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second term is defined as a topological constraint or an angle relation between two junctions. For example, the following descriptions can represent the binary relations. 1. Two lines 1 and 4 should be approximately parallel (parallelism). 2. Scene lines corresponding to two lines 2 and 3 must be a collinear pair [6] or the same line. That is, two junctions are combined by the collinear constraint. 3. Line ordering for two junctions J1 , J2 should be maintained, for example as clockwise or counterclockwise, as the order of line 1, line 2, line 3 and line 4. The relation defined by the connected two junctions includes all three perceptual organization groups that Lowe used in SCERPO. These local relations can be selectively imposed according to the type of the given problem. For example, a convex line triplet [15] is simply defined, by removing the above constraint 1 and letting line 2 and line 3 of constraint 2 be equal to each other. The weighting coefficients and of the energy potential are experimentally given, by considering the variance factor of the line perturbation for image noise.

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var foo:Array = null; foo.length;

+ 2p,. ..

produces the result shown in Figure 5-2. Again, this output shows the call stack that was executing at the time of the error. Code that executes from the timeline will show the frame number as a function in the call stack.

FIGURE 5-2

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is also divisible by p , so we can save the work of testing whether each of these Q values is divisible by p . By repeating this for other choices of .T and other primes in the factor base, we can eventually sieve out the B-smooth integers in the interval [-A[, A l l . This process is somewhat analogous t o the sieve of Eratosthenes, as discussed above. This sieving process is where the sieve in quadratic sieve comes from. Sieving in the most costly part of the QS algorithm, and several tricks are used to speed up the process. For example, suppose y = Q(z) is divisible by p . Then y = 0 (mod p ) and from the definition of Q, we have

One major advantage of using Flash Builder is its ability to notify you of problems in your code as they are written. Whenever you build your source code, markers appear next to line numbers that contain compile-time errors. Hovering over these markers or opening the Problems view shows you more detailed information about the problem, as shown in Figure 5-3. You can click on the red reference markers next to the scroll bar on the right of your code or double-click on an item in the Problems view to jump to the line of code with the error. Warnings are reported in a similar way, but they use a yellow icon instead of red.

Dynamic Programming (DP) is an optimization technique good for problems where not all variables are interrelated simultaneously [8,16]. Suppose that the global energy can be decomposed into the following form: E f1 fM = E1 f1 f2 + E2 f2 f3 + + EM 1 fM 1 fM (18.5)

If Flash Builder is set to automatically build, you will see errors and warnings every time you save a le, as long as that le is an active application or is used by an active application. You can toggle this feature under the Project Build Automatically menu item.

= N (mod p ) .

Similar to Flash Professional s Output panel, Flash Builder also has a Console view, shown in Figure 5-4, that shows traces, logs, and errors when debugging.

(7.9)

FIGURE 5-3

FIGURE 5-4

in which M is the number of the model nodes, such as lines or junctions, and fI is a scene label that can be assigned to the model node I. Figure 18.3 shows a schematic DP diagram to find a trapezoidal model in the scene lines. Figure 18.3(a) presents a typical case in which we cannot define an ordering for the scene lines due

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