基于图像的裂缝分割与裂缝宽度计算（正交骨架线法）

From https://subce.gitee.io/htmls/essays/crack_width_calculation.html

分割

可以使用 opencv 的阈值分割，或者使用 CNN 等深度学习的方法进行裂缝分割，一般得到的分割结果如下，这里不再赘述。

寻找边缘

寻找边缘有两种方法，如下

scikit-image skimage.measure.find_contours, 官方的示例如下：

另一种可以使用 Delaunay 三角网加上 alpha shape 进行边缘的提取，可以参考： Delaunay三角网 alpha shape 2D点集边缘线提取

中轴变换

为了计算裂缝的宽度，一般使用正交骨架线法，所以还需要计算裂缝的骨架线，这里一般使用中轴变换，同样可以使用 scikit-image 库中的算法，参见：Skeletonize — skimage v0.18.0 docs (scikit-image.org)，官方示例：

宽度计算

下面是最重要的一部分，主要包括法向量估计和宽度计算，主要参见下面的两个函数 estimate_normal_for_pos（） 和 get_crack_ctrlpts（）

法向量估计

这里主要是查找给定点的 K 近邻点，可以使用 kd-tree 算法，然后使用奇异值分解（SVD）计算骨架线的法向量。然后，裂缝的宽度计算就是在这个方向量的方向上计算的。

宽度计算

这里的主要思想是：对弈给定的一个位置，根据上方，估计此位置骨架线的方向量，并将此作为局部坐标系的y轴方向，x轴方向与此垂直，然后把裂缝的边缘线变换到这个局部坐标系中，然后在局部坐标系中，查找到骨架线法向量最近的两个裂缝边缘线点，并计算这两个点所形成的线段与骨架线法向量的交点。对于左右侧的两个裂缝边缘线，分别计算。（这一部分具体可参见代码实现，后续会补充具体的图解）

代码解释

如上图所示，两条圆点线为边缘线，叉号线为骨架线，也即中心线，中心线上任意一点的法向量可以通过对邻域点集拟合直线得到。对于Condition1，中心线上一点 c c c, 根据 c c c 点的法向量建立局部坐标系，如上所示，根据 c c c 点的局部坐标系，可将裂缝边缘线上的点分为四个象限，为了找到每一个象限内离 y y y 轴最近的点，定义参数hband（见下面代码），然后只保留点到y轴的距离小于hband的点，也就是上图中三条虚线内的点，即保留中心点 c c c 两侧一定带宽内的点，然后vband是为了规定边缘线的粗细的参数，当发现 c c c 上方或者下方（两条边缘线）任意一侧点集的 y y y 坐标的极差（np.ptp）大于vband，说明这时候检测到的边缘线存在噪点，因为噪点为导致边缘线在 y y y 方向的极差变大，如图中Condition2中所标识处的噪点，噪点在vband带宽外，需要进一步过滤，过滤的方法是对存在噪点的地方，计算 y y y 坐标的均值，然后保留 y y y 坐标大于均值的点。通过hband,vband连个参数将中心点 c c c 处的边缘线分为4块区域，即图中的 b l t , b l b , b r t , b r b blt,blb,brt,brb blt,blb,brt,brb，最后，再在4块去区域中分别计算到 y y y 轴最近的点，即可以从来计算交点啦。

注：使用hband，vband主要是将c点附近的边缘线先初步框定出来。

代码

import numpy as np
from skimage import io
from skimage.morphology import medial_axis, skeletonize
from skimage import measure
from skimage import data
import matplotlib.pyplot as plt
from sklearn.neighbors import KDTreedef show_2dpoints(pointcluster,s=None,quivers=None,qscale=1):# pointcluster should be a list of numpy ndarray# This functions would show a list of pint cloud in different colorsn = len(pointcluster)nmax = nif quivers is not None:nq = len(quivers)nmax = max(n,nq)colors = ['r','g','b','c','m','y','k','tomato','gold']if nmax < 10:colors = np.array(colors[0:nmax])else: colors = np.random.rand(nmax,3)fig = plt.figure(num=1)ax = fig.add_subplot(1,1,1)if s is None:s = np.ones(n)*2for i in range(n):ax.scatter(pointcluster[i][:,0],pointcluster[i][:,1],s=s[i],c=[colors[i]],alpha=0.6)if quivers is not None:for i in range(nq):ax.quiver(quivers[i][:,0],quivers[i][:,1],quivers[i][:,2],quivers[i][:,3],color=[colors[i]],scale=qscale)plt.show()def SVD(points):# 二维，三维均适用# 二维直线，三维平面pts = points.copy()# 奇异值分解c = np.mean(pts, axis=0)A = pts - c # shift the pointsA = A.T #3*nu, s, vh = np.linalg.svd(A, full_matrices=False, compute_uv=True) # A=u*s*vhnormal = u[:,-1]# 法向量归一化nlen = np.sqrt(np.dot(normal,normal))normal = normal / nlen# normal 是主方向的方向向量 与PCA最小特征值对应的特征向量是垂直关系# u 每一列是一个方向# s 是对应的特征值# c >>> 点的中心# normal >>> 拟合的方向向量return u,s,c,normaldef calcu_dis_from_ctrlpts(ctrlpts):if ctrlpts.shape[1]==4:return np.sqrt(np.sum((ctrlpts[:,0:2]-ctrlpts[:,2:4])**2,axis=1))else:return np.sqrt(np.sum((ctrlpts[:,[0,2]]-ctrlpts[:,[3,5]])**2,axis=1))def estimate_normal_for_pos(pos,points,n):# estimate normal vectors at a given pointpts = np.copy(points)tree = KDTree(pts, leaf_size=2)idx = tree.query(pos, k=n, return_distance=False, dualtree=False, breadth_first=False)#pts = np.concatenate((np.concatenate((pts[0].reshape(1,-1),pts),axis=0),pts[-1].reshape(1,-1)),axis=0)normals = []for i in range(0,pos.shape[0]):pts_for_normals = pts[idx[i,:],:]_,_,_,normal = SVD(pts_for_normals)normals.append(normal)normals = np.array(normals)return normalsdef estimate_normals(points,n):pts = np.copy(points)tree = KDTree(pts, leaf_size=2)idx = tree.query(pts, k=n, return_distance=False, dualtree=False, breadth_first=False)#pts = np.concatenate((np.concatenate((pts[0].reshape(1,-1),pts),axis=0),pts[-1].reshape(1,-1)),axis=0)normals = []for i in range(0,pts.shape[0]):pts_for_normals = pts[idx[i,:],:]_,_,_,normal = SVD(pts_for_normals)normals.append(normal)normals = np.array(normals)return normalsdef get_crack_ctrlpts(centers,normals,bpoints,hband=5,vband=2):# main algorithm to obtain crack widthcpoints = np.copy(centers)cnormals = np.copy(normals)xmatrix = np.array([[0,1],[-1,0]])cnormalsx = np.dot(xmatrix,cnormals.T).T # the normal of x axisN = cpoints.shape[0]interp_segm = []widths = []for i in range(N):try:ny = cnormals[i]nx = cnormalsx[i]tform = np.array([nx,ny])bpoints_loc = np.dot(tform,bpoints.T).Tcpoints_loc = np.dot(tform,cpoints.T).Tci = cpoints_loc[i]bl_ind = (bpoints_loc[:,0]-(ci[0]-hband))*(bpoints_loc[:,0]-ci[0])<0br_ind = (bpoints_loc[:,0]-ci[0])*(bpoints_loc[:,0]-(ci[0]+hband))<=0bl = bpoints_loc[bl_ind] # left pointsbr = bpoints_loc[br_ind] # right pointsblt = bl[bl[:,1]>np.mean(bl[:,1])]if np.ptp(blt[:,1])>vband:blt = blt[blt[:,1]>np.mean(blt[:,1])]blb = bl[bl[:,1]<np.mean(bl[:,1])]if np.ptp(blb[:,1])>vband:blb = blb[blb[:,1]<np.mean(blb[:,1])]brt = br[br[:,1]>np.mean(br[:,1])]if np.ptp(brt[:,1])>vband:brt = brt[brt[:,1]>np.mean(brt[:,1])]brb = br[br[:,1]<np.mean(br[:,1])]if np.ptp(brb[:,1])>vband:brb = brb[brb[:,1]<np.mean(brb[:,1])]#bh = np.vstack((bl,br))#bmax = np.max(bh[:,1])#bmin = np.min(bh[:,1])#blt = bl[bl[:,1]>bmax-vband] # left top points#blb = bl[bl[:,1]<bmin+vband] # left bottom points#brt = br[br[:,1]>bmax-vband] # right top points#brb = br[br[:,1]<bmin+vband] # right bottom pointst1 = blt[np.argsort(blt[:,0])[-1]]t2 = brt[np.argsort(brt[:,0])[0]]b1 = blb[np.argsort(blb[:,0])[-1]]b2 = brb[np.argsort(brb[:,0])[0]]interp1 = (ci[0]-t1[0])*((t2[1]-t1[1])/(t2[0]-t1[0]))+t1[1]interp2 = (ci[0]-b1[0])*((b2[1]-b1[1])/(b2[0]-b1[0]))+b1[1]if interp1-ci[1]>0 and interp2-ci[1]<0:widths.append([i,interp1-ci[1],interp2-ci[1]])interps = np.array([[ci[0],interp1],[ci[0],interp2]])interps_rec = np.dot(np.linalg.inv(tform),interps.T).T#show_2dpoints([bpointsxl_loc1,bpointsxl_loc2,bpointsxr_loc1,bpointsxr_loc2,np.array([ptsl_1,ptsl_2]),np.array([ptsr_1,ptsr_2]),interps,ci.reshape(1,-1)],s=[1,1,1,1,20,20,20,20])interps_rec = interps_rec.reshape(1,-1)[0,:]interp_segm.append(interps_rec)except:print("the %d-th was wrong" % i)continueinterp_segm = np.array(interp_segm)widths = np.array(widths)# check# show_2dpoints([np.array([[ci[0],interp1],[ci[0],interp2]]),np.array([t1,t2,b1,b2]),cpoints_loc,bl,br],[10,20,15,2,2])return interp_segm, widthspath = "E:/Users/SubChange/Desktop/"image = io.imread(path+"7Q3A9060-18.png", as_gray=True)
iw,ih = image.shapeblobs  = np.copy(image)
blobs[blobs<128] = 0
blobs[blobs>128] = 1blobs = blobs.astype(np.uint8)
# Generate the data
#blobs = data.binary_blobs(200, blob_size_fraction=.2,#volume_fraction=.35, seed=1)
# using scikit-image
## Compute the medial axis (skeleton) and the distance transform
#skel, distance = medial_axis(blobs, return_distance=True)
## Distance to the background for pixels of the skeleton
#dist_on_skel = distance * skel# Compare with other skeletonization algorithms
skeleton = skeletonize(blobs)
#skeleton_lee = skeletonize(blobs, method='lee')
x, y = np.where(skeleton>0)
centers = np.hstack((x.reshape(-1,1),y.reshape(-1,1)))
normals = estimate_normals(centers,3)# search contours of the crack
contours = measure.find_contours(blobs, 0.8)bl = contours[0]
br = contours[1]bpoints = np.vstack((bl,br))#interp_segm, widths = get_crack_ctrlpts(centers,normals,bpoints,hband=2,vband=2)bpixel = np.zeros((iw,ih,3),dtype=np.uint8)
bpoints = bpoints.astype(np.int)
bpixel[bpoints[:,0],bpoints[:,1],0] = 255skeleton_pixel = np.zeros((iw,ih,3),dtype=np.uint8)
skeleton_pixel[skeleton,1] = 255bpixel_and_skeleton = np.copy(bpixel)
bpixel_and_skeleton[skeleton,1] = 255fig, axes = plt.subplots(1,3, figsize=(8, 8))
ax = axes.ravel()ax[0].imshow(blobs, cmap=plt.cm.gray)
ax[0].axis('off')ax[1].imshow(bpixel_and_skeleton)
#for contour in contours:
#    ax[1].plot(contour[:, 1], contour[:, 0], linewidth=2)#for i in range(interp_segm.shape[0]):
#    ax[1].plot([interp_segm[i,1],interp_segm[i,3]],[interp_segm[i,0],interp_segm[i,2]],'-b')#ax[1].set_title('medial_axis')
ax[1].axis('off')# ================ small window ==================
pos = np.array([191, 291]).reshape(1,-1) # input (x,y) where need to calculate crack width
# pos = np.array([142, 178]).reshape(1,-1)posn = estimate_normal_for_pos(pos,centers,3)interps, widths2 = get_crack_ctrlpts(pos,posn,bpoints,hband=1.5,vband=2)sx = pos[0,0] - 20
sy = pos[0,1] - 20ax[2].imshow(bpixel_and_skeleton)for i in range(interps.shape[0]):ax[2].plot([interps[i,1],interps[i,3]],[interps[i,0],interps[i,2]],c='c',ls='-',lw=5,marker='o',ms=8,mec='c',mfc='c')ax[2].set_ylim(sx,sx+40)
ax[2].set_xlim(sy,sy+40)#ax[2].set_title('skeletonize')
ax[2].axis('off')print(interps)fig.tight_layout()plt.show()

结果

裂缝边缘线和骨架线

宽度计算结果

另外，附上另外一张图片，是整条裂缝的宽度计算结果：

更新

针对裂缝形状比较复杂，即不是单条裂缝，图像中有多条裂缝，且裂缝的宽度在一定的范围的，可以做如下改进：

针对裂缝坐标下的四个象限的裂缝边缘线的点，设置一个预估计的裂缝宽度，并在四个象限中，删除宽度超出预估裂缝宽度的边缘像素点，这样便能够筛选离中轴线最近的边缘线了，具体看下面代码，即添加 est_width参数。

def get_crack_ctrlpts(centers,normals,bpoints,hband=5,vband=2,est_width=0):# main algorithm to obtain crack widthcpoints = np.copy(centers)cnormals = np.copy(normals)xmatrix = np.array([[0,1],[-1,0]])cnormalsx = np.dot(xmatrix,cnormals.T).T # the normal of x axisN = cpoints.shape[0]interp_segm = []widths = []for i in range(N):try:ny = cnormals[i]nx = cnormalsx[i]tform = np.array([nx,ny])bpoints_loc = np.dot(tform,bpoints.T).Tcpoints_loc = np.dot(tform,cpoints.T).Tci = cpoints_loc[i]bl_ind = (bpoints_loc[:,0]-(ci[0]-hband))*(bpoints_loc[:,0]-ci[0])<0br_ind = (bpoints_loc[:,0]-ci[0])*(bpoints_loc[:,0]-(ci[0]+hband))<=0bl = bpoints_loc[bl_ind] # left pointsbr = bpoints_loc[br_ind] # right pointsif est_width>0:# 下面的数值 est_width 是预估计的裂缝宽度half_est_width = est_width / 2blt = bl[(bl[:,1]-(ci[1]+half_est_width))*(bl[:,1]-ci[1])<0]blb = bl[(bl[:,1]-(ci[1]-half_est_width))*(bl[:,1]-ci[1])<0]brt = br[(br[:,1]-(ci[1]+half_est_width))*(br[:,1]-ci[1])<0]brb = br[(br[:,1]-(ci[1]-half_est_width))*(br[:,1]-ci[1])<0]else:blt = bl[bl[:,1]>np.mean(bl[:,1])]if np.ptp(blt[:,1])>vband:blt = blt[blt[:,1]>np.mean(blt[:,1])]blb = bl[bl[:,1]<np.mean(bl[:,1])]if np.ptp(blb[:,1])>vband:blb = blb[blb[:,1]<np.mean(blb[:,1])]brt = br[br[:,1]>np.mean(br[:,1])]if np.ptp(brt[:,1])>vband:brt = brt[brt[:,1]>np.mean(brt[:,1])]brb = br[br[:,1]<np.mean(br[:,1])]if np.ptp(brb[:,1])>vband:brb = brb[brb[:,1]<np.mean(brb[:,1])]# blt = bl[bl[:,1]>np.mean(bl[:,1])]# if np.ptp(blt[:,1])>vband:#    blt = blt[blt[:,1]<ci[1]+50]#    #blt = blt[blt[:,1]>np.mean(blt[:,1])] （外侧）#    #blt = blt[blt[:,1]<(np.max(blt[:,1])-0.5*np.ptp(blt[:,1]))] （内侧）# blb = bl[bl[:,1]<np.mean(bl[:,1])]# if np.ptp(blb[:,1])>vband:#    blb = blb[blb[:,1]>ci[1]-50]#    #blb = blb[blb[:,1]<np.mean(blb[:,1])]#    #blb = blb[blb[:,1]>(np.min(blb[:,1])+0.5*np.ptp(blb[:,1]))]# brt = br[br[:,1]>np.mean(br[:,1])]# if np.ptp(brt[:,1])>vband:#    brt = brt[brt[:,1]<ci[1]+50]#    #brt = brt[brt[:,1]>np.mean(brt[:,1])]#    #brt = brt[brt[:,1]<(np.max(brt[:,1])-0.5*np.ptp(brt[:,1]))]# brb = br[br[:,1]<np.mean(br[:,1])]# if np.ptp(brb[:,1])>vband:#    brb = brb[brb[:,1]>ci[1]-50]#    # brb = brb[brb[:,1]<np.mean(brb[:,1])]#    # brb = brb[brb[:,1]>(np.min(brb[:,1])+0.5*np.ptp(brb[:,1]))]#bh = np.vstack((bl,br))#bmax = np.max(bh[:,1])#bmin = np.min(bh[:,1])#blt = bl[bl[:,1]>bmax-vband] # left top points#blb = bl[bl[:,1]<bmin+vband] # left bottom points#brt = br[br[:,1]>bmax-vband] # right top points#brb = br[br[:,1]<bmin+vband] # right bottom pointst1 = blt[np.argsort(blt[:,0])[-1]]t2 = brt[np.argsort(brt[:,0])[0]]b1 = blb[np.argsort(blb[:,0])[-1]]b2 = brb[np.argsort(brb[:,0])[0]]interp1 = (ci[0]-t1[0])*((t2[1]-t1[1])/(t2[0]-t1[0]))+t1[1]interp2 = (ci[0]-b1[0])*((b2[1]-b1[1])/(b2[0]-b1[0]))+b1[1]if interp1-ci[1]>0 and interp2-ci[1]<0:widths.append([i,interp1-ci[1],interp2-ci[1]])interps = np.array([[ci[0],interp1],[ci[0],interp2]])interps_rec = np.dot(np.linalg.inv(tform),interps.T).T#show_2dpoints([bpointsxl_loc1,bpointsxl_loc2,bpointsxr_loc1,bpointsxr_loc2,np.array([ptsl_1,ptsl_2]),np.array([ptsr_1,ptsr_2]),interps,ci.reshape(1,-1)],s=[1,1,1,1,20,20,20,20])interps_rec = interps_rec.reshape(1,-1)[0,:]interp_segm.append(interps_rec)except:print("the %d-th was wrong" % i)continueinterp_segm = np.array(interp_segm)widths = np.array(widths)# check# show_2dpoints([np.array([[ci[0],interp1],[ci[0],interp2]]),np.array([t1,t2,b1,b2]),cpoints_loc,bl,br],[10,20,15,2,2])return interp_segm, widths

具体效果如下（注意骨架线和边缘线的提取与传参问题）：

鉴于很多人询问怎么测量整条裂缝的宽度，这里我将代码进行了略微的调整，仍然是针对于最先给出的裂缝，可以直接运行的代码和结果如下，大家可以尝试看看效果，应该是可以直接跑的通的，请注意更换裂缝图像路径，跑通后大家再仔细看看里面是怎么调整的。个人水平有限，代码写的有点乱，请见谅，如果还不能跑通，可私信沟通

import numpy as np
from skimage import io
from skimage.morphology import medial_axis, skeletonize
from skimage import measure
from skimage import data
import matplotlib.pyplot as plt
from sklearn.neighbors import KDTreedef show_2dpoints(pointcluster,s=None,quivers=None,qscale=1):# pointcluster should be a list of numpy ndarray# This functions would show a list of pint cloud in different colorsn = len(pointcluster)nmax = nif quivers is not None:nq = len(quivers)nmax = max(n,nq)colors = ['r','g','b','c','m','y','k','tomato','gold']if nmax < 10:colors = np.array(colors[0:nmax])else: colors = np.random.rand(nmax,3)fig = plt.figure(num=1)ax = fig.add_subplot(1,1,1)if s is None:s = np.ones(n)*2for i in range(n):ax.scatter(pointcluster[i][:,0],pointcluster[i][:,1],s=s[i],c=[colors[i]],alpha=0.6)if quivers is not None:for i in range(nq):ax.quiver(quivers[i][:,0],quivers[i][:,1],quivers[i][:,2],quivers[i][:,3],color=[colors[i]],scale=qscale)plt.show()def SVD(points):# 二维，三维均适用# 二维直线，三维平面pts = points.copy()# 奇异值分解c = np.mean(pts, axis=0)A = pts - c # shift the pointsA = A.T #3*nu, s, vh = np.linalg.svd(A, full_matrices=False, compute_uv=True) # A=u*s*vhnormal = u[:,-1]# 法向量归一化nlen = np.sqrt(np.dot(normal,normal))normal = normal / nlen# normal 是主方向的方向向量 与PCA最小特征值对应的特征向量是垂直关系# u 每一列是一个方向# s 是对应的特征值# c >>> 点的中心# normal >>> 拟合的方向向量return u,s,c,normaldef calcu_dis_from_ctrlpts(ctrlpts):if ctrlpts.shape[1]==4:return np.sqrt(np.sum((ctrlpts[:,0:2]-ctrlpts[:,2:4])**2,axis=1))else:return np.sqrt(np.sum((ctrlpts[:,[0,2]]-ctrlpts[:,[3,5]])**2,axis=1))def estimate_normal_for_pos(pos,points,n):"""计算pos处的法向量.Input：------pos: nx2 ndarray 需要计算法向量的位置.points: 骨架线的点集n: 用到的近邻点的个数Output：------normals: nx2 ndarray 在pos位置处的法向量."""# estimate normal vectors at a given pointpts = np.copy(points)tree = KDTree(pts, leaf_size=2)idx = tree.query(pos, k=n, return_distance=False, dualtree=False, breadth_first=False)#pts = np.concatenate((np.concatenate((pts[0].reshape(1,-1),pts),axis=0),pts[-1].reshape(1,-1)),axis=0)normals = []for i in range(0,pos.shape[0]):pts_for_normals = pts[idx[i,:],:]_,_,_,normal = SVD(pts_for_normals)normals.append(normal)normals = np.array(normals)return normalsdef estimate_normals(points,n):"""计算points表示的曲线上的每一个点法向量.等同于 estimate_normal_for_pos(points,points,n)Input：------points: nx2 ndarray 曲线点集.n: 用到的近邻点的个数Output：------normals: nx2 ndarray 在points曲线上的每一处的法向量."""pts = np.copy(points)tree = KDTree(pts, leaf_size=2)idx = tree.query(pts, k=n, return_distance=False, dualtree=False, breadth_first=False)#pts = np.concatenate((np.concatenate((pts[0].reshape(1,-1),pts),axis=0),pts[-1].reshape(1,-1)),axis=0)normals = []for i in range(0,pts.shape[0]):pts_for_normals = pts[idx[i,:],:]_,_,_,normal = SVD(pts_for_normals)normals.append(normal)normals = np.array(normals)return normalsdef get_crack_ctrlpts(centers,normals,bpoints,hband=5,vband=2,est_width=0):# main algorithm to obtain crack widthcpoints = np.copy(centers)cnormals = np.copy(normals)xmatrix = np.array([[0,1],[-1,0]])cnormalsx = np.dot(xmatrix,cnormals.T).T # the normal of x axisN = cpoints.shape[0]interp_segm = []widths = []for i in range(N):try:ny = cnormals[i]nx = cnormalsx[i]tform = np.array([nx,ny])bpoints_loc = np.dot(tform,bpoints.T).Tcpoints_loc = np.dot(tform,cpoints.T).Tci = cpoints_loc[i]bl_ind = (bpoints_loc[:,0]-(ci[0]-hband))*(bpoints_loc[:,0]-ci[0])<0br_ind = (bpoints_loc[:,0]-ci[0])*(bpoints_loc[:,0]-(ci[0]+hband))<=0bl = bpoints_loc[bl_ind] # left pointsbr = bpoints_loc[br_ind] # right pointsif est_width>0:# 下面的数值 est_width 是预估计的裂缝宽度half_est_width = est_width / 2blt = bl[(bl[:,1]-(ci[1]+half_est_width))*(bl[:,1]-ci[1])<0]blb = bl[(bl[:,1]-(ci[1]-half_est_width))*(bl[:,1]-ci[1])<0]brt = br[(br[:,1]-(ci[1]+half_est_width))*(br[:,1]-ci[1])<0]brb = br[(br[:,1]-(ci[1]-half_est_width))*(br[:,1]-ci[1])<0]else:blt = bl[bl[:,1]>np.mean(bl[:,1])]if np.ptp(blt[:,1])>vband:blt = blt[blt[:,1]>np.mean(blt[:,1])]blb = bl[bl[:,1]<np.mean(bl[:,1])]if np.ptp(blb[:,1])>vband:blb = blb[blb[:,1]<np.mean(blb[:,1])]brt = br[br[:,1]>np.mean(br[:,1])]if np.ptp(brt[:,1])>vband:brt = brt[brt[:,1]>np.mean(brt[:,1])]brb = br[br[:,1]<np.mean(br[:,1])]if np.ptp(brb[:,1])>vband:brb = brb[brb[:,1]<np.mean(brb[:,1])]# blt = bl[bl[:,1]>np.mean(bl[:,1])]# if np.ptp(blt[:,1])>vband:#    blt = blt[blt[:,1]<ci[1]+50]#    #blt = blt[blt[:,1]>np.mean(blt[:,1])] （外侧）#    #blt = blt[blt[:,1]<(np.max(blt[:,1])-0.5*np.ptp(blt[:,1]))] （内侧）# blb = bl[bl[:,1]<np.mean(bl[:,1])]# if np.ptp(blb[:,1])>vband:#    blb = blb[blb[:,1]>ci[1]-50]#    #blb = blb[blb[:,1]<np.mean(blb[:,1])]#    #blb = blb[blb[:,1]>(np.min(blb[:,1])+0.5*np.ptp(blb[:,1]))]# brt = br[br[:,1]>np.mean(br[:,1])]# if np.ptp(brt[:,1])>vband:#    brt = brt[brt[:,1]<ci[1]+50]#    #brt = brt[brt[:,1]>np.mean(brt[:,1])]#    #brt = brt[brt[:,1]<(np.max(brt[:,1])-0.5*np.ptp(brt[:,1]))]# brb = br[br[:,1]<np.mean(br[:,1])]# if np.ptp(brb[:,1])>vband:#    brb = brb[brb[:,1]>ci[1]-50]#    # brb = brb[brb[:,1]<np.mean(brb[:,1])]#    # brb = brb[brb[:,1]>(np.min(brb[:,1])+0.5*np.ptp(brb[:,1]))]#bh = np.vstack((bl,br))#bmax = np.max(bh[:,1])#bmin = np.min(bh[:,1])#blt = bl[bl[:,1]>bmax-vband] # left top points#blb = bl[bl[:,1]<bmin+vband] # left bottom points#brt = br[br[:,1]>bmax-vband] # right top points#brb = br[br[:,1]<bmin+vband] # right bottom pointst1 = blt[np.argsort(blt[:,0])[-1]]t2 = brt[np.argsort(brt[:,0])[0]]b1 = blb[np.argsort(blb[:,0])[-1]]b2 = brb[np.argsort(brb[:,0])[0]]interp1 = (ci[0]-t1[0])*((t2[1]-t1[1])/(t2[0]-t1[0]))+t1[1]interp2 = (ci[0]-b1[0])*((b2[1]-b1[1])/(b2[0]-b1[0]))+b1[1]if interp1-ci[1]>0 and interp2-ci[1]<0:widths.append([i,interp1-ci[1],interp2-ci[1]])interps = np.array([[ci[0],interp1],[ci[0],interp2]])interps_rec = np.dot(np.linalg.inv(tform),interps.T).T#show_2dpoints([bpointsxl_loc1,bpointsxl_loc2,bpointsxr_loc1,bpointsxr_loc2,np.array([ptsl_1,ptsl_2]),np.array([ptsr_1,ptsr_2]),interps,ci.reshape(1,-1)],s=[1,1,1,1,20,20,20,20])interps_rec = interps_rec.reshape(1,-1)[0,:]interp_segm.append(interps_rec)except:print("the %d-th was wrong" % i)continueinterp_segm = np.array(interp_segm)widths = np.array(widths)# check# show_2dpoints([np.array([[ci[0],interp1],[ci[0],interp2]]),np.array([t1,t2,b1,b2]),cpoints_loc,bl,br],[10,20,15,2,2])return interp_segm, widthspath = "e:/Users/subchange/Downloads/"image = io.imread(path+"20210706162948837.png", as_gray=True)
iw,ih = image.shapeblobs  = np.copy(image)
#blobs[blobs<128] = 0
#blobs[blobs>128] = 1blobs = blobs.astype(np.uint8)
# Generate the data
#blobs = data.binary_blobs(200, blob_size_fraction=.2,#volume_fraction=.35, seed=1)
# using scikit-image
## Compute the medial axis (skeleton) and the distance transform
#skel, distance = medial_axis(blobs, return_distance=True)
## Distance to the background for pixels of the skeleton
#dist_on_skel = distance * skel# Compare with other skeletonization algorithms
skeleton = skeletonize(blobs)
#skeleton_lee = skeletonize(blobs, method='lee')
x, y = np.where(skeleton>0)
centers = np.hstack((x.reshape(-1,1),y.reshape(-1,1)))normals = estimate_normals(centers, 9) # 这个用于估计法向量的KNN# search contours of the crack
contours = measure.find_contours(blobs, 0.8)bl = contours[0]
br = contours[1]bpoints = np.vstack((bl,br))#interp_segm, widths = get_crack_ctrlpts(centers,normals,bpoints,hband=2,vband=2)bpixel = np.zeros((iw,ih,3),dtype=np.uint8)
bpoints = bpoints.astype(np.int64)
bpixel[bpoints[:,0],bpoints[:,1],0] = 255skeleton_pixel = np.zeros((iw,ih,3),dtype=np.uint8)
skeleton_pixel[skeleton,1] = 255bpixel_and_skeleton = np.copy(bpixel)
bpixel_and_skeleton[skeleton,1] = 255fig, axes = plt.subplots(1,2, figsize=(8, 8))
ax = axes.ravel()ax[0].imshow(blobs, cmap=plt.cm.gray)
ax[0].axis('off')ax[1].imshow(bpixel_and_skeleton)
#for contour in contours:
#    ax[1].plot(contour[:, 1], contour[:, 0], linewidth=2)#for i in range(interp_segm.shape[0]):
#    ax[1].plot([interp_segm[i,1],interp_segm[i,3]],[interp_segm[i,0],interp_segm[i,2]],'-b')#ax[1].set_title('medial_axis')
ax[1].axis('off')interps, widths = get_crack_ctrlpts(centers, normals, bpoints, hband=2, vband=2, est_width=30)interps_show = interps[np.random.choice(interps.shape[0], 120, replace=False),:] # 由于太多，这里随机采样120个测量位置，进行显示for i in range(interps_show.shape[0]):ax[1].plot([interps_show[i,1],interps_show[i,3]],[interps_show[i,0],interps_show[i,2]],c='c', ls='-', lw=2, marker='o',ms=4,mec='c',mfc='c')## ================ small window ==================
#pos = np.array([191, 291]).reshape(1,-1) # input (x,y) where need to calculate crack width
## pos = np.array([142, 178]).reshape(1,-1)#posn = estimate_normal_for_pos(pos,centers,3)#interps, widths2 = get_crack_ctrlpts(pos,posn,bpoints,hband=1.5,vband=2)#sx = pos[0,0] - 20
#sy = pos[0,1] - 20#ax[2].imshow(bpixel_and_skeleton)#for i in range(interps.shape[0]):
#    ax[2].plot([interps[i,1],interps[i,3]],[interps[i,0],interps[i,2]],c='c',ls='-',lw=5,marker='o',ms=8,mec='c',mfc='c')#ax[2].set_ylim(sx,sx+40)
#ax[2].set_xlim(sy,sy+40)##ax[2].set_title('skeletonize')
#ax[2].axis('off')#print(interps)fig.tight_layout()plt.show()