Gaussian Process Morphable Models

by   Marcel Lüthi, et al.

Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of SSMs, called Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loeve expansion. To compute the expansion, we make use of an approximation scheme based on the Nystrom method. The resulting model can be seen as a continuous analogon of an SSM. However, while for SSMs the shape variation is restricted to the span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models, and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, an SSM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics, but is flexible enough to explain shapes that cannot be represented by the SSM. We introduce a simple algorithm for fitting a GPMM to a surface or image. This results in a non-rigid registration approach, whose regularization properties are defined by a GPMM. We show how we can obtain different registration schemes,including methods for multi-scale, spatially-varying or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modelling from the fitting process, this is all achieved without changes to the fitting algorithm. We show the applicability and versatility of GPMMs on a clinical use case, where the goal is the model-based segmentation of 3D forearm images.


page 14

page 19


Dynamic multi feature-class Gaussian process models

In model-based medical image analysis, three features of interest are th...

Probabilistic Registration for Gaussian Process 3D shape modelling in the presence of extensive missing data

Gaussian Processes are a powerful tool for shape modelling. While the ex...

A Variational Model Dedicated to Joint Segmentation, Registration and Atlas Generation for Shape Analysis

In medical image analysis, constructing an atlas, i.e. a mean representa...

Diffeomorphic brain shape modelling using Gauss-Newton optimisation

Shape modelling describes methods aimed at capturing the natural variabi...

Review of Statistical Shape Spaces for 3D Data with Comparative Analysis for Human Faces

With systems for acquiring 3D surface data being evermore commonplace, i...

Statistical shape representations for temporal registration of plant components in 3D

Plants are dynamic organisms. Understanding temporal variations in veget...

Functional Data Analysis and Visualisation of Three-dimensional Surface Shape

The advent of high resolution imaging has made data on surface shape wid...

Please sign up or login with your details

Forgot password? Click here to reset