In 3D face recognition systems, 3D facial shape information plays an important role. 3D face recognizers usually depend on point cloud representation of faces where faces are represented as a set of 3D point coordinates. In many of the previous studies, faces are represented holistically and the discriminative contribution of local regions are assumed to be equivalent. In this work, we aim to design a local regionbased 3D face representation scheme where the discriminative contribution of local facial regions are taken into account by using a subset selection mechanism. In addition to the subset selection methodology, we have extracted patch descriptors and coded them using Linear Discriminant Analysis (LDA). Our experiments on the 3D_RMA database show that both the proposed floating backward subset selection scheme and the LDA-based coding of region descriptors improve the classification accuracy, and reduce the representation complexity significantly.