Image Processing

The coefficients of this matrix are

$A_{m,n}={\displaystyle \sum _{k=0}^n{\left(-1\right)}^{m-n}{\delta }_{m-n,t}.}$

The equation b = A⁻¹w can be written in the following recurrent form:

$\begin{array}{l}{b}_{21}=w\left(21\right),\hfill \\ b_t=w\left(t\right)-b_{t+1},t=20,19,\mathrm{..},0,\hfill \end{array}$

(3.40)

and, therefore, $v=b/\left(4\sqrt{5}\right)$, t = 0 : 21. Thus, the solution v is calculated by the method of back substitution.

3.5.4.2  (1, 2)-projection

We now consider the rays of the projection that corresponds to the generator (p, s) = (1, 2). Twenty-two arithmetical rays of this projection which are used to define all components of the 2-D paired transforms with triplet-numbers of U(1, 2) are shown in Figure 3.25. The set of 22 geometrical rays that coincide with these arithmetical rays are defined as

FIGURE 3.25Set of arithmetical rays for calculating line-sums for ...