将线条的黑白图像矢量化为没有厚度的矢量（即坐标）

Question

我希望能够拍摄图像，例如：

然后return每行开始和结束的坐标（例如示例图像中有 3 行）。我知道有一些方法，例如霍夫线变换，这确实给出了坐标，但是由于输入图像具有厚度，它是所有边缘的 returns 坐标。一个例子如下所示：

是否有不同的方法（或调整霍夫线变换）来获取不考虑线条粗细的坐标？

Answer 1

您可能想使用 skeletonize 来获得线条的骨架。

为了获得行的 tips/corners，这是我遵循的程序：

获取骨架图片
通过 3x3 大小的矩阵过滤骨架图像找到提示。
通过霍夫变换将线条拟合到骨架图像
根据线的交点求线角

这是我的代码。让我们从导入所需的库开始。

import cv2
import matplotlib.pyplot as plt
import numpy as np
from skimage.morphology import skeletonize
from itertools import combinations

我开始获取骨架图像。我将使用此图像来检测所有点。请注意，skeletonize 的默认方法会在骨架图像中创建分叉。但是 lee 方法更适合您的问题。请注意您的其他图片。


img_bgr = cv2.imread('lines.png',1)
img = cv2.cvtColor(img_bgr,cv2.COLOR_BGR2GRAY)

_,img = cv2.threshold(img,10,1,cv2.THRESH_BINARY_INV)

skeleton = skeletonize(img,method='lee')

# display purposes
skeleton_bgr = cv2.cvtColor(skeleton.astype(np.uint8),cv2.COLOR_GRAY2BGR)

接下来是获取线条的提示。

img_conv = cv2.filter2D(skeleton.astype(np.uint8),-1,np.ones((3,3))) #
img_conv = img_conv*skeleton
img_tips = img_conv == 2
tips = np.array(np.nonzero(img_tips)).T

仅供参考，检测到的尖端距离骨架有几个像素，我可能遗漏了一些东西，我把这部分留给你。

正如你在问题中所建议的，在下一步中，我正在为骨架图像拟合线条。

lines = cv2.HoughLines(skeleton.astype(np.uint8), 1, np.pi / 180, 150, None, 0, 0)

lines_points = []

# # Draw the lines
for i in range(0, len(lines)):
    rho = lines[i][0][0]
    theta = lines[i][0][1]
    a = np.cos(theta)
    b = np.sin(theta)
    x0 = a * rho
    y0 = b * rho
    pt1 = (int(x0 + 1000*(-b)), int(y0 + 1000*(a)))
    pt2 = (int(x0 - 1000*(-b)), int(y0 - 1000*(a)))
    # cv2.line(skeleton_bgr, pt1, pt2, (0,0,255), 3, cv2.LINE_AA)
    lines_points.append([pt1,pt2])

然后，我通过交点得到线的角。

def line_intersection(line1, line2):
    xdiff = (line1[0][0] - line1[1][0], line2[0][0] - line2[1][0])
    ydiff = (line1[0][1] - line1[1][1], line2[0][1] - line2[1][1])

    def det(a, b):
        return a[0] * b[1] - a[1] * b[0]

    div = det(xdiff, ydiff)
    if div == 0:
       raise Exception('lines do not intersect')

    d = (det(*line1), det(*line2))
    x = det(d, xdiff) / div
    y = det(d, ydiff) / div
    return x, y

line_combinations = combinations(lines_points, 2)

fig,ax = plt.subplots(1)
ax.imshow(skeleton, cmap = 'gray')
ax.scatter(tips[0,:],tips[1,:],s=4,color='r')

for line_combination in list(line_combinations):
    line1 = line_combination[0]
    line2 = line_combination[1]

    intersection = line_intersection(line1,line2)
    
    # clip the intersection points to the image size    
    if intersection[0]<img.shape[1] and intersection[1]<img.shape[0]:
        ax.scatter(intersection[0],intersection[1],s=4,color='b')

这是原图上的结果。

这是包含绘图函数的完整代码。

import cv2
import matplotlib.pyplot as plt
import numpy as np
from skimage.morphology import skeletonize
from itertools import combinations

def line_intersection(line1, line2):
    xdiff = (line1[0][0] - line1[1][0], line2[0][0] - line2[1][0])
    ydiff = (line1[0][1] - line1[1][1], line2[0][1] - line2[1][1])

    def det(a, b):
        return a[0] * b[1] - a[1] * b[0]

    div = det(xdiff, ydiff)
    if div == 0:
       raise Exception('lines do not intersect')

    d = (det(*line1), det(*line2))
    x = det(d, xdiff) / div
    y = det(d, ydiff) / div
    return x, y


img_bgr = cv2.imread('lines.png',1)
img = cv2.cvtColor(img_bgr,cv2.COLOR_BGR2GRAY)

_,img = cv2.threshold(img,10,1,cv2.THRESH_BINARY_INV)

skeleton = skeletonize(img,method='lee')
skeleton_bgr = cv2.cvtColor(skeleton.astype(np.uint8),cv2.COLOR_GRAY2BGR)


# fig,ax = plt.subplots(1)
# ax.imshow(skeleton, cmap = 'gray')


#get tips
img_conv = cv2.filter2D(skeleton.astype(np.uint8),-1,np.ones((3,3))) #
img_conv = img_conv*skeleton
img_tips = img_conv == 2
tips = np.array(np.nonzero(img_tips)).T



# fig,ax = plt.subplots(1)
# ax.imshow(skeleton, cmap = 'gray')
# ax.scatter(tips[0,:],tips[1,:],s=4,color='r')


lines = cv2.HoughLines(skeleton.astype(np.uint8), 1, np.pi / 180, 150, None, 0, 0)

lines_points = []

# # Draw the lines
for i in range(0, len(lines)):
    rho = lines[i][0][0]
    theta = lines[i][0][1]
    a = np.cos(theta)
    b = np.sin(theta)
    x0 = a * rho
    y0 = b * rho
    pt1 = (int(x0 + 1000*(-b)), int(y0 + 1000*(a)))
    pt2 = (int(x0 - 1000*(-b)), int(y0 - 1000*(a)))
    cv2.line(skeleton_bgr, pt1, pt2, (0,0,255), 3, cv2.LINE_AA)
    lines_points.append([pt1,pt2])


line_combinations = combinations(lines_points, 2)


fig,ax = plt.subplots(1)
ax.imshow(img, cmap = 'gray')
ax.scatter(tips[0,:],tips[1,:],s=4,color='r')

for line_combination in list(line_combinations):
    line1 = line_combination[0]
    line2 = line_combination[1]

    intersection = line_intersection(line1,line2)
    
    # clip the intersection points to the image size    
    if intersection[0]<img.shape[1] and intersection[1]<img.shape[0]:
        ax.scatter(intersection[0],intersection[1],s=4,color='b')

# fig,ax = plt.subplots(1)
# ax.imshow(skeleton_bgr,'gray')

plt.show()

将线条的黑白图像矢量化为没有厚度的矢量（即坐标）

Vectorising black and white image of lines into vectors of no thickness (i.e coordinates)

python

image

opencv

python-imaging-library

vector-graphics