A representation technique for visible three-dimensional object surfaces is presented which uses regions that are homogeneous in certain intrinsic surface properties. First, smooth patches are fitted to the object surfaces; principal curvatures are then computed and surface points classified accordingly. Such a representation scheme has applications in various image processing tasks such as graphics display and recognition of objects. An algorithm is presented for computing object descriptions. The algorithm divides the range data array into windows and fits approximating surfaces to those windows that do not contain discontinuities in range. The algorithm is not restricted to polyhedral objects nor is it committed to a particular type of approximating surface. It uses tension splines which make the fitting patches locally adaptable to the shape of object surfaces. Maximal regions are then formed by coalescing patches with similar intrinsic curvature-based properties. Regions on the surface of the object can be subsequently organized into a labelled graph, where each node represents a region and is assigned a label depicting the type of region and containing the set of feature values computed for that region.