the source is the deformable template of images <math> I \in \mathcal {I} </math>, the channel outputs are the imaging sensors with observables <math> I^D \in {\mathcal I}^{\mathcal D} </math> . The variation in the anatomical configurations are modelled separately from the Medical imaging modalities [[Computed axial tomography|Computed Axial Tomography]] machine, [[Magnetic resonance imaging|MRI]] machine, [[Positron emission tomography|PET]] machine, and others. The [[Bayes' theorem|Bayes theory]] models the prior on the source of images <math> \pi_{\mathcal{I}} (\cdot) </math> on <math>I \in \mathcal{I} </math>, and the conditional density on the observable imagery <math> p(\cdot |I) \ \text{on} \ I^D \in {\mathcal I}^{\mathcal D} </math>, conditioned on <math> I \in \mathcal{I} </math>. For images with [[Computational anatomy#Groups and group actions|diffeomorphism group action]] <math>I \doteq \phi \cdot I_\mathrm{temp}, \phi \in Diff_V</math>, then the prior on the group <math>\pi_{Diff_V} (\cdot)</math> induces the prior on images <math>\pi_{\mathcal{I}} (\cdot)</math>, written as densities the log-posterior takes the form
