Cost Functions for Intramodality Registration

The premise ofintensity-based registration methods is straightforward. If two images are well aligned, they will look similar to one another. More explicitly, ifone image is resampled to match the other image, the image intensities at each voxel should be similar in the two images. One caveat that should be noted early in this discussion is that it may be necessary to globally adjust the intensities of the images to compensate for any number of factors that may induce global changes in intensity from one image to the next. Intensity-based cost functions quantify the degree of similarity between the two images, and registration methods based on these cost functions simply adjust the parameters of an appropriate spatial transformation model (see the chapter "Spatial Transformation Models") until the cost function reaches a local optimum.

FIGURE 1 In the top panel, sagittal slices from two unregistered 3D MRI volumes are shown. Although differences are not easily detected by eye, subtraction of the images from one another reveals that subtle differences are present, as seen on the second row of the top panel. The bottom panel shows similar sagittal slices from the same two data sets after registration of the full three-dimensional volumes using an intensity-based cost function (scaled least squares). Trilinear interpolation was used during registration. After the optimal rigid-body spatial transformation parameters were identified, the images were resampled by using chirp z interpolation [17] to perform three one-dimensional pseudoshears [11], which were preceded by an antialiasing Fourier prepass interpolation [6]. After registration and resampling, the artifacts caused by misregistration within the brain were eliminated, as seen in the second row of the bottom panel. All difference images in both panels were scaled identically here for display. Note that the scalp, which was masked out of the images during registration, can still be detected in the postregistration difference images. Also note that movement of the tip of the tongue is discernible even in the unsubtracted images and represents a blatant violation of the rigid-body model. The estimated three-dimensional rotational displacement identified by the registration algorithm was 0.84° around an axis of rotation oriented at an angle of 71.7° from the plane displayed here. Estimated three-dimensional translational errors in the thalamus near the center of the brain were 1.5 millimeters with almost all of the displacement directed along the brain's anteroposterior axis.

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