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Division of Radiological Sciences, Guy's Hospital, London Bridge, London SE1 9RT Medical image registration can provide useful clinical information relating images of the same patient acquired from different modalities, or from serial studies with a single modality. Current algorithms invariably assume that the objects in the images can be treated as a rigid body. In practice, some parts of a patient, usually bony structures, may move as rigid bodies while others may deform. To address this, we have developed a new technique that allows identified objects in the image to move as rigid bodies, while the remainder smoothly deforms. Euclidean distance transforms calculated from the rigid objects are used to weight a linear combination of pre-defined linear transformations, one for each rigid body in the image, and also to form a modified radial basis function. This ensures that the non-linear deformation tends to zero as we move towards the rigid body boundary. The resulting deformation technique is valid in any dimension, subject to the choice of the basis function.We demonstrate this technique in two dimensions on a pattern of rigid square structures to simulate the vertebral bodies of the spine, and on sagittal magnetic resonance images collected from a volunteer.