User:Kevin baas~enwiki/scratch

pg. 5
$$\mu_{p,q} = \sum_{x,y} (x - \bar{x})^p (y - \bar{y})^q a(x, y)$$

pg. 6
$$a(x, y) = \begin{cases} 1, & \mbox{if BinaryPixel}(x, y) = 1 \\ 0, & \mbox{if BinaryPixel}(x, y) = 0 \end{cases} $$

$$ \eta_{p,q} = \frac{\mu_{p,q}}{\mu^\gamma_{0,0}} $$

$$ \gamma = \frac{p + q}{2} + 1 $$

$$\Phi_1 = \eta_{2,0} + \eta_{0,2} $$

$$\Phi_2 = (\eta_{2,0} - \eta_{0,2})^2 + 4\eta^2_{1,1} $$

$$\Phi_3 = (\eta_{3,0} - 3\eta_{1,2})^2 + (3\eta_{2,1} - \eta_{0,3})^2 $$

$$\Phi_4 = (\eta_{3,0} + \eta_{1,2})^2 + (\eta_{2,1} - \eta_{0,3})^2 $$

pg. 7
$$ \mbox{AL} = \frac{\mbox{area}}{\mbox{diameter}} $$

$$ \mbox{CMP} = \frac{4\pi \times \mbox{area}} {\mbox{perimeter}^2} $$

pg. 8
$$\mbox{CD} = \frac{\mbox{convex area} - \mbox{area}}{\mbox{convex area}}$$

$$\mbox{MAAarea} = \frac{\mbox{diameter}^2}{\mbox{area}}$$

$$\mbox{ECC} = \frac{\mbox{diameter}}{\mbox{width}}$$

pg. 10
$$ P_c = \sum_i n_i t_i $$

$$ P_c = \frac{1}{9}(12) + \frac{1}{9}(56) + \frac{1}{9}(9) + \frac{1}{9}(67) + \frac{1}{9}(13) + \frac{1}{9}(1) + \frac{1}{9}(100) + \frac{1}{9}(33) + \frac{1}{9}(65) =  39.55 $$

pg. 12
$$ G = \frac{R + G + B}{3} $$

pg. 16
$$ P_c = \sum_i n_i t_i $$

$$ P_c = 1(1) + 0(2) + 1(4) + 1(8) + 0(16) + 0(32) + 1(64) + 1(128) = 205 $$

pg. 18
$$\mbox{area} = \frac{1}{2}\sum_{i} { x_i y_{i+1} - x_{i+1} y_i }$$

pg. 19
$$ \begin{matrix} C_x = \frac{\sum_i x_i}{|P|} \\ C_y = \frac{\sum_i y_i}{|P|} \end{matrix} $$

pg. 21
$$c = (x_1 - x_0 )(y_2 - y_0 ) - (x_2 - x_0 )(y_1 - y_0 )$$

pg. 26
$$a'\left( i \right) = a\left( i \right)\frac{\bar{a}}{\sigma_a} $$

pg. 27
$$C(X,Y) = \frac{ \sum_{i} { \left( x_i - \bar{x} \right) \left( y_i - \bar{y} \right) } } { \sqrt{ \sum_{i} { \left( x_i - \bar{x} \right) {}^2 \left( y_i - \bar{y} \right) {}^2 } } }$$

$$ D(a_t, a_s) = |a_t - a_s| $$

pg. 29
$$d_{e}(i, j) = \sqrt{ \sum_{k} { \left( x_{k} \left( i \right) - x_{k} \left( j \right) \right) {}^2 } }$$

pg. 30
$$d_{c}(i, j) = \sum_{k} { \left| x_{k} (i) - x_{k} \left( j \right) \right|}$$

pg. 32
$$d_{c}(i, j) = \sum_{k} { w_{k} \left| x_{k} (i) - x_{k} \left( j \right) \right|}$$

$$d_{e}(i, j) = \sqrt{ \sum_{k} { w_{k} \left( x_{k} \left( i \right) - x_{k} \left( j \right) \right) {}^2 } }$$