PMC

Top left: the moving image. Top right: the fixed image. Bottom left: registered image using the viscous fluid transformation model with viscosity coefficients µ = 1.7, λ = 0.1. Bottom right: registered image using the elastic model, which performs much worse than the fluid model in matching the target image.

2D registration of binary traces of the corpus callosum, a midline structure in the brain: Top left: Fixed image. Top middle: Moving image, from a different subject. Top right: Difference image before registration. Bottom left: Registered image. Bottom middle: Deformation grid. Bottom middle: Difference image after registration.

2D registration of objects with different level of overlap. Column 1 through 4 show the moving images, fixed images, registered images and difference images, respectively. Levels of overlap from top to bottom are taken at 10% intervals from 90% to 10%. The initial MSDs are, from top to bottom: 2613, 2413.72279.7, 2315.3, 2323.2, and the final ones are: 2585.7, 1307.4, 246.9, 96.0, 36.4.

Registration using different phantoms with gradations (0 to 255) in intensity. The moving image consisted of a circle (leftmost image) and the fixed image consisted of a C (second image to the left). The third image is the result of deforming the circle into the C with the viscosity coefficient λ = 0.1; µ = 1.7 and the value of image dis-similarity between the registered image and the fixed image is 156.6 using MSD. Next is the difference image between the registered and fixed images.

3D registration of pairs of brain MRIs from several randomly selected control subjects. Images were downsampled by a factor of 2 along each axis, to a resolution of 128x128x128. Parameters for the code were λ = 1, µ = 1, and the filter size was D = 30, with 30 iterations. From top to bottom: moving image, fixed image, registered image, overlap (red: fixed image, blue: moving image), overlap (red: fixed image, blue: registered image).

This figure shows the results of viscous fluid registration applied to 3D binary phantoms (64x64x64) with levels of intensities varying from 0 to 255, and µ = 0.1, λ = 0.7. The columns correspond to x, y and z slices, respectively. The moving image consisted of a cubic shown in the first row (x slice, y slice and z slice). The fixed image is shown in the second row and the registered image is shown in the third row. The 4th row shows the difference image of the fixed image and the moving image. The 5th row is the difference image of the registered image and the fixed image.

The moving image is a disk and the fixed image is a C with added Gaussian noise of different standard deviations σ (from top to bottom: σ = 0.05, 0.1, 0.2, 0.3, 0.5). The central column shows the registered images and the difference images are shown in the right column. Initial MSD values from top to bottom are: 2204.2, 2175.8, 2137.9, 2081.6, 1981.6. Final ones are: 469.9, 980.0, 1890.7, 2762.2, 4481.4; registration performance only degrades substantially with high amplitude additive noise.

Values of image dissimilarity (MSD), after registration of C to O, as a function of the viscosity coefficients λ (0.01, 0.05, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100, 1000) and µ (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 20.0, 30.0, 40.0, 50.0, 100.0).