Image Registration of Radiographic Images Using an Elastic Approach

In this work, an elastic registration technique is implemented to align different radiographic images to track the movement of gas and determine the colonic response to food in patients with functional abdominal bloating. The registration transformation is made of two components: i) an affine transformation parameterized in terms of 5 parameters (1 rotation, 2 magnification and 2 translation parameters) and ii) an elastic component expressed in terms of radial functions representing the smoothing term. Then, a chi² function defined in terms of the sum of the squared residual distances of corresponding internal point landmarks after they are transformed to the same coordinate system, is formed. Thus, the registration can be achieved by "tuning" the parameters until the residuals become simultaneously small (minimum). Since the parameters of the transformation are related in a non-linear fashion, they are estimated iteratively using a non-linear optimization technique, namely, the Simplex method developed by Nelder and Mead. Finally, the results are evaluated visually and quantitatively to study the precision of the registration.