Introduction

Although the subjects of object recognition and object shape representation seem to be intertwined in many computer vision problems concerned with the identification of objects in natural scenes or clattered environments, there is a large class of applications where the problem of shape characterisation can be treated independently from the problem of shape segmentation. This is for example the situation of inventory type image databases where each image depicts a single object and the problem is to pick the image which depicts a specific object. Then one can concentrate on the best way to represent the shape of an object, assuming that there will always be available the closed contour that represents the shape. For this purpose, some of the best known methods of shape representation include active shape models (eg [ 3 , 2 ]) and polygonal representations with attributes calculated from these representations, like local curvature (eg [ 13 , 1 ]) or moments (eg [ 9 ]).

In a similar fashion, the issue of extracting closed surfaces from 3D data does not arise when each volume ``image'' contains one object only. Such is the case when models of 3D objects are created for top down approaches in computer vision. In response to this need the representations based on the Gaussian sphere were developed in the past [ 8 , 11 ]. More recently proposed methods exploit eigenspaces and modes (eg [ 10 , 12 ]) and geometric model deformations to fit free form surfaces (eg [ 14 , 7 ]). With the proliferation of 3D scanners and new 3D medical image modalities, one can easily envisage the availability of 3D image databases that depict single objects that have to be recognised, or simply characterised. The attributes by which these surfaces are characterised may include their overall shape but also local characteristics, like local roughness.

In this paper we are concerned with the quantification of this type of surface roughness and we are exemplifying our approach in the context of two problems: That of quantifying the roughness of surfaces of intestines for the purpose of aiding the discrimination between subjects suffering from chronic non-ulcerous colitis and non-sufferers. The other problem concerns the characterisation of the roughness of brain surfaces.

Our approach is similar to the approach presented in [ 15 , 4 , 5 ], except that we are concerned with the surface of 3D objects instead of 2D shapes. In section 2 we shall briefly present the approach. In section 3 we shall discuss some practical consideration. In section 4 we shall discuss ways by which the proposed roughness descriptors can be compared for object discrimination and in section 5 we shall present some experimental results. We shall draw our conclusions in section 6.