# Adaptive Bilateral Filter for Sharpness Enhancement and Noise

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```					Adaptive Bilateral Filter for
Sharpness Enhancement
and Noise Removal
IEEE Trans. Image Process., vol. 17, NO. 5,MAY 2008

2009.11.09
王韋弘
Outline
Introduction
Bilateral Filter
Role of in ξ the ABF
Role of in σr the ABF
Summary of the Rationale for the ABF
Results and Discussions
Introduction
• Purpose： 1、edge-preserving
2、de-noising

• Method：modifies the Bilateral Filter
Outline
Introduction
Bilateral Filter
Role of in ξ the ABF
Role of in σr the ABF
Summary of the Rationale for the ABF
Results and Discussions
Bilateral Filter
• shift-variant filtering：

•      ：restored image
•
----response at [m,n] to an impuse at [k,l]
Bilateral Filter

• σd , σr：the standard deviations of domain and range
Gaussian filter

•
Bilateral Filter

Blurred and noisy   Bilateral filter   Gaussian filter
σr=20, σd =2          σd =2
Bilateral Filter
Bilateral Filter

(a) the impulse response of the   (b)the impulse response of the range
domain Gaussian filter (σ d= 2)   Gaussian filter at the edge pixel A (σ r= 2)

(c) the impulse response of the    (d)the transfer function of (c) at pixel A
bilateral filter at pixel A
Bilateral Filter
Outline
Introduction
Bilateral Filter
Role of in ξ the ABF
Role of in σr the ABF
Summary of the Rationale for the ABF
Results and Discussions
• Bilateral filter

• ABF

• Some modifications：
an offset ξ is introduced to the range filter

both ξ and σr are locally adaptive

σd=1 be fixed
Outline
Introduction
Bilateral Filter
Role of in ξ the ABF
Role of in σr the ABF
Summary of the Rationale for the ABF
Results and Discussions
• A range filter shifted by the following choice for ξ.
• 25X25
• σd=1
• σr=20
Outline
Introduction
Bilateral Filter
Role of in ξ the ABF
Role of in σr the ABF
Summary of the Rationale for the ABF
Results and Discussions

DF：σd=1          RF：σr=5         BF： σd=1 、σr=5
• DF：domain filter only
• RF：range filter only
• BF：bilateral filter

DF：σd=1          RF：σr=50       BF： σd=1 、σr=50
• DF：domain filter only
• RF：range filter only
• BF：bilateral filter
Outline
Introduction
Bilateral Filter
Role of in ξ the ABF
Role of in σr the ABF
Summary of the Rationale for the ABF
Results and Discussions
• ξ is the key to slope restoration.
• The output is bounded between MIN(Ωm0,n0)
and MAX(Ω m0,n0).
• To smooth：shift RF towards MEAN (Ωm0,n0)
use a large σr
• To sharpen：shift RF away from the midpoint
use a small σr
Outline
Introduction
Bilateral Filter
Role of in ξ the ABF
Role of in σr the ABF
Summary of the Rationale for the ABF
Results and Discussions
Results and Discussions

ABF      OUM

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