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Many image matching schemes are based on mapping coordinate locations, such as the locations of landmarks, in one image to corresponding locations in a second image. A new approach to this mapping (coordinate transformation), called the elastic body spline (EBS), is described. The spline is based on a physical model of a homogeneous, isotropic three-dimensional (3-D) elastic body. The model can approximate the way that some physical objects deform. The EBS as well as the affine transformation, the thin plate spline and the volume spline are used to match 3-D magnetic resonance images (MRI's) of the breast that are used in the diagnosis and evaluation of breast cancer. These coordinate transformations are evaluated with different types of deformations and different numbers of corresponding (paired) coordinate locations. In all but one of the cases considered, using the EBS yields more similar images than the other methods.