Economical Representation of Image DeformationFunctions Using a Wavelet Mixture

Deriving a function that maps one image on to another similar image is a useful method in medical imaging. The modelling of this deformation function in terms of a functional basis leads to numerical methods of obtaining a good deformation. It is advantageous to be able to represent a wide class commonly observed deformations economically, i.e. where most coeecients are zero. We proposed a wavelet model for the deformation, where each wavelet coeecient has the mixture distribution of the form pp 0 +(1?p)N(0; 2). This distribution reeects our prior belief in the wavelet coeecients and results in an economical representation for the deformation. To implement this method, a penalised least squares methodology is adopted and three algorithms are devised. A numerical assessment of the method is made by applying the algorithms to images of femoral condyles, in which the deformations have predominantly localised features. A new method of visualising the wavelet decomposition of the deformation is presented.