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.
Highlights
Kendall (1977) defined a shape as the geometric feature of an object that is invariant to rigid motions and global scaling
U = (u3, v3, . . . , up, vp)T is known as the Bookstein coordinates and it is in the shape space
We propose an extension of the projected normal distribution to the shape regression setting, where we include the effect of predictors through the parameter μ
Summary
Kendall (1977) defined a shape as the geometric feature of an object that is invariant to rigid motions and global scaling. Small, 1996), with a more recent trend focusing on techniques for closed curves, e.g. to describe the boundary of an object (Klassen et al, 2004; Srivastava et al, 2005; Kurtek et al, 2012; Cheng et al, 2015). These extensions go back to the original question: On which space should we define the probability models required for shape analysis?. Zn of m-dimensional shapes are depicted by p landmarks This is the space where raw objects are represented.
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