Canny算法原理和应用

Canny算法的原理

• 使用高斯滤波器滤波

• 使用 Sobel 滤波器滤波获得在 x 和 y 方向上的输出，在此基础上求出梯度的强度和梯度的角度

edge为边缘强度，tan为梯度方向

上图表示的是中心点的梯度向量、方位角以及边缘方向（任一点的边缘与梯度向量正交）

• 对梯度角度进行量化处理

划重点：是沿着梯度方向对幅值进行非极大值抑制，而非边缘方向，这里初学者容易弄混。

例如：3*3区域内，边缘可以划分为垂直、水平、45°、135°4个方向，同样，梯度反向也为四个方向（与边缘方向正交）。因此为了进行非极大值，将所有可能的方向量化为4个方向，如下图：

量化后的情况可以总结为：

• 根据梯度角度对边缘强度进行非极大值抑制（Non-maximum suppression），使图像边缘变得更细

非极大值抑制算法：0°时取(x,y)、(x+1,y)、(x-1,y) 中的最大值，其它角度类似

• 使用滞后阈值对图像进行二值化处理，优化图像显示效果

1. 选取系数TH和TL，比率为2:1或3:1。（一般取TH=0.3或0.2,TL=0.1）；

b. 将小于低阈值的点抛弃，赋0；将大于高阈值的点立即标记（这些点为确定边缘点），赋1或255；

c. 将小于高阈值，大于低阈值的点使用8连通区域确定（即：只有与TH像素连接时才会被接受，成为边缘点，赋 1或255）

python算法实现

import cv2
import numpy as np
import matplotlib.pyplot as plt

def Canny(img):

    # Gray scale
    def BGR2GRAY(img):
        b = img[:, :, 0].copy()
        g = img[:, :, 1].copy()
        r = img[:, :, 2].copy()

        # Gray scale
        out = 0.2126 * r + 0.7152 * g + 0.0722 * b
        out = out.astype(np.uint8)

        return out


    # Gaussian filter for grayscale
    def gaussian_filter(img, K_size=3, sigma=1.4):

        if len(img.shape) == 3:
            H, W, C = img.shape
            gray = False
        else:
            img = np.expand_dims(img, axis=-1)
            H, W, C = img.shape
            gray = True

        ## Zero padding
        pad = K_size // 2
        out = np.zeros([H + pad * 2, W + pad * 2, C], dtype=np.float)
        out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)

        ## prepare Kernel
        K = np.zeros((K_size, K_size), dtype=np.float)
        for x in range(-pad, -pad + K_size):
            for y in range(-pad, -pad + K_size):
                K[y + pad, x + pad] = np.exp( - (x ** 2 + y ** 2) / (2 * sigma * sigma))
        #K /= (sigma * np.sqrt(2 * np.pi))
        K /= (2 * np.pi * sigma * sigma)
        K /= K.sum()

        tmp = out.copy()

        # filtering
        for y in range(H):
            for x in range(W):
                for c in range(C):
                    out[pad + y, pad + x, c] = np.sum(K * tmp[y : y + K_size, x : x + K_size, c])

        out = np.clip(out, 0, 255)
        out = out[pad : pad + H, pad : pad + W]
        out = out.astype(np.uint8)

        if gray:
            out = out[..., 0]

        return out


    # sobel filter
    def sobel_filter(img, K_size=3):
        if len(img.shape) == 3:
            H, W, C = img.shape
        else:
            H, W = img.shape

        # Zero padding
        pad = K_size // 2
        out = np.zeros((H + pad * 2, W + pad * 2), dtype=np.float)
        out[pad : pad + H, pad : pad + W] = img.copy().astype(np.float)
        tmp = out.copy()

        out_v = out.copy()
        out_h = out.copy()

        ## Sobel vertical
        Kv = [[1., 2., 1.],[0., 0., 0.], [-1., -2., -1.]]
        ## Sobel horizontal
        Kh = [[1., 0., -1.],[2., 0., -2.],[1., 0., -1.]]

        # filtering
        for y in range(H):
            for x in range(W):
                out_v[pad + y, pad + x] = np.sum(Kv * (tmp[y : y + K_size, x : x + K_size]))
                out_h[pad + y, pad + x] = np.sum(Kh * (tmp[y : y + K_size, x : x + K_size]))

        out_v = np.clip(out_v, 0, 255)
        out_h = np.clip(out_h, 0, 255)

        out_v = out_v[pad : pad + H, pad : pad + W]
        out_v = out_v.astype(np.uint8)
        out_h = out_h[pad : pad + H, pad : pad + W]
        out_h = out_h.astype(np.uint8)

        return out_v, out_h


    # get edge strength and edge angle
    def get_edge_angle(fx, fy):
        # get edge strength
        edge = np.sqrt(np.power(fx.astype(np.float32), 2) + np.power(fy.astype(np.float32), 2))
        edge = np.clip(edge, 0, 255)

        # make sure the denominator is not 0
        fx = np.maximum(fx, 1e-10)
        #fx[np.abs(fx) <= 1e-5] = 1e-5

        # get edge angle
        angle = np.arctan(fy / fx)

        return edge, angle


    # 将角度量化为0°、45°、90°、135°
    def angle_quantization(angle):
        angle = angle / np.pi * 180
        angle[angle < -22.5] = 180 + angle[angle < -22.5]
        _angle = np.zeros_like(angle, dtype=np.uint8)
        _angle[np.where((angle <= 22.5) | (angle > 157.5))] = 0
        _angle[np.where((angle > 22.5) & (angle <= 67.5))] = 45
        _angle[np.where((angle > 67.5) & (angle <= 112.5))] = 90
        _angle[np.where((angle > 112.5) & (angle <= 157.5))] = 135

        return _angle


    def non_maximum_suppression(angle, edge):
        H, W = angle.shape
        _edge = edge.copy()

        for y in range(H):
            for x in range(W):
                    if angle[y, x] == 0:
                            dx1, dy1, dx2, dy2 = -1, 0, 1, 0
                    elif angle[y, x] == 45:
                            dx1, dy1, dx2, dy2 = -1, 1, 1, -1
                    elif angle[y, x] == 90:
                            dx1, dy1, dx2, dy2 = 0, -1, 0, 1
                    elif angle[y, x] == 135:
                            dx1, dy1, dx2, dy2 = -1, -1, 1, 1
                    # 边界处理
                    if x == 0:
                            dx1 = max(dx1, 0)
                            dx2 = max(dx2, 0)
                    if x == W-1:
                            dx1 = min(dx1, 0)
                            dx2 = min(dx2, 0)
                    if y == 0:
                            dy1 = max(dy1, 0)
                            dy2 = max(dy2, 0)
                    if y == H-1:
                            dy1 = min(dy1, 0)
                            dy2 = min(dy2, 0)
                    # 如果不是最大值，则将这个位置像素值置为0
                    if max(max(edge[y, x], edge[y + dy1, x + dx1]), edge[y + dy2, x + dx2]) != edge[y, x]:
                            _edge[y, x] = 0

        return _edge


    # 滞后阈值处理二值化图像
    # > HT 的设为255，< LT 的设置0，介于它们两个中间的值，使用8邻域判断法
    def hysterisis(edge, HT=100, LT=30):
        H, W = edge.shape

        # Histeresis threshold
        edge[edge >= HT] = 255
        edge[edge <= LT] = 0

        _edge = np.zeros((H + 2, W + 2), dtype=np.float32)
        _edge[1 : H + 1, 1 : W + 1] = edge

        ## 8 - Nearest neighbor
        nn = np.array(((1., 1., 1.), (1., 0., 1.), (1., 1., 1.)), dtype=np.float32)

        for y in range(1, H+2):
                for x in range(1, W+2):
                        if _edge[y, x] < LT or _edge[y, x] > HT:
                                continue
                        if np.max(_edge[y-1:y+2, x-1:x+2] * nn) >= HT:
                                _edge[y, x] = 255
                        else:
                                _edge[y, x] = 0

        edge = _edge[1:H+1, 1:W+1]

        return edge

    # grayscale
    gray = BGR2GRAY(img)

    # gaussian filtering
    gaussian = gaussian_filter(gray, K_size=5, sigma=1.4)

    # sobel filtering
    fy, fx = sobel_filter(gaussian, K_size=3)

    # get edge strength, angle
    edge, angle = get_edge_angle(fx, fy)

    # angle quantization
    angle = angle_quantization(angle)

    # non maximum suppression
    edge = non_maximum_suppression(angle, edge)

    # hysterisis threshold
    out = hysterisis(edge, 80, 20)

    return out


if __name__ == '__main__':
    # Read image
    img = cv2.imread("../paojie.jpg").astype(np.float32)
    image = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY).astype(np.uint8)

    # Canny
    edge = Canny(img)

    out = edge.astype(np.uint8)

    # Save result
    cv2.imshow('src and canny', np.hstack((image, out)))
    cv2.waitKey(0)
    cv2.destroyAllWindows()

参考链接：

https://www.cnblogs.com/wojianxin/p/12533526.html

https://blog.csdn.net/weixin_40647819/article/details/91411424