Digital-Image-Processing

1

Image Restoration
Image Enhancement
Image ReconstructionCT
Image Coding
Image Segmentation

2

** P (0, 0) $N_{4}(P)$$N_{D}(P)$ $N_{8}(P)$ **

$N_{4}(P)$ (0,1)(1,0)(0,-1)(-1,0)

$N_{D}(P)$ (1,1)(-1,1)(1,-1)(-1,-1)

$N_{8}(P)$ (0,1)(1,0)(0,-1)(-1,0)(1,1)(-1,1)(1,-1)(-1,-1)

3

45 $$ \left{\begin{matrix} x = 0.707x_{0} + 0.707y_{0} \ y = -0.707x_{0} + 0.707y_{0} \end{matrix}\right. $$ 1110

4

$$ \begin{bmatrix} 2 & 1 & 1 & 1\ 0 & 2 & 1 & 1\ 0 & 0 & 2 & 1\ 0 & 0 & 0 & 2 \end{bmatrix} $$

$$ F = C * f * C' $$

$$
C = \sqrt{\frac{2}{N}}
\begin{bmatrix}
\sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} & ... & \sqrt{\frac{1}{2}}\
\cos{\frac{1}{2N}\pi} & \cos{\frac{3}{2N}\pi} & ... & \cos{\frac{2N - 1}{2N}\pi}\
. & . & . & .\
. & . & . & .\
. & . & . & .\
\cos{\frac{N - 1}{2N}\pi} & \cos{\frac{3(N - 1)}{2N}\pi} & ... & \cos{\frac{(2N - 1)(N - 1)}{2N}\pi}
\end{bmatrix}
$$
N = 4
$$
C = \sqrt{\frac{2}{4}}
\begin{bmatrix}
\sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}}\
\cos{\frac{1}{8}\pi} & \cos{\frac{3}{8}\pi} & \cos{\frac{5}{8}\pi} & \cos{\frac{7}{8}\pi}\
\cos{\frac{2}{8}\pi} & \cos{\frac{6}{8}\pi} & \cos{\frac{10}{8}\pi} & \cos{\frac{14}{8}\pi}\
\cos{\frac{3}{8}\pi} & \cos{\frac{9}{8}\pi} & \cos{\frac{15}{8}\pi} & \cos{\frac{21}{8}\pi}
\end{bmatrix}

\begin{bmatrix} 0.500 & 0.500 & 0.500 & 0.500 \ 0.653 & 0.271 & -0.271 & -0.653 \ 0.500 & -0.500 & -0.500 & 0.500 \ 0.271 & -0.653 & 0.653 & -0.271 \end{bmatrix} $$

$$ \begin{eqnarray*} (F(u,v)) &=& (C)(f(x,y))(C)' \ &=& \begin{bmatrix} 0.500 & 0.500 & 0.500 & 0.500 \ 0.653 & 0.271 & -0.271 & -0.653 \ 0.500 & -0.500 & -0.500 & 0.500 \ 0.271 & -0.653 & 0.653 & -0.271 \end{bmatrix} \begin{bmatrix} 2 & 1 & 1 & 1\ 0 & 2 & 1 & 1\ 0 & 0 & 2 & 1\ 0 & 0 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0.500 & 0.653 & 0.500 & 0.271 \ 0.500 & 0.271 & -0.500 & -0.653 \ 0.500 & -0.271 & -0.500 & 0.653 \ 0.500 & -0.653 & 0.500 & -0.271 \end{bmatrix} \ &=& \begin{bmatrix} 3.500 & -1.115 & 0 & -0.080 \ 1.115 & 1.500 & -0.462 & 0 \ 0 & 0.462 & 1.500 & -0.191 \ 0.080 & 0 & 0.191 & 1.500 \end{bmatrix} \ \end{eqnarray*} $$