Bayesian Analysis

A Bayesian Approach to Statistical Shape Analysis via the Projected Normal Distribution

Luis Gutiérrez, Eduardo Gutiérrez-Peña, and Ramsés H. Mena

Full-text: Open access

Abstract

This work presents a Bayesian predictive approach to statistical shape analysis. A modeling strategy that starts with a Gaussian distribution on the configuration space, and then removes the effects of location, rotation and scale, is studied. This boils down to an application of the projected normal distribution to model the configurations in the shape space, which together with certain identifiability constraints, facilitates parameter interpretation. Having better control over the parameters allows us to generalize the model to a regression setting where the effect of predictors on shapes can be considered. The methodology is illustrated and tested using both simulated scenarios and a real data set concerning eight anatomical landmarks on a sagittal plane of the corpus callosum in patients with autism and in a group of controls.

Article information

Source
Bayesian Anal., Volume 14, Number 2 (2019), 427-447.

Dates
First available in Project Euclid: 23 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ba/1529719227

Digital Object Identifier
doi:10.1214/18-BA1113

Mathematical Reviews number (MathSciNet)
MR3934092

Zentralblatt MATH identifier
07045437

Subjects
Primary: 62F15: Bayesian inference 62H35: Image analysis
Secondary: 62J05: Linear regression

Keywords
Bookstein coordinates identifiability medical image shape regression

Rights
Creative Commons Attribution 4.0 International License.

Citation

Gutiérrez, Luis; Gutiérrez-Peña, Eduardo; Mena, Ramsés H. A Bayesian Approach to Statistical Shape Analysis via the Projected Normal Distribution. Bayesian Anal. 14 (2019), no. 2, 427--447. doi:10.1214/18-BA1113. https://projecteuclid.org/euclid.ba/1529719227


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Supplemental materials

  • Supplementary Material for ‘A Bayesian approach to statistical shape analysis via the projected normal distribution’. The online Supplementary Material contains the proofs of Theorems 1 and 2, as well as those of Propositions 1 and 2. It also contains Algorithm 1 from Section 4 and some images relating to the application described in Section 8.