Statistical models for manifold data with applications to the human face

TL;DR

This paper develops statistical models for manifold surface data, using ridge and valley curves guided by landmarks and curvature, with applications to analyzing human face shape differences.

Contribution

It introduces a novel surface representation based on ridge and valley curves for statistical analysis of manifold data, especially human faces.

Findings

Curves effectively capture key shape features.

Models reveal significant sexual dimorphism in faces.

Surface patches are standardized for analysis.

Abstract

One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Raw images are in the form of triangulated surfaces and the first step is to create a standardised representation of surface shape which provides a meaningful correspondence across different images, to provide a basis for statistical analysis. Point locations with anatomical definitions, referred to as landmarks, have been the traditional approach, with analysis and interpretation which is widely used and well understood. Landmarks can also be taken as the starting point for more general surface representations, often using templates which are warped on to an observed surface by matching landmark positions and subsequent local adjustment of the surface. The aim of the present paper is to use the intermediate structures of ridge and valley curves to capture the principal features of the manifold (surface) of interest. Landmarks are used as anchoring points, as usual, but curvature information across the surface is used to guide the curve locations. Once the ridges and valleys have been located, the intervening surface patches are relatively flat and can be represented in a standardised manner by appropriate surface transects, to give a complete surface model. However, the intermediate curve representation is of considerable interest in its own right, as it captures the principal features of the surface and therefore embodies much of the shape information on the object of interest. Methods of identifying these curves are described and evaluated. While the methods are generic, the human face is used as an important application. In particular, the models are used to investigate sexual dimorphism (the differences in shape between male and female faces). The curve representation is shown to capture a major component of the relevant information.