TAILIEUCHUNG - The Essential Guide to Image Processing- P26

The Essential Guide to Image Processing- P26:We are in the middle of an exciting period of time in the field of image processing. Indeed, scarcely a week passes where we do not hear an announcement of some new technological breakthrough in the areas of digital computation and telecommunication. | 762 CHAPTER 26 Computed Tomography Disks phantom Vertical Transverse Vertical Transverse Object Reconstruction Vertical Transverse Vertical Transverse FIGURE Example of cone-beam reconstructions from a circular orbit the obvious artifacts are a result of the incompleteness in the data. Other trajectories such as a helix or a circle plus line give complete data and artifact free reconstructions. œ 1 A g u v 2 g u vH h u - u du. 4 2 J VA2 u 2 v 2 œ Similarly to r x a is the distance between x and the source position a and ux Vx are the coordinates on the detector of the cone-beam projection of x see Fig. . Figure shows two images of reconstructions from mathematically simulated data. Using a magnified grayscale to reveal the 1 contrast structures the top images show both a high quality reconstruction in the horizontal transverse slice at the level of the circular trajectory and apparent decreased intensity on planes above and below this level. These artifacts are characteristic of the Feldkamp algorithm. The bottom images showing reconstructions for the disks phantom exhibit cross-talkbetween transverse planes and some other less dramatic artifacts. The disk phantom is specifically designed to illustrate the difficulty in using cone-beam measurements for a circular trajectory. Frequencies along and near the scanner axis are not measured and objects with high amplitudes in this direction produce poor reconstructions. Generally the artifacts manifested in the reconstructed images depend on the object being imaged and on its position relative to the plane of the trajectory. For the cone-beam configuration requirements for a tomographically complete set of measurements are known as Tuy s condition. Tuy s condition is expressed in terms of a geometric relationship among the trajectory of the cone-beam vertex point the source point and the size and position of the object being scanned. Tuy s condition requires that every plane that cuts through

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