马尔可夫随机场的python实现
前几天看图网络的时候，不知怎么从贝叶斯网络突然跳到了马尔科夫随机场，感觉还有点意思，不过还是没有完全理清其中的逻辑，网上讲的比较乱,参考博主on2way这篇博文《从贝叶斯理论到图像马尔科夫随机场》我梳理了一下思路，找时间总结一下，先挖一个坑吧，由于博主给出的是matlab实现，我本身不怎么使用matlab，于是就简单的用python复现了一下思路，由于没有使用kmeans算法初始化，结果差距比较明显，但是还算不错，其中应该是有一些问题，包括最后多分类的接口没有调好，还有四分类显示结果貌似不太对，由于后天要考英语今天看来是没法调完了，依旧是放着这个坑，有时间的时候代码改一下，以下是python3的代码，直接用jupyter notebook写的：
import numpy as np
import cv2
import copy
from scipy.stats import norm
import matplotlib as plot
img = cv2.imread('Lena.jpeg',0)
cluster_num = 4
maxiter = 50
#随机初始化标签
label = np.random.randint(0,cluster_num,img.shape)
def cal_pp(label):
result = np.zeros((cluster_num, 8, label.shape[0], label.shape[1]))
statis_result = np.zeros((cluster_num, label.shape[0], label.shape[1]))
for i in range(cluster_num):
label_temp = copy.deepcopy(label)
#先设置为4再设置为0，防止处理0时出错
label_temp[label_temp!=i] = 4
label_temp[label_temp==i] = 1
label_temp[label_temp==4] = 0
#根据label_temp可以计算出8个方向的标签
#从左上角起顺时针方向，依次为0-8
result[i][0][:,0] = 0
result[i][0][0,:] = 0
result[i][0][1:,1:] = label_temp[:-1,:-1]
result[i][1][:,0] = 0
result[i][1][1:,:] = label_temp[:-1,:]
result[i][2][:,0] = 0
result[i][2][0,:] = 0
result[i][2][1:,1:] = label_temp[1:,:-1]
result[i][3][:,0] = 0
result[i][3][:,1:] = label_temp[:,:-1]
result[i][4][:,-1] = 0
result[i][4][:,:-1] = label_temp[:,1:]
result[i][5][:,0] = 0
result[i][5][-1,:] = 0
result[i][5][1:,:-1] = label_temp[1:,:-1]
result[i][6][-1,:] = 0
result[i][6][:-1,:] = label_temp[1:,:]
result[i][7][:,-1] = 0
result[i][7][-1,:] = 0
result[i][7][:-1,:-1] = label_temp[1:,1:]
statis_result[i] = result[i][0]+result[i][1]+result[i][2]+result[i][3]+result[i][4]+result[i][5]+result[i][6]+result[i][7]
statis_result = np.array(statis_result,dtype=np.float) / 8
#防止出现0，原因不清楚
statis_result[statis_result==0] = 0.001
return statis_result
def cal_lf(img, label):
result = np.zeros((cluster_num, 8, label.shape[0], label.shape[1]))
distribution_parameter = np.zeros((cluster_num,2),np.float)
for i in range(cluster_num):
img_temp = copy.deepcopy(img)
img_temp[label!=i] = 0
#根据原图灰度统计每一个标签的分布和方差
img_list = img_temp.tolist()
img_list = [item for sublist in img_list for item in sublist if item!= 0]
#再根据原图的灰度数值算出似然函数值
distribution_parameter[i][0] = np.mean(img_list)
distribution_parameter[i][1] = np.std(img_list)
#计算每一点属于不同类型的概率
result_lf = np.zeros((cluster_num,label.shape[0],label.shape[1]),np.float)
for i in range(cluster_num):
result_lf[i] = norm(distribution_parameter[i][0],distribution_parameter[i][1]).pdf(img)
return result_lf
def update_label(img, init_label, maxiter):
label = init_label
for i in range(maxiter):
prior_probability = cal_pp(label)
likelihood = cal_lf(img,label)
probability = np.zeros((cluster_num,label.shape[0],label.shape[1]))
for j in range(cluster_num):
probability[j] = prior_probability[j]*likelihood[j]
#根据概率值更新label
max_probability = probability.max(0)
#label_one不需要，这一部分代码需要做一下调整，时间紧迫先演示一下
label_two = probability[1]-max_probability
label_two[label_two!=0] = 4
label_two[label_two==0] = 1
label_two[label_two==4] = 0
label_three = probability[2]-max_probability
label_three[label_three!=0] = 4
label_three[label_three==0] = 2
label_three[label_three==4] = 0
label_four = probability[3]-max_probability
label_four[label_four!=0] = 4
label_four[label_four==0] = 3
label_four[label_four==4] = 0
label= label_two + label_three + label_four
#每次绘制一张图片
cv2.imshow("test",label)
cv2.waitKey(500)
cv2.destroyAllWindows()
return label
#main函数中运行，博主使用jupyter notebook就没有改了，请需要的自行改一下
final = update_label(img,label,maxiter)原图放这里供大家下载使用：
贴一下大致效果：
其中前两排是第1-8次迭代结果，最后一排是第12、16、20、24次迭代结果，效果还行