This paper presents a new approach to object categorisation in range images using our novel hierarchical compositional representation of surfaces. The atomic elements at the bottom layer of the hierarchy encode quantized relative depth of pixels in a local neighbourhood. Subsequent layers are formed in the recursive manner, each higher layer is statistically learnt on the layer below via a growing receptive field. In this paper we mainly focus on the part selection problem, i.e. the choice of the optimisation criteria which provide the information on which parts should be promoted to the higher layer of the hierarchy. Namely, two methods based on Minimum Description Length and category based entropy are introduced. The proposed approach was extensively tested on two widely-used datasets for object categorisation with results that are of the same quality as the best results achieved for those datasets.