【算法应用】基于鲸鱼优化算法求解OTSU多阈值图像分割问题
目录
- 1.鲸鱼优化算法WOA 原理
- 2.OTSU多阈值图像分割模型
- 3.结果展示
- 4.参考文献
- 5.代码获取
1.鲸鱼优化算法WOA 原理
SCI二区|鲸鱼优化算法（WOA）原理及实现
2.OTSU多阈值图像分割模型
Otsu 算法（最大类间方差法）设灰度图像有 L L L 个灰度级，各灰度级对应像素点个数为 n i n_i ni，总的像素点个数为 N N N，则灰度值为 i i i 的像素点的概率如下公式所示：
p i = n i N p_i = \frac{n_i}{N} pi=Nni
设灰度级
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K 把像素点分为前景像素点和背景像素点两类，则两类像素点灰度值概率及两类像素点的平均灰度值分别由下面式子给出：
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\omega_0 = \sum_{i=0}^{K} p_i\\ \omega_1 = \sum_{i=K+1}^{L-1} p_i = 1 - \omega_0\\ u_0 = \frac{\sum_{i=0}^{K} ip_i}{\omega_0}\\ u_1 = \frac{\sum_{i=K+1}^{L-1} ip_i}{\omega_1}
ω0=i=0∑Kpiω1=i=K+1∑L−1pi=1−ω0u0=ω0∑i=0Kipiu1=ω1∑i=K+1L−1ipi
整个图像像素点的平均灰度值为：
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u = \sum_{i=0}^{L-1} ip_i = \omega_0 u_0 + \omega_1 u_1
u=i=0∑L−1ipi=ω0u0+ω1u1
则类间方差为：
σ = ω 0 ( u 0 − u ) 2 + ω 1 ( u 1 − u ) 2 = ω 0 ω 1 ( u 1 − u 0 ) 2 \sigma = \omega_0 (u_0 - u)^2 + \omega_1 (u_1 - u)^2 = \omega_0 \omega_1 (u_1 - u_0)^2 σ=ω0(u0−u)2+ω1(u1−u)2=ω0ω1(u1−u0)2
由灰度值
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K 扩展到多阈值时，使用一组给定的阈值
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(0≤t1≤t2≤⋯≤tn)，将图像分割为
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n+1 个区域，每一区域的灰度均值和对应的概率值可表示为：
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u_0 = \frac{\sum_{i=0}^{t_1} i p_i}{\omega_0}, \quad \omega_0 = \sum_{i=0}^{t_1} p_i\\ u_1 = \frac{\sum_{i=t_1+1}^{t_2} i p_i}{\omega_1}, \quad \omega_1 = \sum_{i=t_1+1}^{t_2} p_i\\ ... \\u_n = \frac{\sum_{i=t_n+1}^{L-1} i p_i}{\omega_n}, \quad \omega_n = \sum_{i=t_n+1}^{L-1} p_i
u0=ω0∑i=0t1ipi,ω0=i=0∑t1piu1=ω1∑i=t1+1t2ipi,ω1=i=t1+1∑t2pi...un=ωn∑i=tn+1L−1ipi,ωn=i=tn+1∑L−1pi
整个图像像素点的平均灰度值为：
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u = \sum_{i=0}^{L-1} i p_i
u=i=0∑L−1ipi
此时，图像的类间方差可表示为：
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\sigma = \omega_0 (u_0 - u)^2 + \omega_1 (u_1 - u)^2 + \cdots + \omega_n (u_n - u)^2
σ=ω0(u0−u)2+ω1(u1−u)2+⋯+ωn(un−u)2
使上述最大值的一组阈值即为所求的阈值。
3.结果展示
4.参考文献
[1] Ma G, Yue X. An improved whale optimization algorithm based on multilevel threshold image segmentation using the Otsu method[J]. Engineering Applications of Artificial Intelligence, 2022, 113: 104960.