LoG滤波器

一. LoG滤波器

        LoG 即 高斯-拉普拉斯（Laplacian of Gaussian）的缩写。为了防止拉普拉斯滤波器计算二次微分时使图像的噪声更加明显，所以先使用高斯滤波器使图像更加平滑，再使用拉普拉斯滤波器使图像的轮廓更加清晰。       

LoG 滤波器，s 代表高斯滤波的标准差 ↑

 

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二. 实验：LoG滤波器的实现及用于图像边缘检测

        实验中，我们先将BGR图像转换为灰度图像，再给灰度图像添加高斯噪声，再使用LoG滤波器对图像进行处理，最后输出处理结果

import cv2
import numpy as np

# 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

# add gaussian noise
def gasuss_noise(image, mean=0, var=0.001):
    '''
        添加高斯噪声
        mean : 均值
        var : 方差
    '''
    image = np.array(image/255, dtype=float)
    noise = np.random.normal(mean, var ** 0.5, image.shape)
    out = image + noise
    if out.min() < 0:
        low_clip = -1.
    else:
        low_clip = 0.
    out = np.clip(out, low_clip, 1.0)
    out = np.uint8(out*255)
    return out

# LoG filter
def LoG_filter(img, K_size=5, sigma=3):
    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] = gray.copy().astype(np.float)
    tmp = out.copy()

    # LoG 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] = (x ** 2 + y ** 2 - sigma ** 2) * np.exp( -(x ** 2 + y ** 2) / (2 * (sigma ** 2)))
    K /= (2 * np.pi * (sigma ** 6))
    K /= K.sum()

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

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

    return out


# Read image
img = cv2.imread("../paojie.jpg")

# grayscale
gray = BGR2GRAY(img)
# add gaussian noise
gray = gasuss_noise(gray)
# LoG filtering
out = LoG_filter(gray, K_size=5, sigma=3)

# Save result
cv2.imwrite("out_g_g.jpg",gray)
cv2.imshow("result_g_g",gray)
cv2.imwrite("out.jpg", out)
cv2.imshow("result", out)
cv2.waitKey(0)
cv2.destroyAllWindows()

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三. 实验结果：

图1：灰度图像添加高斯噪声后 ↑

 

图2：LoG滤波器对图1图像处理后 ↑

 

        从图像中可以观察到，LoG滤波器不仅有效地抑制了高斯噪声，还一定程度上增强了图像的边缘。

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四. 参考内容：

　　https://www.jianshu.com/p/c70be0cccd46