Polyhedral Surface Decomposition Based on Curvature Analysis Bianca Fa1cidieno and Michela Spagnuolo ABSTRACf This paper describes a method to characterize the shape of a generic surface approximated with a triangulation. Combining classical topological techniques and differential geometry provides simple methods for evaluating several shape descriptors. Based on this idea a qualitative analysis is defined to estimate the curvature "along" edges and "around" triangles in order to identify regions whose shape is classified as concave, convex, plane or saddle. The proposed curvature regions are defined as connected components of the graph surface model and give rise to a unique surface decomposition which is suitable for parallel implementation and has a linear computational complexity. Key words: shape decomposition, surface modeling, topology, differential geometry. 1. INTRODUCTION Much of the potential of contemporary geometric modelling resides in its techniques for synthesizing, providing means to easily describe complex shapes as arrangements of simpler ones. In particular, the problem addressed by shape decomposition is the reduction of a generic surface to a compact symbolic description which picks out the essential information about the surface structure and leaves out low level details. In many fields it is necessary to handle very large and complex shape data. For example, many industrial and navigational robotics tasks definitely benefit from an explicit and effective representation of the information contained in range or intensity images. Indeed, a symbolic description based on characteristic shape elements can be used to perform high level pattern or object recognition by matching the description with pre-computed sample scenes (Besl et al. 1986, Medioni et al. 1984, Haralick et al. 1983, Watson et al. 1985). Spatial data handling is another context where surface characterization is desirable. Natural terrains are usually represented by large number of low level geometric primitives and the availability of abstraction mechanisms could be very useful to define generalized models based on morphological features (Falcidieno et al. 1992, Weibel et al. 1990). There are several ways of solving the problem of shape decomposition. Mathematical morphology is gaining increasing attention for being pleasingly neat and suitable for image processing (Pitas et al. 1990). Classical methods use concepts from differential geometry or analysis to subdivide a surface into regions having equivalent mathematical characteristics. The shape operators, i.e. Gaussian and mean curvature, are widely used and considered satisfactory especially in image processing (Besl et al. 1986). 57 T. L. Kunii et al. (eds.), Modern Geometric Computing for Visualization © Springer-Verlag Tokyo 1992