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One of the data structures generated by medical imaging technology is highresolution point clouds representing anatomical surfaces. Raw images are in theform of triangulated surfaces and the first step is to create a standardisedrepresentation of surface shape which provides a meaningful correspondenceacross different images, to provide a basis for statistical analysis. Pointlocations with anatomical definitions, referred to as landmarks, have been thetraditional approach, with analysis and interpretation which is widely used andwell understood. Landmarks can also be taken as the starting point for moregeneral surface representations, often using templates which are warped on toan observed surface by matching landmark positions and subsequent localadjustment of the surface. The aim of the present paper is to use theintermediate structures of ridge and valley curves to capture the principalfeatures of the manifold (surface) of interest. Landmarks are used as anchoringpoints, as usual, but curvature information across the surface is used to guidethe curve locations. Once the ridges and valleys have been located, theintervening surface patches are relatively flat and can be represented in astandardised manner by appropriate surface transects, to give a completesurface model. However, the intermediate curve representation is ofconsiderable interest in its own right, as it captures the principal featuresof the surface and therefore embodies much of the shape information on theobject of interest.  Methods of identifying these curves are described and evaluated. While themethods are generic, the human face is used as an important application. Inparticular, the models are used to investigate sexual dimorphism (thedifferences in shape between male and female faces). The curve representationis shown to capture a major component of the relevant information.

Statistical models for manifold data with applications to the human face