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encrypted to form a digital signature (DS) of the whole volume using a public key encryption method such as RSA (see Reference in this chapter). Finally, the DS is embedded in pixels of all images within the volume by using a lossless embedding algorithm similar to the one described in Section 17.8.1. Since the images are still in random order, the DS is embedded according to this order. The result of embedding is a signature embedded image volume. After embedding, the images within the volume are re-arranged back to the original order; therefore the LDSE method does not affect clinical data ow. The embedding algorithm used in the 3-D LDSE method is different than the 2-D LDSE method in that it involves all images of the volume in the embedding. In comparison, the 2-D method embeds the 2-D image signature in each individual image within the volume. Figure 17.16 shows the 3-D LDSERS using a Z-shape walking pattern to search the R and S groups for data embedding. Four volexs are used to form a group to increase the compression ratio to accommodate the DS embedding. For more detail on the 3-D LDSERS algorithm, see the references at the end of this chapter. 17.8.2.3 Extracting and Verifying In extracting and verifying, the same random seed is used to reproduce the same random order as in the signature embedded volume. Images in the 3-D volume are then re-arranged according to this random order. Since embedding is an invertible process, the DS can be extracted and the original volume can be completely recovered. The extracted DS is then decrypted and veri ed with the hash value computed from the recovered volume. The veri ed volume is re-arranged back to the original order for clinical use.

reliable growth information. These image analyses are further discussed in literature listed at the end of the chapter. Figure 26.19 shows the CAD algorithm work ow. After image preprocessing, three regions of interest (ROIs) carpal bones (see left, large white rectangle), wrist joint (large white rectangle), and the phalangeal region, which has six sub-regions (six white rectangles) are automatically located and extracted as shown in the gure. Anatomical features are then extracted from the segmented osseous structures from each of the ROIs and inputted into the respective fuzzy subsystems. The results from the three regions are then aggregated to determine the nal bone age. The following subsections describe fuzzy system development (see the four color boxes in Figure 26.19). For each subsystem, the generation methodology for membership functions and fuzzy rules refer to the references at the end of the chapter. 26.8.2.2 Phalangeal Fuzzy Subsystem The middle and distal epimetaphyseal regions of the second through fourth digits were localized and extracted from each hand radiograph. A total of six phalangeal subregions of interest were thus isolated and acquired in the phalangeal ROI. Through image segmentation and feature extraction, 8 quantitative size and shape features for those 0 to 12 years of age and

A2.1. A galaxy emits light of a particular wavelength. As the light travels, the expansion of Universe slows down and stops. Just after the Universe begins to recollapse, the light is received by an observer in another galaxy. Does the observer see the light redshifted or blueshifted A2.2. This question concerns the luminosity distance in a closed cosmological model, with metric given by equation (A2.l) with k > O. The present physical distance from the origin to an object at radial coordinate ro is given by integrating ds at fixed time, i.e.

surface and the surface under test are placed in contact at the vertex, they would not have exactly the same curvature. 12.12.5. Combination of CGH with Null Optics Although a CGH can be designed for any optical system, a point is reached where the time and expense required to make a CGH are unreasonable. Also, given enough time and money, null optics, either re ective or refractive, can be designed and built to test almost any arbitrarily complicated optical system. It is possible to replace the complicated CGH or the complicated null optics required to test complicated optical surfaces (notably aspherical surfaces) with a combination of relatively simple null optics and a relatively simple CGH. To illustrate the potential of the combined test, results for a CGH-null-lens test of the primary mirror of an eccentric Cassegrain system with a departure of approximately 455 waves (at 514.5 nm) and a maximum slope of approximately 1500 waves per radius are shown in Figure 12.54 (Wyant and O Neill, 1974). The mirror was a

and Liu, P (2003) Leptin: a novel link between obesity, diabetes, cardiovascular risk, and ventricular hypertrophy Circulation, 108, 644 6 Sasson, Z, Rasooly, Y, Gupta, R and Rasooly, I (1996) Left atrial enlargement in healthy obese: prevalence and relation to left ventricular mass and diastolic function The Canadian Journal of Cardiology, 12, 257 63 Sch chinger, V, Britten, MB and Zeiher, AM (2000) Prognostic impact of coronary vasodilator dysfunction on adverse long-term outcome of coronary heart disease Circulation, 101, 1899 906 Schmieder, RE and Messerli, FH (1993) Does obesity in uence early target organ damage in hypertensive patients Circulation, 87, 1482 8 Seyfeli, E, Duru, M, Kuvandik, G et al (2006) Effect of obesity on P-wave dispersion and QT dispersion in women International Journal of Obesity (London), 30, 957 61 Sharma, AM (2001) Sibutramine in overweight/obese hypertensive patients.