μ p , q = ∑ x , y ( x − x ¯ ) p ( y − y ¯ ) q a ( x , y ) {\displaystyle \mu _{p,q}=\sum _{x,y}(x-{\bar {x}})^{p}(y-{\bar {y}})^{q}a(x,y)}
a ( x , y ) = { 1 , if BinaryPixel ( x , y ) = 1 0 , if BinaryPixel ( x , y ) = 0 {\displaystyle a(x,y)={\begin{cases}1,&{\mbox{if BinaryPixel}}(x,y)=1\\0,&{\mbox{if BinaryPixel}}(x,y)=0\end{cases}}}
η p , q = μ p , q μ 0 , 0 γ {\displaystyle \eta _{p,q}={\frac {\mu _{p,q}}{\mu _{0,0}^{\gamma }}}}
γ = p + q 2 + 1 {\displaystyle \gamma ={\frac {p+q}{2}}+1}
Φ 1 = η 2 , 0 + η 0 , 2 {\displaystyle \Phi _{1}=\eta _{2,0}+\eta _{0,2}}
Φ 2 = ( η 2 , 0 − η 0 , 2 ) 2 + 4 η 1 , 1 2 {\displaystyle \Phi _{2}=(\eta _{2,0}-\eta _{0,2})^{2}+4\eta _{1,1}^{2}}
Φ 3 = ( η 3 , 0 − 3 η 1 , 2 ) 2 + ( 3 η 2 , 1 − η 0 , 3 ) 2 {\displaystyle \Phi _{3}=(\eta _{3,0}-3\eta _{1,2})^{2}+(3\eta _{2,1}-\eta _{0,3})^{2}}
Φ 4 = ( η 3 , 0 + η 1 , 2 ) 2 + ( η 2 , 1 − η 0 , 3 ) 2 {\displaystyle \Phi _{4}=(\eta _{3,0}+\eta _{1,2})^{2}+(\eta _{2,1}-\eta _{0,3})^{2}}
AL = area diameter {\displaystyle {\mbox{AL}}={\frac {\mbox{area}}{\mbox{diameter}}}}
CMP = 4 π × area perimeter 2 {\displaystyle {\mbox{CMP}}={\frac {4\pi \times {\mbox{area}}}{{\mbox{perimeter}}^{2}}}}
CD = convex area − area convex area {\displaystyle {\mbox{CD}}={\frac {{\mbox{convex area}}-{\mbox{area}}}{\mbox{convex area}}}}
MAAarea = diameter 2 area {\displaystyle {\mbox{MAAarea}}={\frac {{\mbox{diameter}}^{2}}{\mbox{area}}}}
ECC = diameter width {\displaystyle {\mbox{ECC}}={\frac {\mbox{diameter}}{\mbox{width}}}}
P c = ∑ i n i t i {\displaystyle P_{c}=\sum _{i}n_{i}t_{i}}
P c = 1 9 ( 12 ) + 1 9 ( 56 ) + 1 9 ( 9 ) + 1 9 ( 67 ) + 1 9 ( 13 ) + 1 9 ( 1 ) + 1 9 ( 100 ) + 1 9 ( 33 ) + 1 9 ( 65 ) = 39.55 {\displaystyle 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}
G = R + G + B 3 {\displaystyle G={\frac {R+G+B}{3}}}
P c = 1 ( 1 ) + 0 ( 2 ) + 1 ( 4 ) + 1 ( 8 ) + 0 ( 16 ) + 0 ( 32 ) + 1 ( 64 ) + 1 ( 128 ) = 205 {\displaystyle P_{c}=1(1)+0(2)+1(4)+1(8)+0(16)+0(32)+1(64)+1(128)=205}
area = 1 2 ∑ i x i y i + 1 − x i + 1 y i {\displaystyle {\mbox{area}}={\frac {1}{2}}\sum _{i}{x_{i}y_{i+1}-x_{i+1}y_{i}}}
C x = ∑ i x i | P | C y = ∑ i y i | P | {\displaystyle {\begin{matrix}C_{x}={\frac {\sum _{i}x_{i}}{|P|}}\\C_{y}={\frac {\sum _{i}y_{i}}{|P|}}\end{matrix}}}
c = ( x 1 − x 0 ) ( y 2 − y 0 ) − ( x 2 − x 0 ) ( y 1 − y 0 ) {\displaystyle c=(x_{1}-x_{0})(y_{2}-y_{0})-(x_{2}-x_{0})(y_{1}-y_{0})}
a ′ ( i ) = a ( i ) a ¯ σ a {\displaystyle a'\left(i\right)=a\left(i\right){\frac {\bar {a}}{\sigma _{a}}}}
C ( X , Y ) = ∑ i ( x i − x ¯ ) ( y i − y ¯ ) ∑ i ( x i − x ¯ ) 2 ( y i − y ¯ ) 2 {\displaystyle 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 | {\displaystyle D(a_{t},a_{s})=|a_{t}-a_{s}|}
d e ( i , j ) = ∑ k ( x k ( i ) − x k ( j ) ) 2 {\displaystyle d_{e}(i,j)={\sqrt {\sum _{k}{\left(x_{k}\left(i\right)-x_{k}\left(j\right)\right){}^{2}}}}}
d c ( i , j ) = ∑ k | x k ( i ) − x k ( j ) | {\displaystyle d_{c}(i,j)=\sum _{k}{\left|x_{k}(i)-x_{k}\left(j\right)\right|}}
d c ( i , j ) = ∑ k w k | x k ( i ) − x k ( j ) | {\displaystyle d_{c}(i,j)=\sum _{k}{w_{k}\left|x_{k}(i)-x_{k}\left(j\right)\right|}}
d e ( i , j ) = ∑ k w k ( x k ( i ) − x k ( j ) ) 2 {\displaystyle d_{e}(i,j)={\sqrt {\sum _{k}{w_{k}\left(x_{k}\left(i\right)-x_{k}\left(j\right)\right){}^{2}}}}}
