傅立叶变换在图像处理中的重要作用：

(A) 图像增强与图像去噪

绝大部分噪音都是图像的高频分量，通过低通滤波器来滤除高频噪声；边缘也是图像的高频分量，可以通过添加高频分量来增强原始图像的边缘；

(B) 图像分割与边缘检测

提取图像高频分量

(C) 图像特征提取

形状特征：傅里叶描述子

纹理特征：直接通过傅里叶系数来计算纹理特征

其他特征：将提取的特征值进行傅里叶变换来使特征具有平移、伸缩、旋转不变性

(D ) 图像压缩

可以直接通过傅里叶系数来压缩数据；常用的离散余弦变换是傅立叶变换的实变换；

-Fourier transform in the important role of image processing:

(A) image enhancement and image denoising

Most of all images of high frequency noise by low pass filter to filter out high frequency noise　edge is the image of the high frequency components can be enhanced by adding high frequency components to the edge of the original image　

(B) Image segmentation and edge detection

High frequency components extracted image

(C) image feature extraction

Shape features: Fourier descr iptors

Texture: directly through the Fourier coefficients to calculate the texture features

Other features: The characteristic value extracted by Fourier transform to the characteristics of translation, scaling, rotation invariance

(D) image compression

Fourier coefficients can be directly compressed data　commonly used discrete cosine transform is the Fourier transform of the real transformation　



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