大地seo,广东seo推广费用,快速建手机网站,潜江资讯网一手机版标题自适应滤波器自适应局部降噪滤波器自适应中值滤波器自适应滤波器
自适应局部降噪滤波器
均值是计算平均值的区域上的平均灰度#xff0c;方差是该区域上的图像对比度 g(x,y)g(x, y)g(x,y)噪声图像在(x,y)(x, y)(x,y)处的值 ση2\sigma_{\eta}^2ση2 为噪声的方差方差是该区域上的图像对比度
g(x,y)g(x, y)g(x,y)噪声图像在(x,y)(x, y)(x,y)处的值 ση2\sigma_{\eta}^2ση2 为噪声的方差为常数需要通过估计得到 zˉSxy\bar{z}_{S_{xy}}zˉSxy 为局部平均灰度 σSxy2\sigma_{S_{xy}}^2σSxy2 为局部方差
f^(x,y)g(x,y)−ση2σSxy2[g(x,y)−zˉSxy](5.32)\hat{f}(x,y) g(x,y) - \frac{\sigma_{\eta} ^ 2 }{\sigma_{S_{xy}}^2} \big[ g(x,y) - \bar z_{S_{xy}}\big] \tag{5.32}f^(x,y)g(x,y)−σSxy2ση2[g(x,y)−zˉSxy](5.32)
当ση2ση2\sigma_{\eta}^2 \sigma_{\eta}^2ση2ση2 时将比率设置为1这样做会使得滤波器是非线性的但可阻止因缺少图像噪声方差的知识而产生无意义的结果即负灰度级。
若ση2\sigma_{\eta}^2ση2估计值太低时算法会因校正量小于就有的值而返回与原图像接近的图像。估计值太高会使得方差的比率在1.0处被水平与正常情况相比算法会更频繁地从图像中减去平均值。若允许为负值且最后重新标定图像则如前所述结果 将损失图像的动态范围。
整个图像的相关值 μn∑i0L−1(ri−m)np(ri)\mu_n \sum_{i0}^{L-1}(r_i -m)^n p(r_i)μn∑i0L−1(ri−m)np(ri) 为灰度值r相对于其均值同的第n阶矩 m∑i0L−1rip(ri)m \sum_{i0}^{L-1} r_i p(r_i)m∑i0L−1rip(ri) 均值 σ2μ2∑i0L−1(ri−m)2p(ri)\sigma^2 \mu_2 \sum_{i0}^{L-1}(r_i - m)^2 p(r_i)σ2μ2∑i0L−1(ri−m)2p(ri) 方差
邻域内的相关值 mSxy∑i0L−1riPSxy(ri)m_{S_{xy}} \sum_{i0}^{L-1} r_i P_{S_{xy}}(r_i)mSxy∑i0L−1riPSxy(ri) 均值 σSxy2μ2∑i0L−1(ri−mSxy)2PSxy(ri)\sigma_{S_{xy}}^2 \mu_2 \sum_{i0}^{L-1}(r_i - m_{S_{xy}})^2 P_{S_{xy}}(r_i)σSxy2μ2∑i0L−1(ri−mSxy)2PSxy(ri) 方差
def calculate_sigma_eta(image)::param image: input image:return: sigma eta of imagehist, bins np.histogram(image.flatten(), bins256, range[0, 256], densityTrue)r bins[:-1]m np.sum(r * hist)sigma np.sum((r - m)**2 * hist)return sigmadef calculate_sigma_sxy(block):param block: input blockreturn: sigma sxy of block#公式法hist, bins np.histogram(block.flatten(), bins256, range[0, 256], densityTrue)r bins[:-1]m (r * hist).sum()sigma ((r - m)**2 * hist).sum()#等价于
# m np.mean(block)
# sigma np.var(block)return sigma, mdef adaptive_local_denoise(image, kernel, sigma_eta1):adaptive local denoising math: $$\hat{f}(x,y) g(x,y) - \frac{\sigma_{\eta} ^ 2 }{\sigma_{S_{xy}}^2} \big[ g(x,y) - \bar z_{S_{xy}}\big]$$param: image: input image for denoisingparam: kernel: input kernel, actually only use kernel shape, just want to keep the format as mean filterreturn: image after adaptive local denoising epsilon 1e-8height, width image.shape[:2]m, n kernel.shape[:2]padding_h int((m -1)/2)padding_w int((n -1)/2)# 这样的填充方式可以奇数核或者偶数核都能正确填充image_pad np.pad(image, ((padding_h, m - 1 - padding_h), \(padding_w, n - 1 - padding_w)), modeedge)img_result np.zeros(image.shape)for i in range(height):for j in range(width):block image_pad[i:i m, j:j n]gxy image[i, j]z_sxy np.mean(block)sigma_sxy np.var(block)rate sigma_eta / (sigma_sxy epsilon)if rate 1:rate 1img_result[i, j] gxy - rate * (gxy - z_sxy)return img_result# 自适应局部降噪滤波器处理高斯噪声
img_ori cv2.imread(DIP_Figures/DIP3E_Original_Images_CH05/Fig0513(a)(ckt_gaussian_var_1000_mean_0).tif, 0) #直接读为灰度图像kernel np.ones([7, 7])
img_arithmentic_mean arithmentic_mean(img_ori, kernelkernel)
img_geometric_mean geometric_mean(img_ori, kernelkernel)
img_adaptive_local adaptive_local_denoise(img_ori, kernelkernel, sigma_eta1000)plt.figure(figsize(10, 10))plt.subplot(221), plt.imshow(img_ori, gray), plt.title(With Gaussian noise), plt.xticks([]),plt.yticks([])
plt.subplot(222), plt.imshow(img_arithmentic_mean, gray), plt.title(Arithmentic mean), plt.xticks([]),plt.yticks([])
plt.subplot(223), plt.imshow(img_geometric_mean, gray), plt.title(Geomentric mean), plt.xticks([]),plt.yticks([])
plt.subplot(224), plt.imshow(img_adaptive_local, gray), plt.title(Adaptive local denoise), plt.xticks([]),plt.yticks([])
plt.tight_layout()
plt.show()自适应中值滤波器
zmin是Sxyz_{\text{min}}是S_{xy}zmin是Sxy邻域中的最小灰度值zmax是Sxyz_{\text{max}}是S_{xy}zmax是Sxy邻域中的最大灰度值zmed是Sxyz_{\text{med}}是S_{xy}zmed是Sxy邻域中的中值 zxyz_{xy}zxy是坐标(x,y)(x,y)(x,y)处的灰度值SmaxS_{\text{max}}Smax是SxyS_{xy}Sxy允许的最大尺寸是大于1的奇正整数。
自适应中值滤波算法在点(x,y)(x, y)(x,y)处使用两个处理层次分别表示为层次AAA和层次BBB:
层次AAA: 若zminzmedzmaxz_{\text{min}} z_{\text{med}} z_{\text{max}}zminzmedzmax 则转到层次B 否则增SxyS_{xy}Sxy的尺寸 若Sxy≤SmaxS_{xy} \leq S_{\text{max}}Sxy≤Smax, 则重复层次A 否则输出zmedz_{\text{med}}zmed
层次BBB 若zminzxyzmaxz_{\text{min}} z_{xy} z_{\text{max}}zminzxyzmax则输出zxyz_{xy}zxy 否则输出 zmedz_{\text{med}}zmed
这算法有3个主要的目的去除椒盐冲激噪声平滑其他非常冲激噪声减少失真如目标边界的过度细化。该算法统计上认为zminz_{\text{min}}zmin和zmaxz_{\text{max}}zmax是区域SxyS_{xy}Sxy的“类冲激”噪声分量即使它们不是图像中的最小像素和最大像素值。
能很好的处理椒盐噪声但对高斯噪声不敏感
def adaptive_median_denoise(image, sxy3, smax7):adaptive median denoising param: image: input image for denoisingparam: sxy : minimum kernel sizeparam: smax : maximum kernel sizereturn: image after adaptive median denoising epsilon 1e-8height, width image.shape[:2]m, n smax, smaxpadding_h int((m -1)/2)padding_w int((n -1)/2)# 这样的填充方式可以奇数核或者偶数核都能正确填充image_pad np.pad(image, ((padding_h, m - 1 - padding_h), \(padding_w, n - 1 - padding_w)), modeedge)img_new np.zeros(image.shape)for i in range(padding_h, height padding_h):for j in range(padding_w, width padding_w):sxy 3 #每一轮都重置 k int(sxy/2)block image_pad[i-k:ik1, j-k:jk1]zxy image[i - padding_h][j - padding_w]zmin np.min(block)zmed np.median(block)zmax np.max(block)if zmin zmed zmax:if zmin zxy zmax:img_new[i - padding_h, j - padding_w] zxyelse:img_new[i - padding_h, j - padding_w] zmedelse:while True:sxy sxy 2k int(sxy / 2)if zmin zmed zmax or sxy smax:breakblock image_pad[i-k:ik1, j-k:jk1]zmed np.median(block)zmin np.min(block)zmax np.max(block)if zmin zmed zmax or sxy smax:if zmin zxy zmax:img_new[i - padding_h, j - padding_w] zxyelse:img_new[i - padding_h, j - padding_w] zmedreturn img_new# 自适中值滤波器处理椒盐噪声
img_ori cv2.imread(DIP_Figures/DIP3E_Original_Images_CH05/Fig0514(a)(ckt_saltpep_prob_pt25).tif, 0) #直接读为灰度图像kernel np.ones([7, 7])img_arithmentic_mean median_filter(img_ori, kernelkernel)
img_adaptive_median adaptive_median_denoise(img_ori)plt.figure(figsize(15, 10))
plt.subplot(231), plt.imshow(img_ori, gray), plt.title(Salt pepper noise), plt.xticks([]),plt.yticks([])
plt.subplot(232), plt.imshow(img_arithmentic_mean, gray), plt.title(Arithmentic mean), plt.xticks([]),plt.yticks([])
plt.subplot(233), plt.imshow(img_adaptive_median, gray), plt.title(Adaptive median), plt.xticks([]),plt.yticks([])
plt.tight_layout()
plt.show()# 自适中值滤波器处理高斯噪声
img_ori cv2.imread(DIP_Figures/DIP3E_Original_Images_CH05/Fig0513(a)(ckt_gaussian_var_1000_mean_0).tif, 0) #直接读为灰度图像kernel np.ones([7, 7])
img_arithmentic_mean median_filter(img_ori, kernelkernel)
img_adaptive_median adaptive_median_denoise(img_ori)plt.figure(figsize(15, 10))plt.subplot(231), plt.imshow(img_ori, gray), plt.title(With Gaussian noise), plt.xticks([]),plt.yticks([])
plt.subplot(232), plt.imshow(img_arithmentic_mean, gray), plt.title(Arithmentic mean), plt.xticks([]),plt.yticks([])
plt.subplot(233), plt.imshow(img_adaptive_median, gray), plt.title(Adaptive median), plt.xticks([]),plt.yticks([])
plt.tight_layout()
plt.show()
