Within Modality Registration Using Intensity Based Cost Functions

Roger P. Woods 1 Cost Functions for Intramodality Registration 529

UCLA School of Medicine 1,1 Cross-Correlation • 1.2 Ratio Image Uniformity • 1.3 Least Squares and Scaled Least Squares •

1.4 Other Cost Functions

2 Interpolation Method 531

3 Calculus-Based Optimization 532

3.1 Univariate Optimization • 3.2 Multivariate Optimization • 3.3 Special Simplifying Approximations for Least Squares Problems

4 Speed and Accuracy Trade-offs 534

5 Scope and Limitations 535

6 Future Directions 535

References 535

The past decade has seen tremendous growth in the demand for intramodality registration of images. Much of this demand has been driven by the increasing use of image subtraction techniques to detect changes in images that are too subtle to be reliably detected or quantified by simple visual inspection (see Fig. 1). Image subtraction was first used primarily in functional imaging studies of the brain, where these subtle changes could be correlated with cognitive tasks performed by the subject. Early functional imaging studies were based on positron emission tomography (PET) where only a dozen or so images are typically collected from any given subject. Now that functional imaging with magnetic resonance imaging (MRI) is common, the demand for rapid, reliable, automated registration of images has grown enormously since several hundred images are commonly acquired from each subject over the course of an hour or so. Interest in registration of standard structural images has also grown with the realization that registration and subtraction can be used to detect subtle changes that may reflect clinically important disease progression (see the chapter entitled "Clinical Applications of Image Registration"). The high spatial resolution of MRI images demands extreme registration accuracy, and the current thinking is that subvoxel accuracy is needed. In this context, intensity-based methods that do not require the identification of explicit landmarks or features have emerged as the workhorses of intramodality image registration.

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