  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.
