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第544行：
第544行： − < math > eta _ (i，j)} = tfrac {1}{ z } * Vc _ (i，j)} </math > 第557行：
第556行： − + − [ math ] z = sum { i = 1: m _ 1} sum { j = 1: m _ 2} Vc (i _ { i，j }) </math > ，是一个归一化因子 第565行：
第563行： − − < math > begin { align } Vc (i _ { i，j }) = & f left (left vert i _ {(i-2，j-1)}-i _ {(i + 2，j + 1)}右垂直 + 左垂直 i _ {(i-2，j + 1)}-i _ (i + 2，j-1)}右垂直。\\ − − & +\left\vert I_{(i-1,j-2)} - I_{(i+1,j+2)} \right\vert + \left\vert I_{(i-1,j-1)} - I_{(i+1,j+1)} \right\vert\\ − − − − & +\left\vert I_{(i-1,j)} - I_{(i+1,j)} \right\vert + \left\vert I_{(i-1,j+1)} - I_{(i-1,j-1)} \right\vert\\ 第583行：
第573行： − − 左边。(i-1，j + 2)}-i _ {(i-1，j-2)}右 vert + 左 vert i _ {(i，j-1)}-i _ {(i，j + 1)}右 vert 右 vert { align } </math > 第603行：
第591行： − − Sin (frac { pi x }{2 lambda }) ，& text { for 0≤ x ≤} lambda text { ; (3)} − − − 0，& text { else } − − 结束{ cases } </math > < br/> < math > f (x) = − − 开始{ cases } 第628行：
第607行： − \pi x \sin(\frac{\pi x}{2 \lambda}), & \text{for 0 ≤ x ≤} \lambda \text{; (4)} \\ − − 0，& text { else } 第644行：
第620行： − − − (1-psi) tau _ { old } + psi tau _ {0} 第699行：
第672行： − −
→Image processing
<math>\eta_{(i,j)}= \tfrac{1}{Z}*Vc*I_{(i,j)}</math>
<math>\eta_{(i,j)}= \tfrac{1}{Z}*Vc*I_{(i,j)}</math>
The following are the steps involved in edge detection using ACO:<ref>{{cite book|last1=Tian|first1=Jing|title=2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)|pages=751–756|last2=Yu|first2=Weiyu|last3=Xie|first3=Shengli|doi=10.1109/CEC.2008.4630880|year=2008|isbn=978-1-4244-1822-0|s2cid=1782195}}</ref><ref>{{cite web|last1=Gupta|first1=Charu|last2=Gupta|first2=Sunanda|title=Edge Detection of an Image based on Ant ColonyOptimization Technique|url=https://www.academia.edu/4688002}}</ref><ref>{{Cite book|title = Edge detection using ant colony search algorithm and multiscale contrast enhancement|journal = IEEE International Conference on Systems, Man and Cybernetics, 2009. SMC 2009|pages = 2193–2198|doi = 10.1109/ICSMC.2009.5345922|first1 = A.|last1 = Jevtić|first2 = J.|last2 = Quintanilla-Dominguez|first3 = M.G.|last3 = Cortina-Januchs|first4 = D.|last4 = Andina|year = 2009|isbn = 978-1-4244-2793-2|s2cid = 11654036}}</ref>
The following are the steps involved in edge detection using ACO:<ref>{{cite book|last1=Tian|first1=Jing|title=2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)|pages=751–756|last2=Yu|first2=Weiyu|last3=Xie|first3=Shengli|doi=10.1109/CEC.2008.4630880|year=2008|isbn=978-1-4244-1822-0|s2cid=1782195}}</ref><ref>{{cite web|last1=Gupta|first1=Charu|last2=Gupta|first2=Sunanda|title=Edge Detection of an Image based on Ant ColonyOptimization Technique|url=https://www.academia.edu/4688002}}</ref><ref>{{Cite book|title = Edge detection using ant colony search algorithm and multiscale contrast enhancement|journal = IEEE International Conference on Systems, Man and Cybernetics, 2009. SMC 2009|pages = 2193–2198|doi = 10.1109/ICSMC.2009.5345922|first1 = A.|last1 = Jevtić|first2 = J.|last2 = Quintanilla-Dominguez|first3 = M.G.|last3 = Cortina-Januchs|first4 = D.|last4 = Andina|year = 2009|isbn = 978-1-4244-2793-2|s2cid = 11654036}}</ref>
<math>Z =\sum_{i=1:M_1} \sum_{j=1:M_2} Vc(I_{i,j})</math>, which is a normalization factor
<math>Z =\sum_{i=1:M_1} \sum_{j=1:M_2} Vc(I_{i,j})</math>, which is a normalization factor
是一个归一化因子
<math>\begin{align}Vc(I_{i,j}) = &f \left( \left\vert I_{(i-2,j-1)} - I_{(i+2,j+1)} \right\vert + \left\vert I_{(i-2,j+1)} - I_{(i+2,j-1)} \right\vert \right. \\
<math>\begin{align}Vc(I_{i,j}) = &f \left( \left\vert I_{(i-2,j-1)} - I_{(i+2,j+1)} \right\vert + \left\vert I_{(i-2,j+1)} - I_{(i+2,j-1)} \right\vert \right. \\
the local statistics at the pixel position (i,j).
the local statistics at the pixel position (i,j).
& +\left\vert I_{(i-1,j-2)} - I_{(i+1,j+2)} \right\vert + \left\vert I_{(i-1,j-1)} - I_{(i+1,j+1)} \right\vert\\
& +\left\vert I_{(i-1,j-2)} - I_{(i+1,j+2)} \right\vert + \left\vert I_{(i-1,j-1)} - I_{(i+1,j+1)} \right\vert\\
& +\left\vert I_{(i-1,j)} - I_{(i+1,j)} \right\vert + \left\vert I_{(i-1,j+1)} - I_{(i-1,j-1)} \right\vert\\
& +\left\vert I_{(i-1,j)} - I_{(i+1,j)} \right\vert + \left\vert I_{(i-1,j+1)} - I_{(i-1,j-1)} \right\vert\\
& + \left. \left\vert I_{(i-1,j+2)} - I_{(i-1,j-2)} \right\vert + \left\vert I_{(i,j-1)} - I_{(i,j+1)} \right\vert \right) \end{align}</math>
& + \left. \left\vert I_{(i-1,j+2)} - I_{(i-1,j-2)} \right\vert + \left\vert I_{(i,j-1)} - I_{(i,j+1)} \right\vert \right) \end{align}</math>
\sin(\frac{\pi x}{2 \lambda}), & \text{for 0 ≤ x ≤} \lambda \text{; (3)} \\
\sin(\frac{\pi x}{2 \lambda}), & \text{for 0 ≤ x ≤} \lambda \text{; (3)} \\
<math>\begin{align}Vc(I_{i,j}) = &f \left( \left\vert I_{(i-2,j-1)} - I_{(i+2,j+1)} \right\vert + \left\vert I_{(i-2,j+1)} - I_{(i+2,j-1)} \right\vert \right. \\
<math>\begin{align}Vc(I_{i,j}) = &f \left( \left\vert I_{(i-2,j-1)} - I_{(i+2,j+1)} \right\vert + \left\vert I_{(i-2,j+1)} - I_{(i+2,j-1)} \right\vert \right. \\
0, & \text{else}
0, & \text{else}
& +\left\vert I_{(i-1,j-2)} - I_{(i+1,j+2)} \right\vert + \left\vert I_{(i-1,j-1)} - I_{(i+1,j+1)} \right\vert\\
& +\left\vert I_{(i-1,j-2)} - I_{(i+1,j+2)} \right\vert + \left\vert I_{(i-1,j-1)} - I_{(i+1,j+1)} \right\vert\\
\end{cases}</math><br /><math>f(x) =
\end{cases}</math><br /><math>f(x) =
& +\left\vert I_{(i-1,j)} - I_{(i+1,j)} \right\vert + \left\vert I_{(i-1,j+1)} - I_{(i-1,j-1)} \right\vert\\
& +\left\vert I_{(i-1,j)} - I_{(i+1,j)} \right\vert + \left\vert I_{(i-1,j+1)} - I_{(i-1,j-1)} \right\vert\\
\begin{cases}
\begin{cases}
& + \left. \left\vert I_{(i-1,j+2)} - I_{(i-1,j-2)} \right\vert + \left\vert I_{(i,j-1)} - I_{(i,j+1)} \right\vert \right) \end{align}</math>
& + \left. \left\vert I_{(i-1,j+2)} - I_{(i-1,j-2)} \right\vert + \left\vert I_{(i,j-1)} - I_{(i,j+1)} \right\vert \right) \end{align}</math>
\pi x \sin(\frac{\pi x}{2 \lambda}), & \text{for 0 ≤ x ≤} \lambda \text{; (4)} \\
\pi x \sin(\frac{\pi x}{2 \lambda}), & \text{for 0 ≤ x ≤} \lambda \text{; (4)} \\
0, & \text{else}
0, & \text{else}
<math>f(\cdot)</math> can be calculated using the following functions:<br /><math>f(x) = \lambda x, \quad \text{for x ≥ 0; (1)} </math><br /><math>f(x) = \lambda x^2, \quad \text{for x ≥ 0; (2)} </math><br /><math>f(x) =
<math>f(\cdot)</math> can be calculated using the following functions:<br /><math>f(x) = \lambda x, \quad \text{for x ≥ 0; (1)} </math><br /><math>f(x) = \lambda x^2, \quad \text{for x ≥ 0; (2)} </math><br /><math>f(x) =
\tau_{new} \leftarrow
\tau_{new} \leftarrow
\sin(\frac{\pi x}{2 \lambda}), & \text{for 0 ≤ x ≤} \lambda \text{; (3)} \\
\sin(\frac{\pi x}{2 \lambda}), & \text{for 0 ≤ x ≤} \lambda \text{; (3)} \\
(1-\psi)\tau_{old} + \psi \tau_{0}
(1-\psi)\tau_{old} + \psi \tau_{0}
0, & \text{else}
0, & \text{else}
* '''Edge linking:'''<ref>{{cite book|last1 = Jevtić|first1 = A.|title = 2009 35th Annual Conference of IEEE Industrial Electronics|last2 = Melgar|first2 = I.|last3 = Andina|first3 = D.|pages = 3353–3358|year = 2009|location = 35th Annual Conference of IEEE Industrial Electronics, 2009. IECON '09.|doi = 10.1109/IECON.2009.5415195|isbn = 978-1-4244-4648-3|s2cid = 34664559}}</ref> ACO has also been proven effective in edge linking algorithms too.
* '''Edge linking:'''<ref>{{cite book|last1 = Jevtić|first1 = A.|title = 2009 35th Annual Conference of IEEE Industrial Electronics|last2 = Melgar|first2 = I.|last3 = Andina|first3 = D.|pages = 3353–3358|year = 2009|location = 35th Annual Conference of IEEE Industrial Electronics, 2009. IECON '09.|doi = 10.1109/IECON.2009.5415195|isbn = 978-1-4244-4648-3|s2cid = 34664559}}</ref> ACO has also been proven effective in edge linking algorithms too.
=== Other applications ===
=== Other applications ===