Loadbalancing of computational tasks over heterogeneous architectures is an area of paramount importance due to the growing heterogeneity of HPC platforms and the higher performance and energy efficiency they could offer. This paper aims to address this challenge for a heterogeneous platform comprising Intel Xeon multi-core processors and Intel Xeon Phi accelerators (MIC) using an empirical approach. The proposed approach is investigated through a case study of the spin-image algorithm, selected due to its computationally intensive nature and a wide range of applications including 3D database retrieval systems and object recognition. The contributions of this paper are threefold. Firstly, we introduce a parallel spin-image algorithm (PSIA) that achieves a speedup of 19.8 on 24 CPU cores. Secondly, we provide results for a hybrid implementation of PSIA for a heterogeneous platform comprising CPU and MIC: to the best of our knowledge, this is the first such heterogeneous implementation of the spin-image algorithm. Thirdly, we use a range of 3D objects to empirically find a strategy to loadbalance computations between the MIC and CPU cores, achieving speedups of up to 32.4 over the sequential version. The LIRIS 3D mesh watermarking dataset is used to investigate performance analysis and optimization.