In this paper a method suitable for partial matching between 3D objects is presented. The 3D objects are firstly segmented into meaningful parts extending a method which is based on the medial surface of the objects. Then, geometric features are extracted for each part based on the Spherical Trace Transform. The extracted features are combined and their covariance matrix is computed as a descriptor of each part. The contribution of the proposed approach is that a meaningful segmentation of 3D objects based on medial surface is achieved and that partial matching is performed on meaningful parts, in a rotation, translation and scaling invariant manner. The experimental results performed, proved that the proposed approach achieves accurate partial matching in terms of distinct meaningful parts as well as satisfactory overall accuracy.