Bayesian Analysis

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

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

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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

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

First available in Project Euclid: 23 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Bookstein coordinates identifiability medical image shape regression

Creative Commons Attribution 4.0 International License.


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.

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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.