Python手动实现Hough圆变换的示例代码

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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