Image Processing

Instead of parallel rays of the (6, 1)-projection, we consider the (−2,1)-projection which defines the same set of masks of the paired functions. Indeed, the equation 6n + m = t mod 8 can be written as (8 – 2)n + m = −2n + m = t mod 8. The change of the projection allows for reducing the number of rays from 50 to 22. The set of all parallel rays for this projection is shown in Figure 3.75.

The control points of this set of rays are given below

$\left[\begin{array}{rrrrrrrr}\hfill 0^{}•& \hfill {-2}^{}•& \hfill {-4}^{}•& \hfill {-6}^{}•& \hfill {-8}^{}•& \hfill {-10}^{}•& \hfill {-12}^{}•& \hfill {-14}^{}•\\ \hfill 1^{}•& \hfill {-1}^{}•& \hfill {-3}^{}•& \hfill {-5}^{}•& \hfill {-7}^{}•& \hfill {-9}^{}•& \hfill {-11}^{}•& \hfill {-13}^{}•\\ \hfill 2^{}•& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .\\ \hfill 3^{}•& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .\\ \hfill 4^{}•& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .\\ \hfill 5^{}•& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .\\ \hfill 6^{}•& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .\\ \hfill 7^{}•& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .& \hfill .\end{array}\right]\left({\text{angle\hspace{0.17em}of\hspace{0.17em}rays\hspace{0.17em}is\hspace{0.17em}tan}}^{-1}\left(2\right)=63.435°\right)$

The set of the 29 geometrical rays of this projection is described as

$l\left(t\right)=l_{-2,1}\left(t\right)=\left\{\left(x,y\right);-2x+y=\frac{t}{8}-\frac{1}{16}\right\},t=7:-1:-14,$

(3.98)

where (x, y) ∈ ...