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4 頻域之影像強化

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4 頻域之影像強化. 4.1 背景介紹 4.2 頻域與傅立葉轉換 4.3 頻域平滑化濾波器 4.4 頻域銳化濾波器 4.5 同態濾波. 4.1 背景介紹. 傅立葉序列與傅立葉轉換. 4.2 頻域與傅立葉轉換. 一維傅立葉轉換與反轉換 定義連續函數 f(x) 的傅立葉轉換如下 其反轉換為以上兩式稱為傅立葉轉換偶 (Fourier Transform Pair) ，其中 j = √-1 ， f(x) 為連續可積分函數， F(u) 為可積分函數。就影像處理而言， f(x) 經常為實數函數， F(u) 則一般為複數函數

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## 4 頻域之影像強化

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### 4 頻域之影像強化

4.1 背景介紹

4.2 頻域與傅立葉轉換

4.3 頻域平滑化濾波器

4.4 頻域銳化濾波器

4.5 同態濾波

4.1 背景介紹
• 傅立葉序列與傅立葉轉換
4.2 頻域與傅立葉轉換

F(u) = R(u) + j I(u)

(1)如(4.2.21)式對原影像乘上(-1)x+y，將轉換後

(2)將步驟(1)所得之影像進行DFT，求得F(u,v)。

(3)對F(u,v)乘上一過濾器函數H(u,v)。

G(u,v)=H(u,v)F(u,v)

(4)將步驟(3)所得之結果進行DFT反轉換。

Filtered image=F-1|G(u,v)|

(5)取得步驟(4)所得結果之實數部。

(6)將步驟(5)所得結果乘上(-1)x+y

“複製”該函數在脈衝函數所在位置的函數值

4.3 頻域平滑化濾波器

G(u,v)=H(u,v)F(u,v)

– H(u,v)為零相位偏離濾波器(Zero-phase-shift

Filter)

Butterworth低通濾波器

Butterworth低通濾波器(BLPF)

4.4 頻域銳化濾波器

4.5 同態(Homomorphic)濾波

Brightness range compression及Contrast

enhancement

f(x,y) = i(x,y) r(x,y)

i(x,y): slow spatial variation low frequencies

dynamic range

r(x,y): abrupt spatial variation high frequency

contrast