MRF理论部分

理论部分可参考下面博客，我在这就不多赘述

https://blog.csdn.net/dlaicxf/article/details/52625932?ops_request_misc=%257B%2522request%255Fid%2522%253A%2522158748842719724845049845%2522%252C%2522scm%2522%253A%252220140713.130102334.pc%255Fall.%2522%257D&request_id=158748842719724845049845&biz_id=0&utm_source=distribute.pc_search_result.none-task-blog-2_allfirst_rank_v2~rank_v25-1

MRF实现

import matplotlib.pyplot as plt
import cv2
import numpy as np
from sklearn.cluster import k_means_path = r"D:\360MoveData\Users\hp\Desktop\ForStudents2020\实验用图\1 kmeans\test.bmp"
img = np.array(plt.imread(path))
imgGray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
imgGray = imgGray / 255
imgCopy = imgGray.copy()
imgpixel = (imgCopy.flatten()).reshape((imgGray.shape[0]*imgGray.shape[1], 1))
kind = 2
kmeans = k_means_.KMeans(n_clusters=kind)
label = kmeans.fit(imgpixel)
imgLabel = np.array(label.labels_).reshape(imgGray.shape)
plt.figure()
plt.imshow(imgLabel, cmap="gray")
imgMrf = np.zeros_like(imgLabel)
cycle = 10
c = 0
sumList = [0] * kind
numList = [0] * kind
MeanList = [0] * kind
stdSumList = [0] * kind
stdList = [0] * kind
for i in range(1, imgLabel.shape[0] - 1):for j in range(1, imgLabel.shape[1] - 1):x = imgLabel[i, j]sumList[x] += imgGray[i, j]numList[x] += 1
for k in range(kind):MeanList[k] = sumList[k] / numList[k]for i in range(1, imgLabel.shape[0] - 1):for j in range(1, imgLabel.shape[1] - 1):x = imgLabel[i, j]stdSumList[x] += (imgGray[i, j] - MeanList[x]) ** 2
for i in range(kind):stdList[i] = np.sqrt(stdSumList[i] / numList[i])
def gas(mean, std, x):return 1 / (np.sqrt(2 * np.pi) * std) * np.exp(-0.5 * (x - mean)**2 / std**2)while c < cycle:for i in range(1, imgLabel.shape[0] - 1):for j in range(1, imgLabel.shape[1] - 1):uList = [0] * kindfor k in range(kind):template = np.ones((3, 3)) * ktemplate[1, 1] = np.infu = np.exp(- np.sum(template == imgLabel[i - 1: i + 2, j - 1: j + 2]) + 8) *\gas(MeanList[k], stdList[k], imgGray[i, j])uList[k] = usumList[k] += imgGray[i, j]numList[k] += 1imgMrf[i, j] = uList.index(max(uList))for i in range(kind):MeanList[i] = sumList[i] / numList[i]for i in range(1, imgLabel.shape[0] - 1):for j in range(1, imgLabel.shape[1] - 1):x = imgLabel[i, j]stdSumList[x] += (imgGray[i, j] - MeanList[x]) ** 2for i in range(kind):stdList[i] = np.sqrt(stdSumList[i] / numList[i])imgLabel = imgMrf.copy()c += 1print("第{}代结束".format(c))
plt.figure()
plt.imshow(imgLabel, cmap="gray")
plt.figure()
plt.imshow(1-imgLabel, cmap="gray")
plt.show()

上述的思路为：先用kmean进行初始化得到每个像素属于哪一类，<>在假设每类的像素值属于高斯分布的情况下，估计出高斯分布的均值与方差，然后利用马尔科夫随机场中能量函数和朴素贝叶斯的概念，最大化后验概率的方法得到每一个像素值新的一轮的分类，然后在重新回到<>进行循环，知道迭代次数达到。

分割结果展示

以下分别是原图、2聚类、2分割的图像。

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