This paper presents a statistical framework for recognising 2D shapes which are represented as an arrangement of curves or strokes. The approach is a hierarchical one which mixes geometric and symbolic information in a three-layer architecture. Each curve primitive is represented using a point-distribution model which describes how its shape varies over a set of training data. We assign stroke labels to the primitives and these indicate to which class they belong. Shapes are decomposed into an arrangement of primitives and the global shape representation has two components. The first of these is a second point distribution model that is used to represent the geometric arrangement of the curve centre-points. The second component is a string of stroke labels that represents the symbolic arrangement of strokes. Hence each shape can be represented by a set of centre-point deformation parameters and a dictionary of permissible stroke label configurations. The hierarchy is a two-level architecture in which the curve models reside at the nonterminal lower level of the tree. The top level represents the curve arrangements allowed by the dictionary of permissible stroke combinations. The aim in recognition is to minimise the cross entropy between the probability distributions for geometric alignment errors and curve label errors. We show how the stroke parameters, shape-alignment parameters and stroke labels may be recovered by applying the expectation maximization EM algorithm to the utility measure. We apply the resulting shape-recognition method to Arabic character recognition.