一：频域高通滤波

频域高通滤波：是一种基于频域表示的图像处理技术，用于增强或突出图像中高频成分的方法。它通过将图像转换到频域，应用高通滤波器来抑制或减弱低频成分，从而增强图像的边缘和细节

在频域中，可以设计各种类型的高通滤波器来实现不同的频率响应

（1）理想的高通滤波器

理想的高通滤波器：通过在频率域上施加一个截止频率，将低于该截止频率的成分完全抑制，而保留高于截止频率的成分。这种滤波器具有陡峭的截止特性，但会引入振铃效应

$$H(u,v)=\{\begin{array}{ll}0& D(u,v)\le D_0\\ 1& D(u,v)>D_0\end{array}$$

（2）巴特沃斯高通滤波器

巴特沃斯高通滤波器：提供了更平滑的频率过渡，并且没有振铃效应。它可以根据设计参数调整截止频率和滚降特性的斜率

$$H(u,v)=\frac{1}{1+{\left[D_0/D(u,v)\right]}^{2n}}$$

（3）指数高通滤波器

指数高通滤波器：基于指数函数的特性，在频域上实现对低频信号的抑制，从而提取图像的高频细节

$$H(u,v)=\exp \left\{-{\left[\frac{D_0}{D(u,v)}\right]}^u\right\}$$

（4）梯形高通滤波器

梯形高通滤波器：与其他高通滤波器不同，梯形高通滤波器的频率响应以梯形的形状逐渐减弱低频信号并保留高频信号

$$H(u,v)=\{\begin{array}{cc}0& D(u,v)<D_0\\ \frac{1}{D_1-D_0}\left[D(u,v)-D_0\right]& D_0\le D(u,v)\le D_1\\ 1& D(u,v)>D_1\end{array}$$

二：综合案例——人像美化

（1）设计思路

要求：尽可能地使皮肤变得平滑、白皙。采用所学基础处理方法实现题目要求

操作：

• 图像平滑处理，去除瑕疵
• 基于肤色模型的皮肤区域分割；
• 将原始图像的背景部分和平滑的皮肤图像进行融合；
• 对融合后的图像进行适度锐化

（2）各模块设计

主程序

平滑：双边滤波

皮肤区域分割

图像融合：将双边滤波后的图像提取肤色区域，原图提取背景区域，两图融合

图像锐化：p采用拉普拉斯算子锐化，锐化力度降为1/3

（3）程序

matlab实现：

clear,clc,close all;
ImageOrigin=im2double(imread('face8.jpg'));
figure,imshow(ImageOrigin),title('原图');
DBImage=DBfilt(ImageOrigin);SkinImage1=FirstFilter(ImageOrigin);            %%初步过滤
SkinArea=SecondFilter(SkinImage1);           %%YCgCr空间范围肤色检测SkinFuse=Fuse(ImageOrigin,DBImage,SkinArea);
SkinBeautify=Sharp(SkinFuse);function Out=DBfilt(In)[height,width,c] = size(In); win=15;       % 定义双边滤波窗口宽度  sigma_s=6; sigma_r=0.1; % 双边滤波的两个标准差参数  [X,Y] = meshgrid(-win:win,-win:win); Gs = exp(-(X.^2+Y.^2)/(2*sigma_s^2));%计算邻域内的空间权值    Out=zeros(height,width,c); for k=1:cfor j=1:height    for i=1:width  temp=In(max(j-win,1):min(j+win,height),max(i-win,1):min(i+win,width),k);Gr = exp(-(temp-In(j,i,k)).^2/(2*sigma_r^2));%计算灰度邻近权值        % W为空间权值Gs和灰度权值Gr的乘积       W = Gr.*Gs((max(j-win,1):min(j+win,height))-j+win+1,(max(i-win,1):min(i+win,width))-i+win+1);      Out(j,i,k)=sum(W(:).*temp(:))/sum(W(:));            endend  endfigure,imshow(Out),title('双边滤波');
end
function Out=FirstFilter(In)Out=In;[height,width,c] = size(In); IR=In(:,:,1); IG=In(:,:,2);IB=In(:,:,3);for j=1:heightfor i=1:widthif (IR(j,i)<160/255 && IG(j,i)<160/255 && IB(j,i)<160) && (IR(j,i)>IG(j,i) && IG(j,i)>IB(j,i))Out(j,i,:)=0;endif IR(j,i)+IG(j,i)>500/255Out(j,i,:)=0;endif IR(j,i)<70/255 && IG(j,i)<40/255 && IB(j,i)<20/255Out(j,i,:)=0;endendendfigure,imshow(Out);title('非肤色初步过滤'); 
end
function Out=SecondFilter(In)IR=In(:,:,1); IG=In(:,:,2);IB=In(:,:,3);       [height,width,c] = size(In);Out=zeros(height,width);for i=1:widthfor j=1:height  R=IR(j,i); G=IG(j,i); B=IB(j,i);       Cg=(-81.085)*R+(112)*G+(-30.915)*B+128;  Cr=(112)*R+(-93.786)*G+(-18.214)*B+128;         if Cg>=85 && Cg<=135 && Cr>=-Cg+260 && Cr<=-Cg+280       Out(j,i)=1;          endendendOut=medfilt2(Out,[3 3]);figure,imshow(Out),title('YCgCr空间范围肤色检测');    
endfunction Out=Fuse(ImageOrigin,DBImage,SkinArea)Skin=zeros(size(ImageOrigin));Skin(:,:,1)=SkinArea;   Skin(:,:,2)=SkinArea;  Skin(:,:,3)=SkinArea;Out=DBImage.*Skin+double(ImageOrigin).*(1-Skin);figure,imshow(Out);title('肤色与背景图像融合');
end
function Out=Sharp(In)H=[0 -1 0;-1 4 -1;0 -1 0]; %Laplacian锐化模板Out(:,:,:)=imfilter(In(:,:,:),H); Out=Out/3+In;
%     imwrite(Out,'man4.jpg');figure,imshow(Out),title('Laplacia锐化图像');
end

Python实现：

import cv2
import numpy as np
import matplotlib.pyplot as pltdef DBfilt(image):height, width, c = image.shapewin = 15sigma_s = 6sigma_r = 0.1X, Y = np.meshgrid(np.arange(-win, win + 1), np.arange(-win, win + 1))Gs = np.exp(-(X**2 + Y**2) / (2 * sigma_s**2))output = np.zeros((height, width, c))for k in range(c):for j in range(height):for i in range(width):temp = image[max(j - win, 0):min(j + win, height), max(i - win, 0):min(i + win, width), k]Gr = np.exp(-(temp - image[j, i, k])**2 / (2 * sigma_r**2))W = Gr * Gs[max(j - win, 0):min(j + win, height) - j + win + 1,max(i - win, 0):min(i + win, width) - i + win + 1]output[j, i, k] = np.sum(W * temp) / np.sum(W)return outputdef FirstFilter(image):output = np.copy(image)height, width, _ = image.shapeIR = image[:, :, 2]IG = image[:, :, 1]IB = image[:, :, 0]for j in range(height):for i in range(width):if (IR[j, i] < 160/255 and IG[j, i] < 160/255 and IB[j, i] < 160/255) and \(IR[j, i] > IG[j, i] and IG[j, i] > IB[j, i]):output[j, i, :] = 0if IR[j, i] + IG[j, i] > 500/255:output[j, i, :] = 0if IR[j, i] < 70/255 and IG[j, i] < 40/255 and IB[j, i] < 20/255:output[j, i, :] = 0return outputdef SecondFilter(image):height, width, _ = image.shapeIR = image[:, :, 2]IG = image[:, :, 1]IB = image[:, :, 0]output = np.zeros((height, width))for i in range(width):for j in range(height):R = IR[j, i]G = IG[j, i]B = IB[j, i]Cg = (-81.085) * R + (112) * G + (-30.915) * B + 128Cr = (112) * R + (-93.786) * G + (-18.214) * B + 128if Cg >= 85 and Cg <= 135 and Cr >= -Cg + 260 and Cr <= -Cg + 280:output[j, i] = 1output = cv2.medianBlur(output.astype(np.float32), 3)return outputdef Fuse(image, db_image, skin_area):skin = np.zeros(image.shape)skin[:, :, 0] = skin_areaskin[:, :, 1] = skin_areaskin[:, :, 2] = skin_areaoutput = db_image * skin + image * (1 - skin)return outputdef Sharp(image):kernel = np.array([[0, -1, 0], [-1, 4, -1], [0, -1, 0]], dtype=np.float32)output = cv2.filter2D(image, -1, kernel)output = output / 3 + imagereturn output# 读取图像
image_origin = cv2.imread('face8.jpg')
image_origin = cv2.cvtColor(image_origin, cv2.COLOR_BGR2RGB)
# 显示原图
plt.figure()
plt.imshow(image_origin)
plt.title('原图')
plt.axis('off')
# 双边滤波
db_image = DBfilt(image_origin)
# 初步过滤
skin_image1 = FirstFilter(image_origin)
plt.figure()
plt.imshow(skin_image1)
plt.title('非肤色初步过滤')
plt.axis('off')
# YCgCr空间范围肤色检测
skin_area = SecondFilter(skin_image1)
plt.figure()
plt.imshow(skin_area, cmap='gray')
plt.title('YCgCr空间范围肤色检测')
plt.axis('off')
# 肤色与背景图像融合
skin_fuse = Fuse(image_origin, db_image, skin_area)
plt.figure()
plt.imshow(skin_fuse)
plt.title('肤色与背景图像融合')
plt.axis('off')
# Laplacian锐化图像
skin_beautify = Sharp(skin_fuse)
plt.figure()
plt.imshow(skin_beautify)
plt.title('Laplacia锐化图像')
plt.axis('off')plt.show()