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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
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