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We introduce a novel family of geometrical transformations for the non-rigid registration of medical images, called polyrigid and polyaffine. These transformations have nice mathematical properties, in- cluding differentiability and invertibility (i.e diffeomorphism). They are parameterized by a small number of intuitive parameters which allow to recover locally rigid and locally affine deformations often encountered in medical imagery. These transformations are a nice alternative to classical B-Spline transformations (which do not guaranty invertibility). Prelim- inary experiments on synthetic and real images already illustrate the potentialities and good properties of this approach.

Polyrigid and Polyaffine Transformations: A New Class of Diffeomorphisms for Locally Rigid or Affine Registration