Hough圆变换的原理很多博客都已经说得非常清楚了,但是手动实现的比较少,所以本文直接贴上手动实现的代码。
这里使用的图片是一堆硬币:

首先利用通过计算梯度来寻找边缘,代码如下:
- def detect_edges(image):
- h = image.shape[0]
- w = image.shape[1]
- sobeling = np.zeros((h, w), np.float64)
- sobelx = [[-3, 0, 3],
- [-10, 0, 10],
- [-3, 0, 3]]
- sobelx = np.array(sobelx)
-
- sobely = [[-3, -10, -3],
- [0, 0, 0],
- [3, 10, 3]]
- sobely = np.array(sobely)
- gx = 0
- gy = 0
- testi = 0
- for i in range(1, h - 1):
- for j in range(1, w - 1):
- edgex = 0
- edgey = 0
- for k in range(-1, 2):
- for l in range(-1, 2):
- edgex += image[k + i, l + j] * sobelx[1 + k, 1 + l]
- edgey += image[k + i, l + j] * sobely[1 + k, 1 + l]
- gx = abs(edgex)
- gy = abs(edgey)
- sobeling[i, j] = gx + gy
- # if you want to imshow ,run codes below first
- # if sobeling[i,j]>255:
- # sobeling[i, j]=255
- # sobeling[i, j] = sobeling[i,j]/255
- return sobeling
需要注意的是,这里使用的kernel内的数值比较大,所以得到了结果图中的某些位置的数值超过255,但并不影响显示,但如果想通过cv2.imshow来显示,就需要将超过255的地方设为255即可(已经在代码中用注释标出),结果如下:

接下来就是要进行Hough圆变换,先看代码:
- def hough_circles(edge_image, edge_thresh, radius_values):
- h = edge_image.shape[0]
- w = edge_image.shape[1]
- # print(h,w)
- edgimg = np.zeros((h, w), np.int64)
- for i in range(h):
- for j in range(w):
- if edge_image[i][j] > edge_thresh:
- edgimg[i][j] = 255
- else:
- edgimg[i][j] = 0
-
- accum_array = np.zeros((len(radius_values), h, w))
- # return edgimg , []
- for i in range(h):
- print('Hough Transform进度:', i, '/', h)
- for j in range(w):
- if edgimg[i][j] != 0:
- for r in range(len(radius_values)):
- rr = radius_values[r]
- hdown = max(0, i - rr)
- for a in range(hdown, i):
- b = round(j+math.sqrt(rr*rr - (a - i) * (a - i)))
- if b>=0 and b<=w-1:
- accum_array[r][a][b] += 1
- if 2 * i - a >= 0 and 2 * i - a <= h - 1:
- accum_array[r][2 * i - a][b] += 1
- if 2 * j - b >= 0 and 2 * j - b <= w - 1:
- accum_array[r][a][2 * j - b] += 1
- if 2 * i - a >= 0 and 2 * i - a <= h - 1 and 2 * j - b >= 0 and 2 * j - b <= w - 1:
- accum_array[r][2 * i - a][2 * j - b] += 1
-
- return edgimg, accum_array
其中输入是我们之前得到的边缘图,以及确定强边缘的阈值,以及一个包含着我们估计的半径的数组;返回值是强边缘图以及参数域矩阵。代码中首先遍历边缘图,通过阈值留下那些较强的位置,这里的阈值需要自己根据自己的输入图进行调节。接着就是进行Hough变换,这里的候选半径集合需要根据自己的输入图进行调节。在绘制参数域的过程中,只遍历了所需正方形区域(大小为 r*r)的 1/4,这是因为在坐出参数域上的一个点之后,由于圆的对称性,就可以找到与之对称的另外三个点,无需额外进行遍历。
最后一步就是从参数域矩阵中提取出结果圆,代码如下,其中筛选阈值需要根据你的输入图像自己调节:
- def find_circles(image, accum_array, radius_values, hough_thresh):
- returnlist = []
- hlist = []
- wlist = []
- rlist = []
- returnimg = deepcopy(image)
- for r in range(accum_array.shape[0]):
- print('Find Circles 进度:', r, '/', accum_array.shape[0])
- for h in range(accum_array.shape[1]):
- for w in range(accum_array.shape[2]):
- if accum_array[r][h][w] > hough_thresh:
-
- tmp = 0
- for i in range(len(hlist)):
- if abs(w-wlist[i])<10 and abs(h-hlist[i])<10:
- tmp = 1
- break
-
- if tmp == 0:
- #print(accum_array[r][h][w])
- rr = radius_values[r]
- flag = '(h,w,r)is:(' + str(h) + ',' + str(w) + ',' + str(rr) + ')'
- returnlist.append(flag)
- hlist.append(h)
- wlist.append(w)
- rlist.append(rr)
-
- print('圆的数量:', len(hlist))
-
- for i in range(len(hlist)):
- center = (wlist[i], hlist[i])
- rr = rlist[i]
-
- color = (0, 255, 0)
- thickness = 2
- cv2.circle(returnimg, center, rr, color, thickness)
-
- return returnlist, returnimg
注意一下在这一步中需要将那些圆心相近的圆剔除掉,只保留一个结果。
接着是main函数,这没啥好说的:
- def main(argv):
- img_name = argv[0]
-
- img = cv2.imread('data/' + img_name + '.png', cv2.IMREAD_COLOR)
- # print(img.shape[0], img.shape[1])
- gray_image = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
-
- # print(gray_image.shape[0], gray_image.shape[1])
- img1 = detect_edges(gray_image)
- cv2.imwrite('output/' + img_name + "_after_find_detect.png", img1)
-
- thresh = 1500
- # 需要注意的是,在img1中有些地方的像素值是高于255的,这是由于之前的kernel内的数更大
- # 但这并不影响图像的显示
- # 因此这里的thresh要大于255
- radius_values = []
- for i in range(10):
- radius_values.append(20 + i)
-
- edgeimg, accum_array = hough_circles(img1, thresh, radius_values)
- cv2.imwrite('output/' + img_name + "_after_binary.png", edgeimg)
- # Findcircle
- hough_thresh = 70
- resultlist, resultimg = find_circles(img, accum_array, radius_values, hough_thresh)
-
- print(resultlist)
- cv2.imwrite('output/' + img_name + "_circles.png", resultimg)
-
-
- if __name__ == '__main__':
- sys.argv.append("coins")
- main(sys.argv[1:])
- # TODO
下面是我的运行结果:

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