Applications of Frequency Dependent Wavelet Shrinkage to Analyzing Quality of Image Registration

A fundamental problem in medical imaging is to transport an atlas associated with a template image onto new data. This is sometimes achieved by registering (warping) the template to the data and using the induced (spatial) deformation field to impose an atlas on the data. There are a number of alignment techniques which bring two images in register; however, few studies have been done to quantitatively compare various warping methods. In this paper we compare different wavelet space thresholding schemes (uniform, spatially, and frequency adaptive, Bayesian) and develop two approaches for quantitative evaluation of the performance of three nonaffine warping techniques and one affine polynomial (12 parameter) registration on groups of data. The results of the affine and nonaffine warps are evaluated, both on structural magnetic resonance imaging (MRI) data and on the corresponding functional positron emission tomography (PET) data using a quantitative approach based on the discrete wavelet transform. Using ideas from Donoho and Johnstone, we employed different thresholding schemes to the wavelet transforms of the volumetric data. The induced PET- and MRI-based warp rankings are in agreement. However, we observe differences in warp ranking and classification sensitivity between the wavelet space and the image (time-domain) space analyses.