Parametric regression of 3D medical images through the exploration of non-parametric regression models

Currently there is an increase usage of CT-based bone diagnosis because low-radiation and cost-effective 2D imaging modalities do not provide the necessary 3D information for bone diagnosis. The fundamental objective of our work is to build a model connecting 2D X-ray information to 3D CT information through regression. As a first step we propose an univariate non-parametric regression on individual predictor variables to explore the non-linearity of the data. To later combine these univariate models we then replace them with parametric models. We examine two predictors, shaft length and caput collum diaphysis angle on a database of 182 CT images of femurs. We show that for each predictor it is possible to describe 99% of the variance through a simple up to second order parametric model. These findings will allow us to extend to the multivariate case in the future.