第10章 Python 数字图像处理(DIP) - 图像分割基础知识标准差分割法

This Chapter is all about image segmentation.
I still not finished whole chapter, but here try to publish some for reference.

这里写目录标题

- 基础知识

import sys
import numpy as np
import cv2
import matplotlib 
import matplotlib.pyplot as plt
import PIL
from PIL import Imageprint(f"Python version: {sys.version}")
print(f"Numpy version: {np.__version__}")
print(f"Opencv version: {cv2.__version__}")
print(f"Matplotlib version: {matplotlib.__version__}")
print(f"Pillow version: {PIL.__version__}")

def normalize(x, ymin=0, ymax=1):"""Description:- Map x into desired range[ymin, ymax], according to the math function $$y = \frac{(y_{\text{max}} - y_{\text{min}}) (x - x_{\text{min}})}{(x_{\text{max}} - x_{\text{min}})} + y_{\text{min}}$$Parameters:- x:    input array- ymin: desired min value, such as -1, or whatever you want- ymax: desired max value, such as 1, or other you need"""result = (ymax - ymin) * (x - x.min()) / (x.max()-x.min()) + ymin#################### old one ####################### result = (x - x.min()) / (x.max() - x.min())return result

基础知识

令 $R$ 表示一幅图像占据的整个空间区域。我们可以将图像分割视为把 $R$ 分为 $n$ 个子区域 $R1，R2，⋯，RnR_1，R_2，\cdots，R_n$ 的过程，满足：

(a) $⋃i=1nRi=R\bigcup_{i=1}^{n} R_{i} = R$ 。
(b) $Ri,i=0,1,2,⋯,nR_{i}, i=0, 1, 2, \cdots, n$ 是一个连通集。
(c) 对所有 $i$ 和 $j$ ， $i≠j,Ri⋂Rj=∅i\neq j, R_{i}\bigcap R_{j} = \emptyset$ 。
(d) $Q(Ri)=TRUE,i=0,1,2,⋯,nQ(R_{i})=TRUE, i=0, 1, 2, \cdots, n$ 。
(e) 对于任何邻接区域 $R_{i}$ 和 $R_{j}$ ， $Q(Ri⋃Rj)=FALSEQ(R_{i} \bigcup R_{j}) = FALSE$ 。

其中 $Q(R_{i})$ 是定义在集合 $R_{k}$ 中的点上的一个谓词逻辑。

def std_seg(image, thred=0, stride=4):"""Description:Segment image caculating standard deviationParemeters:image: input grayscale imagethred: thredshold of the standard diviationstride: control the neighborhoodReturn:Binary segment image"""h, w = image.shape[:2]result = image.copy()# here we use stride the create non-overlap region, if we not need stride here, we still can get very good result# or we set stride smaller than 8, then we can get better resultfor i in range(0, h, stride):for j in range(0, w, stride):temp = image[i:i+stride, j:j+stride]if np.std(temp) <= thred:result[i:i+stride, j:j+stride] = 0else:result[i:i+stride, j:j+stride] = 255return result

# standard deviation segment, according the result below, it seems the img_f is not 8x8 region, is about 4-5
img_d = cv2.imread("DIP_Figures/DIP3E_Original_Images_CH10/Fig1001(d)(noisy_region).tif", -1)
img_seg = std_seg(img_d, thred=0, stride=5)fig = plt.figure(figsize=(10, 5))
plt.subplot(1, 2, 1), plt.imshow(img_d, 'gray'), plt.xticks([]), plt.yticks([])
plt.subplot(1, 2, 2), plt.imshow(img_seg, 'gray'), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()