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The 2D Gaussian function de nes the spatial spread of the Gabor lter. This spread is de ned by the variance parameters of the Gaussian, along the x and y direction together with the orientation parameter . Figure 5.1a shows a 3D representation of the Gaussian mask generated with x = 10 and y = 15 and rotation angle = 0. The image in Figure 5.1b shows the region of spatial in uence of an elliptical mask on an image, where the variance in the x direction is larger than the variance in the y direction. Typically the Gaussian lter has the same variance along both the x and y directions, that is, x = y = . Under such conditions the rotation parameter does not play any role as the spread will be circular.

ival: 16 oct set: 020 dval: 16 hex set: 16 ival: 0x10 dec set: 16

The noshowbase manipulator resets cout not to display the notational base of the integral values By default, a floating point value has a precision value of 6 This value may be modified by using either the precision(int) member function or the setprecision() stream manipulator (to use the latter, the iomanip header file must be included) precision() returns the current precision value For example:

Data Link Protocol [EAP request]

Figure 5.2. (a) 3D representation of a sinusoid S , . (b) Image representation of the real part of the

#include <iostream> #include <iomanip> #include <mathh> int main() { cout "Precision: " coutprecision() endl sqrt(20) endl; coutprecision(12); cout "\nPrecision: " coutprecision() endl sqrt(20) endl; cout "\nPrecision: " setprecision(3) coutprecision() endl sqrt(20) endl; return 0; }

When compiled and executed, the program generates the following output:

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Precision: 6 141421 Precision: 12 141421356237 Precision: 3 141

complex sinusoid {S , }. (c) Image representation of the imaginary part of complex sinusoid {S , }.

file:///F|/WinDDK/resources/CPPPrimer/c++primerhtm (1003 / 1065) [2001-3-29 11:32:15]

Manipulators that take an argument, such as setprecision() and setw() that we looked at earlier, require that we include the iomanip header file:

The 2D complex sinusoid de ned by Eq. (5.3) generates the two sinusoidal components of the Gabor lters which (when applied to an image) extracts the local frequency content of the intensity variations in the signal. The complex sinusoid has two components (the real and the imaginary parts) which are two 2D sinusoids that are phase-shifted by radians. Figure 5.2a shows the 3D representation of a sinu2 soidal signal (either real or imaginary) at = 0.554 radians and = 0 radians, while Figures 5.2b and 5.2c show an image of the real and imaginary parts of the same complex sinusoid, respectively. It can be seen that the two lters are similar, except for the /2-radian phase shift. Multiplying the Gaussian and the sinusoid generates the complex Gabor lter, as de ned in Eq. (5.1). If x = y = , then the real and imaginary parts of this complex lter can be described as follows.

Our example does not illustrate two further aspects of setprecision(): (1) integral values are unaffected and (2) floating point values are rounded, not truncated Thus, 314159 becomes 3142 with precision set to 4, and 314 with precision set to 3 By default, the decimal point is not displayed when the fractional part of the value is 0 For example,

encapsulated within layer-2 protocols on the client side and within the AAA protocol on the AAA server side Both RADIUS and Diameter provide specific support for transport of EAP, as we explained in s 6 and 7 The reader is referred to those chapters or to RFC 3579 [RADEAP3579] for RADIUS and the Internet draft specification [DIAEAPDR] for Diameter for more details From a transport point of view, when EAP is encapsulated inside a AAA protocol packet, it will enjoy the same transport guarantees that the deployed AAA protocol receives from its underlying transport protocol (UDP for RADIUS and TCP or SCTP for Diameter) Since EAP was intended to run over links where IP services are absent, it was designed to provide some native reliability features, such as support for retransmissions and duplicate packet elimination.

To force the display of the decimal point, we use the showpoint manipulator:

(x, y) = (x, y) =

cout showpoint 100 noshowpoint '\n';

The noshowpoint manipulator reinstates the default behavior Again, by default, floating point values are displayed in fixed decimal notation To change the display to scientific notation, we use the scientific manipulator To change it back to fixed decimal, we use the fixed manipulator:

"scientific: " scientific 100 "fixed decimal: " fixed 100 '\n';

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