第4章频率域滤波【数字图像处理课程精品PPT】
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© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
只使用相位重建
只使用谱重建
© 1992–2008 R. C. Gonzalez & R. E. Woods
用矩形的谱+ 妇女的相位重建
Digital Image Processing, 3rd ed.
Chapter 4
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
Chapter 4
Filtering in the Frequency Domain
一个简单函数的傅立叶变换
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
F(M/2,N/2)=:0
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
相位_正弦分量关于原点位移的角度
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
第四章 频率域滤波
© 1992–2008 R. C. Gonzalez & R. E. Woods
下面的函数曲线是
上面4条函数曲线之和。 Fourier在1807年认为： 周期函数可以表示为
Sines和Cosine的加权和。 这在当时倍受怀疑。
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
冲激函数-采样
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
使用DFT时二维图像固有的周期性
(a)图像扩展周期前的周期性 (b)图像扩展周期后的周期性
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
c→d:在空间域扩展周期后的变换效果
ຫໍສະໝຸດ Baidu
IDFT
© 1992–2008 R. C. Gonzalez & R. E. Woods
a与d比较
Digital Image Processing, 3rd ed.
Chapter 4
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
一个简单函数的二维傅立叶谱
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
取样
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
不同取样后的变换结果
© 1992–2008 R. C. Gonzalez & R. E. Woods
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Chapter 4
Filtering in the Frequency Domain
4.7 频率域滤波基础
Page 161
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Filtering in the Frequency Domain
幅度不变，相位角分别除2和除4的反变换效果
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Filtering in the Frequency Domain
周期信号引起卷积混叠的现象：
© 1992–2008 R. C. Gonzalez & R. E. Woods
j图实际上是由 e图的梯形复制 平移后叠加
Digital Image Processing, 3rd ed.
Chapter 4
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Filtering in the Frequency Domain
2D傅立叶变换性质小结
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
只使用相位重建
只使用谱重建
© 1992–2008 R. C. Gonzalez & R. E. Woods
用矩形的谱+ 妇女的相位重建
Digital Image Processing, 3rd ed.
Chapter 4
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
Chapter 4
Filtering in the Frequency Domain
一个简单函数的傅立叶变换
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
F(M/2,N/2)=:0
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
相位_正弦分量关于原点位移的角度
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
第四章 频率域滤波
© 1992–2008 R. C. Gonzalez & R. E. Woods
下面的函数曲线是
上面4条函数曲线之和。 Fourier在1807年认为： 周期函数可以表示为
Sines和Cosine的加权和。 这在当时倍受怀疑。
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
冲激函数-采样
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
使用DFT时二维图像固有的周期性
(a)图像扩展周期前的周期性 (b)图像扩展周期后的周期性
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
c→d:在空间域扩展周期后的变换效果
ຫໍສະໝຸດ Baidu
IDFT
© 1992–2008 R. C. Gonzalez & R. E. Woods
a与d比较
Digital Image Processing, 3rd ed.
Chapter 4
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
一个简单函数的二维傅立叶谱
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
取样
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
不同取样后的变换结果
© 1992–2008 R. C. Gonzalez & R. E. Woods
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Chapter 4
Filtering in the Frequency Domain
4.7 频率域滤波基础
Page 161
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Filtering in the Frequency Domain
幅度不变，相位角分别除2和除4的反变换效果
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Filtering in the Frequency Domain
周期信号引起卷积混叠的现象：
© 1992–2008 R. C. Gonzalez & R. E. Woods
j图实际上是由 e图的梯形复制 平移后叠加
Digital Image Processing, 3rd ed.
Chapter 4
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Filtering in the Frequency Domain
2D傅立叶变换性质小结
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods
Digital Image Processing, 3rd ed.
Chapter 4
Filtering in the Frequency Domain
© 1992–2008 R. C. Gonzalez & R. E. Woods