A wavelet approach to shape analysis for spinal curves

We present a new method to describe shape change and shape differences in curves, by constructing a deformation function in terms of a wavelet decomposition. Wavelets form an orthonormal basis which allows representations at multiple resolutions. The deformation function is estimated, in a fully Bayesian framework, using a Markov chain Monte Carlo algorithm. This Bayesian formulation incorporates prior information about the wavelets and the deformation function. The flexibility of the MCMC approach allows estimation of complex but clinically important summary statistics, such as curvature in our case, as well as estimates of deformation functions with variance estimates, and allows thorough investigation of the posterior distribution. This work is motivated by multi-disciplinary research involving a large-scale longitudinal study of idiopathic scoliosis in UK children. This paper provides novel statistical tools to study this spinal deformity, from which 5% of UK children suffer. Using the data we consider statistical inference for shape differences between normals, scoliotics and developers of scoliosis, in particular for spinal curvature, and look at longitudinal deformations to describe shape changes with time.