自适应双边滤波器：锐化增强与降噪新方法

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"Adaptive Bilateral Filter for Sharpness Enhancement and Noise Removal" 本文介绍了一种用于图像锐化和降噪的自适应双边滤波器(Adaptive Bilateral Filter, ABF)。作者Buyue Zhang和Jan P. Allebach在2008年的IEEE Transactions on Image Processing期刊上发表的研究中，提出了一种全新的图像处理方法，该方法在增强图像边缘清晰度的同时，有效去除噪声。传统的未锐化掩蔽(Unsharp Mask, USM)技术通过对比度增强来实现图像锐化，但可能会导致过锐或欠锐的现象。而ABF则通过不同的机制实现边缘斜率的增强，它不涉及边缘检测、边缘方向估计或边缘轮廓提取，使得算法更为简洁且高效。 ABF的核心在于利用自适应的范围滤波器来调整直方图，从而增加边缘的斜率。这种处理方式可以在保持图像细节的同时，平滑噪声，对边缘和纹理进行有效的增强。值得注意的是，ABF的参数可以通过训练过程进行优化，确保了在锐化和降噪之间的平衡。与传统的USM方法相比，ABF恢复的图像在清晰度上有显著提升。ABF不仅能更有效地保留图像的边缘细节，还能避免USM可能导致的假象或失真问题。在实际应用中，这种自适应的双边滤波器对于图像处理和分析领域具有重要的意义，特别是在高噪声环境下的图像增强和恢复任务中。 ABF提供了一种新的思路来处理图像处理中的关键问题，即在保持图像原有细节的同时增强图像的清晰度并去除噪声。这一技术的创新之处在于其自适应性和对边缘处理的独特方式，使得它在实际应用中展现出优于传统方法的性能。对于图像处理和计算机视觉领域的研究者和开发者来说，理解并掌握ABF的原理和技术，可以极大地提升图像处理的质量和效率。

666 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 17, NO. 5, MAY 2008

compare it with that of the OUM and the bilateral ﬁlter. Finally,

we provide conclusions in Section VI.

II. B

ILATERAL

FILTER AND

ITS

PROPERTIES

The bilateral ﬁlter proposed by Tomasi and Manduchi in 1998

is a nonlinear ﬁlter that smoothes the noise while preserving

edge structures [23]. The shift-variant ﬁltering operation of the

bilateral ﬁlter is given by

(1)

where

is the restored image, is the

response at

to an impulse at , and

is the degraded image. For the bilateral ﬁlter, see (2),

shown at the bottom of the page, where

the center pixel of the window,

, and

are the standard deviations of the domain and range Gaussian

ﬁlters, respectively, and

(3)

is a normalization factor that assures that the ﬁlter preserves

average gray value in constant areas of the image.

The edge-preserving de-noising bilateral ﬁlter adopts a low-

pass Gaussian ﬁlter for both the domain ﬁlter and the range ﬁlter.

The domain low-pass Gaussian ﬁlter gives higher weight to

pixels that are spatially close to the center pixel. The range low-

pass Gaussian ﬁlter gives higher weight to pixels that are similar

to the center pixel in gray value. Combining the range ﬁlter and

the domain ﬁlter, a bilateral ﬁlter at an edge pixel becomes an

elongated Gaussian ﬁlter that is oriented along the edge. This

ensures that averaging is done mostly along the edge and is

greatly reduced in the gradient direction. This is the reason why

the bilateral ﬁlter can smooth the noise while preserving edge

structures.

Fig. 1(b) shows that a bilateral ﬁlter with

and

removes much of the noise that appears in the degraded image

shown in Fig. 1(a) and preserves the edge structures. In Fig. 1(c),

where the spatial domain Gaussian with

is applied alone,

the edges are signiﬁcantly blurred. The range ﬁlter with

at the edge pixel A is shown in Fig. 1(e). Combining the

spatial domain Gaussian ﬁlter [Fig. 1(d)] and the range Gaussian

ﬁlter [Fig. 1(e)] results in the bilateral ﬁlter at pixel A shown

in Fig. 1(f). The transfer function of the bilateral ﬁlter shown

in Fig. 1(g) demonstrates that the bilateral ﬁlter at pixel A is

low pass in one direction, and almost all-pass in the orthogonal

direction. This explains, from a frequency domain perspective,

why this ﬁlter is able to preserve edges while removing noise.

On the other hand, the bilateral ﬁlter is essentially a smoothing

ﬁlter. It does not sharpen edges. As shown in Fig. 1(h) and (i),

the edge rendered by the bilateral ﬁlter has the same level of

blurriness as in the original degraded image, although the noise

is greatly reduced.

The results of the bilateral ﬁltering are a signiﬁcant improve-

ment over a conventional linear low-pass ﬁlter. However, in

order to enhance the sharpness of an image, we need to make

some modiﬁcations to this ﬁlter.

III. A

DAPTIVE BILATERAL

FILTER

(ABF) FOR

IMAGE

SHARPENING AND

DE-NOISING

In this section, we present a new sharpening and smoothing

algorithm: the adaptive bilateral ﬁlter (ABF). The response at

of the proposed shift-variant ABF to an impulse at

is given by (4), shown at the bottom of the page, where

and are deﬁned as before, and the normaliza-

tion factor is given by

(5)

The ABF retains the general form of a bilateral ﬁlter, but

contains two important modiﬁcations. First, an offset

is in-

troduced to the range ﬁlter in the ABF. Second, both

and the

width of the range ﬁlter

in the ABF are locally adaptive. If

and is ﬁxed, the ABF will degenerate into a con-

ventional bilateral ﬁlter. For the domain ﬁlter, a ﬁxed low-pass

Gaussian ﬁlter with

is adopted in the ABF. The com-

bination of a locally adaptive

and transforms the bilateral

ﬁlter into a much more powerful ﬁlter that is capable of both

smoothing and sharpening. Moreover, it sharpens an image by

increasing the slope of the edges. To understand how the ABF

works, we need to understand the role of

and in the ABF.

else

(2)

else

(4)

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