Co-registration of clinical images acquired using different imaging modalities and equipment is finding increasing use in patient studies. Here we present a method for registering high-resolution positron emission tomography (PET) data of the hand acquired using high-density avalanche chambers with magnetic resonance (MR) images of the finger obtained using a 'microscopy coil'. This allows the identification of the anatomical location of the PET radiotracer and thereby locates areas of active bone metabolism/'turnover'. Image fusion involving data acquired from the hand is demanding because rigid-body transformations cannot be employed to accurately register the images. The non-rigid registration technique that has been implemented in this study uses a variational approach to maximize the mutual information between images acquired using these different imaging modalities. A piecewise model of the fingers is employed to ensure that the methodology is robust and that it generates an accurate registration. Evaluation of the accuracy of the technique is tested using both synthetic data and PET and MR images acquired from patients with osteoarthritis. The method outperforms some established non-rigid registration techniques and results in a mean registration error that is less than approximately 1.5 mm in the vicinity of the finger joints.