The existence of affine invariant scale spaces for shapes opens possibilities for shape recognition. While affine invariant shape recognition is easily performed when shapes are complete, partially occluded or incomplete shapes must be recognized by dividing them into intrinsic parts. The characteristic point method, for instance, focuses on configurations of points with maximal curvature of the shape (in an euclidian invariant framework). Using the affine invariant scale space, we define affine invariant characteristic points and affine invariant parts of a shape. We prove that compatibility scale relations make feasible the matching of scale spaces and show experiments with noisy affine distorted and occluded shapes.