基于分数阶小波与引导滤波的多聚焦图像融合方法

doi:10.11996/JG.j.2095-302X.2023010077

图学学报 ›› 2023, Vol. 44 ›› Issue (1): 77-87.DOI: 10.11996/JG.j.2095-302X.2023010077

• 图像处理与计算机视觉 • 上一篇下一篇

基于分数阶小波与引导滤波的多聚焦图像融合方法

张晨阳(), 曹艳华, 杨晓忠()

华北电力大学数理学院信息与计算研究所，北京 102206

收稿日期:2022-05-21 修回日期:2022-10-12 出版日期:2023-10-31 发布日期:2023-02-16
通讯作者: 杨晓忠
作者简介:张晨阳(1999-)，女，硕士研究生。主要研究方向为数字图像处理。E-mail：793637218@qq.com
基金资助:
国家自然科学基金项目(11371135);中央高校基本科研业务费专项基金项目(2021MS045)

Multi-focus image fusion method based on fractional wavelet combined with guided filtering

ZHANG Chen-yang(), CAO Yan-hua, YANG Xiao-zhong()

Institute of Information and Computation, School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

Received:2022-05-21 Revised:2022-10-12 Online:2023-10-31 Published:2023-02-16
Contact: YANG Xiao-zhong
About author:ZHANG Chen-yang (1999-), master student. Her main research interest covers digital image processing. E-mail：793637218@qq.com
Supported by:
National Natural Science Foundation of China(11371135);Fundamental Research Funds for the Central Universities(2021MS045)

摘要/Abstract

摘要：

针对多聚焦图像融合中存在易丢失细节信息、图像边缘处产生伪影等问题，提出了一种基于离散分数阶小波变换(DFRWT)结合引导滤波的多聚焦图像融合新方法。首先，采用DFRWT将多聚焦源图像进行多尺度分解，得到低频部分与高频部分。其次，为了使图像信息有效地融合，根据小波模系数的能量在不同阶数下的分布特征，选取最适合分数阶阶数，在低频部分应用拉普拉斯能量并获得初始决策，再用引导滤波修正决策图得到融合规则；高频部分采用分数阶空间频率的融合规则。最后，通过DFRWT逆变换获得融合后的图像。新方法与现有5种算法进行视觉对比和定量评估，仿真实验表明，本文方法有效抑制了Gibbs效应和边缘处的伪影效应，视觉效果和客观评价均令人满意，融合图像的质量优于已有的几类经典算法。

关键词: 多聚焦图像融合, 离散分数阶小波变换, 引导滤波, 分数阶空间频率

Abstract:

To address the problems of losing details and producing artifacts at image edges in multi-focus image fusion, a new multi-focus image fusion method was proposed based on discrete fractional wavelet transform (DFRWT) combined with guided filtering. First, DFRWT was utilized to decompose the source images at multiple scales, obtaining the low frequency part and high frequency part. Then, in light of the energy distribution traits of wavelet modulus coefficients at different orders, the most suitable fractional order was selected. In the low frequency part, the initial decision was obtained by applying the Laplacian energy sum, and then the fusion rule was yielded by modifying the decision graph with guided filtering. For the high frequency part, the fractional spatial frequency fusion rule was adopted. Such rules, which can improve the efficiency of the image information on fusion. Lastly, the inverse DFRWT processing was carried out to obtain the composite image. The new method was compared with the existing five algorithms for visual comparison experiments and quantitative evaluation. The simulation experiments show that the proposed method could effectively suppress Gibbs effects and edge artifacts effects. The validity and advantages of the proposed method were verified in terms of the visual effect and objective evaluation, outperforming several classical algorithms in the quality of image fusion.

Key words: multi-focus image fusion, discrete fractional wavelet transform, guided filtering, fractional spatial frequency

中图分类号:

TP391.41

张晨阳, 曹艳华, 杨晓忠. 基于分数阶小波与引导滤波的多聚焦图像融合方法[J]. 图学学报, 2023, 44(1): 77-87.

ZHANG Chen-yang, CAO Yan-hua, YANG Xiao-zhong. Multi-focus image fusion method based on fractional wavelet combined with guided filtering[J]. Journal of Graphics, 2023, 44(1): 77-87.

图/表 9

图1 二层DFRWT分解系数图(p=1) ((a)一层近似分量；(b)一层细节分量；(c)二层近似分量；(d)二层细节分量)

Fig. 1 Two-level DFRWT decomposition coefficient diagram (p=1) ((a) Approximate component of the first layer; (b) Detail component of the first layer; (c) Approximate component of the second layer; (d) Detail component of the second layer)

图2 二层DFRWT分解系数图(p=0.5) ((a)一层近似分量；(b)一层细节分量；(c)二层近似分量；(d)二层细节分量)

Fig. 2 Two-layer DFRWT decomposition coefficient diagram (p=0.5) ((a) Approximate component of the first layer; (b) Detail component of the first layer; (c) Approximate component of the second layer; (d) Detail component of the second layer)

图3 Lena图像一层DFRWT分解结果((a) p=1；(b) p=0.9；(c) p=0.7；(d) p=0.5；(e) p=0.1；(f)原图与重构)

Fig. 3 DFRWT decomposition results of the first-layer about Lena image ((a) p=1; (b) p=0.9; (c) p=0.7; (d) p=0.5; (e) p=0.1; (f) Original image and reconstructed image)

图4 引导滤波平滑效果图((a)原图；(b) ε=0.01；(c) ε=0.04；(d) ε=0.16)

Fig. 4 Smoothing effect images of guided filtering ((a) Original image; (b) ε=0.01; (c) ε=0.04; (d) ε=0.16)

图5 源图像((a) Clock左聚焦图像；(b) Clock右聚焦图像；(c) Pepsi左聚焦图像；(d) Pepsi右聚焦图像；(e) Peppers前聚焦图像；(f) Peppers后聚焦图像)

Fig. 5 Source images ((a) Clock left focused image; (b) Clock right focused image; (c) Pepsi left focuesd image; (d) Pepsi right focuesd image; (e) Peppers pre-focused image; (f) Peppers post-focused image)

图6 实验1结果

Fig. 6 Results of experiment 1 ((a) L_P; (b) DWT; (c) PCNN; (d) NSCT; (e) DFRWT; (f) Ours)

图7 实验2结果

Fig. 7 Results of experiment 2 ((a) L_P; (b) DWT; (c) PCNN; (d) NSCT; (e) DFRWT; (f) Ours)

图8 实验3结果

Fig. 8 Results of experiment 3 ((a) L_P; (b) DWT; (c) PCNN; (d) NSCT; (e) DFRWT; (f) Ours)

表1 图像融合客观评价结果

Table 1 Objective evaluation results of image fusion

实验及指标				融合方法
实验及指标	L_P^[1]	DWT^[8]	PCNN^[25]	NSCT^[26]	DFRWT_var^[27]	本文方法
实验1					p=0.4	p=0.5
MI	4.533 1	4.653 8	4.742 9	4.813 9	4.756 4	5.120 8
Q_AB/F	0.520 6	0.607 2	0.654 0	0.675 2	0.693 7	0.740 8
SF	5.983 6	6.535 0	7.687 8	7.976 2	8.877 9	9.097 8
实验2					p=0.6	p=0.5
MI	4.7323	4.949 5	4.707 4	5.015 2	4.838 4	5.103 7
Q_AB/F	0.551 0	0.651 5	0.621 9	0.698 1	0.654 8	0.736 1
SF	5.468 7	6.434 9	6.242 3	7.034 6	7.259 1	8.216 9
实验3					p=0.6	p=0.4
MI	4.767 4	4.810 2	4.623 0	4.922 8	4.773 7	5.018 6
Q_AB/F	0.601 9	0.669 4	0.611 7	0.681 7	0.643 3	0.698 4
SF	7.598 3	7.328 4	8.610 3	9.033 1	10.316 2	12.658 8

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基于分数阶小波与引导滤波的多聚焦图像融合方法

Multi-focus image fusion method based on fractional wavelet combined with guided filtering

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