The imaging process is modeled as illustrated in this figure, as a high resolution image which has been blurred, corrupted by noise, and then subsampled. The mathematics of Mean Field Annealing, applied to the measuredimage, allows an optimal estimate of the missing data (every other pixel in 2:1 zoom).
Even in this high resolution (512 x 512) spiral CT-scan of the lung, the bronchial tree rapidly becomes so small that it is difficult to trackindividual structures deep in the lung. The interpolation mathematics promises to allow at least double the number of pixels in each dimension,and perhaps even better. In CT and MRI, another factor promises to make the algorithms even more robust: the fact that three-dimensional information is available.
Status: this is a new project; the mathematical derivations have beencompleted, and software is being written to test the concept, both intwo-dimensional and three-dimensional images.
Click here to see a good quality version of an image which compares all the results discussed below
Image 1.
This image above is a segment of a mammogram scanned at 200 micron (2.5 linepairs per mm) resolution.The image is of a mass which, upon subsequent ultrasound examination, demonstrated a well defined hypoechoic mass. In the original radiologist's report, there were "no associated pleomorphic microcalcifications".
Image2.
The image above is interpolated to equivalent of 100 micron resolution usingbilinear interpolation.
Image 3.
The image above demonstrates the result of running a preliminary versionof the optimal interpolation software on image 1, to produce an estimate to what the image would look like if it had been scanned at 100 micron resolution. The edges and fine details are much sharper. Furthermore, two microcalcifications are apparent in the 3:00 position of the lesion.
Image 4.
The image above reflects the same film, but scanned at 100 micron resolution. Using a higher quality scanner is clearly superior to any of the interpolation methods, and clearly demonstrates the microcalcifications. Of the interpolation methods, however, Image 3 is clearly the best.
optimal zooming of thermal images
Following are ten thermal images, acquired with a very old, first generation
scanner. We should note that these images are deliberately taken with a very
noisy, low resolution scanner in order to test the capabilities of the
algorithm. Modern thermal imagers produce far better quality images, better
in both resolution, dynamic range, and noise. If the algorithm can do this
well on these poor images, imagine how well it will do on data from a modern
imager.
ORIGINAL IMAGE
ZOOMED BY
PIXEL REPLICATIONZOOMED BY
OPTIMAL INTERPOLATION
