Image Processing

FIGURE 3.42The set of geometrical rays for the (3, 1)-projection.

Figure 3.42 shows the new set of geometrical rays.

The following should be mentioned. If we denote the lines l(7) and l(8) in Figure 3.41 by $\tilde{l}\left(6\right)$ and $\tilde{l}\left(7\right)$, respectively, the line-integrals along these rays will be defined as

$\begin{array}{l}w\left(6\right)=w\left(\tilde{l}\left(6\right)\right)=8\sqrt{10}/3\left[v\left(6\right)+v\left(7\right)+v\left(8\right)\right],\hfill \\ w\left(7\right)=w\left(\tilde{l}\left(7\right)\right)=8\sqrt{10}/3\left[v\left(7\right)+v\left(8\right)+v\left(9\right)\right].\hfill \end{array}$

We obtain the system of equations

$w\left(t\right)=w\left(\tilde{l}\left(t\right)\right)=8\sqrt{10}/3\left[v\left(t\right)+v\left(t+1\right)+v\left(t+2\right)\right],t=0:28,$

(3.59)

for the set of 29 geometrical rays which are defined as

$\tilde{l}\left(t\right)=l_{3,1}\left(t+1\right)=\left\{\left(x,y\right);3x+y=\frac{t}{8}+\frac{3}{8}\right\},t=0:28.$

This set of geometrical rays is shown in Figure 3.43. The system of ...