Recognition of partially-occluded three dimensional (3D) objects is an essential task for many industrial applications of machine vision. In the paper, the authors tackle the problem of 3D object recognition using depth map representations. The method consists of two stages: the first is a subtemplate matching scheme that breaks down the object to be recognised into surface patches, called subtemplates, for matching. A special spherical windowing scheme is used to extract the correct patches. The algorithm estimates the orientation of a surface patch and performs the matching using mainly the outer boundary of the patch. In the second stage, dynamic programming (DP) is used to obtain a constrained optimal solution. It selects, among a number of probable matches resulting from the subtemplate matching stage, an optimal consistent set of matches. Experimental results show that the algorithm works well on objects that are truly irregularly shaped. Great reduction in computing time can also be achieved if the search regions for matching can be restricted to the neighbourhoods of extremal points or easily detected features.