### OpenCV 中 Canny 边缘检测算法实现 #### 高斯滤波器平滑处理 为了减少图像中的噪声并保留边缘信息，在应用Canny算子之前通常会先利用高斯滤波器对输入图片做预处理操作。这一步骤有助于提高后续阶段对于实际边界定位精度的同时也降低了误报率[^1]。 ```python import cv2 import numpy as np def gaussian_blur(image, kernel_size=(5, 5), sigma=0): """Apply Gaussian blur to an image.""" blurred_image = cv2.GaussianBlur(image, kernel_size, sigma) return blurred_image ``` #### 计算梯度幅值与方向 经过初步去噪后的灰度化处理过的单通道图像作为下一步运算的基础数据源；接着采用Sobel微分算子分别沿X轴Y轴两个方向上估算各点处的一阶偏导数值，并据此得出该位置对应的强度变化情况即所谓的“梯度”。此外还需记录下当前坐标的主导方位角以便于之后执行非最大抑制策略时能够更加精准地判断哪些地方才是真正的轮廓线所在之处[^2]。 ```python def compute_gradients(blurred_image): """Compute gradients using Sobel operator.""" grad_x = cv2.Sobel(blurred_image, ddepth=cv2.CV_64F, dx=1, dy=0, ksize=3) grad_y = cv2.Sobel(blurred_image, ddepth=cv2.CV_64F, dx=0, dy=1, ksize=3) magnitude = np.sqrt(grad_x ** 2 + grad_y ** 2) angle = np.arctan2(grad_y, grad_x) * (180 / np.pi) return magnitude, angle ``` #### 执行非极大值抑制 此环节旨在去除那些不属于局部极值点的候选边沿线段——具体做法是在每一个像素单元格内仅保留具有最强响应特征的那个方向上的连接关系而将其余竞争者统统抹掉，从而使得最终得到的结果更接近理想状态下的细长线条形式[^3]。 ```python def non_max_suppression(magnitude, angles): """Suppress pixels that are not local maxima along their gradient direction.""" suppressed = np.zeros_like(magnitude, dtype=np.uint8) for i in range(1, magnitude.shape[0]-1): for j in range(1, magnitude.shape[1]-1): # Quantize the angle into one of four possible directions. theta = angles[i,j] q = 255 r = 255 # ...省略部分代码... if ((theta >= -22.5 and theta <= 22.5) or \ (theta <= -157.5 and theta >= 157.5)): q = magnitude[i, j+1] r = magnitude[i, j-1] elif((theta > 22.5 and theta < 67.5) or \ (theta < -112.5 and theta > -157.5)): q = magnitude[i+1, j-1] r = magnitude[i-1, j+1] elif((theta >= 67.5 and theta <= 112.5) or \ (theta <= -67.5 and theta >= -112.5)): q = magnitude[i+1, j] r = magnitude[i-1, j] elif((theta > 112.5 and theta < 157.5) or \ (theta < -22.5 and theta > -67.5)): q = magnitude[i-1, j-1] r = magnitude[i+1, j+1] if (magnitude[i,j] >= q) and (magnitude[i,j] >= r): suppressed[i,j] = magnitude[i,j] return suppressed ``` #### 双阈值检测及边缘追踪 设定高低两档不同的判定标准用于区分强弱两类不同性质的边缘成分：当某个像素满足较高水平的要求则直接确认其属于有效轮廓的一部分；而对于介于两者之间的中间地带，则需进一步考察周围是否存在已知的确切边界点才能决定是否接纳它们加入到整体结构之中形成连续完整的路径[^4]。 ```python def hysteresis_thresholding(suppressed, low_ratio=0.09, high_ratio=0.17): """Perform double-threshold detection on edges.""" high_thresh = int(high_ratio * np.max(suppressed)) low_thresh = int(low_ratio * high_thresh) strong_edges = (suppressed >= high_thresh).astype(np.uint8)*255 weak_edges = ((suppressed >= low_thresh) & (suppressed < high_thresh)).astype(np.uint8)*100 final_edges = strong_edges.copy() while True: num_strong_prev = cv2.countNonZero(final_edges==255) final_edges =