In this paper, we present a new framework for analyzing and segmenting point-sampled 3D objects. Our method first computes for each surface point the surface curvature distribution by applying the Principal Component Analysis on local neighborhoods with different sizes. Then we model in the four dimensional space the joint distribution of surface curvature and position features as a mixture of Gaussians using the Expectation Maximization algorithm. Central to our method is the extension of the scale-space theory from the 2D domain into the three-dimensional space to allow feature analysis and classification at different scales. Our algorithm operates directly on points requiring no vertex connectivity information. We demonstrate and discuss the performance of our framework on a collection of point sampled 3D objects.