柏濤濤，王茜娟，譚云蘭

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基于非下采樣Contourlet變換耦合近似度規(guī)則的多聚焦圖像融合算法

柏濤濤1，王茜娟2，*譚云蘭2

（1. 安徽廣播電視大學(xué)滁州分校，安徽，滁州 239000；2. 井岡山大學(xué)電子與信息工程學(xué)院，江西，吉安 343009）

當(dāng)前多聚焦圖像融合算法主要通過(guò)單一的比值取大法來(lái)完成高頻系數(shù)的融合，忽略了不同高頻系數(shù)間的近似度，導(dǎo)致融合圖像存在模糊效應(yīng)與塊效應(yīng)等不足，采用非下采樣Contourlet變換耦合近似度規(guī)則對(duì)多聚焦圖像進(jìn)行融合，來(lái)改善以上不足。利用非下采樣Contourlet變換對(duì)圖像進(jìn)行多尺度、多方向的分解，獲取圖像的高、低頻分解系數(shù)。利用圖像的區(qū)域能量對(duì)低頻系數(shù)的信息量進(jìn)行度量，構(gòu)造低頻系數(shù)融合函數(shù)，用于低頻系數(shù)融合。利用圖像的平均梯度差值對(duì)不同高頻系數(shù)的差異度進(jìn)行度量，建立近似度規(guī)則，根據(jù)不同高頻系數(shù)的近似度采用不同的融合方法獲取融合高頻系數(shù)。將融合后系數(shù)通過(guò)非下采樣Contourlet逆變換獲取最后融合圖像。仿真表明，所提算法與當(dāng)前多聚焦圖像融合方法相比，融合的圖像具有較好的質(zhì)量。

圖像融合；非下采樣contourlet變換；區(qū)域能量；平均梯度；近似度規(guī)則

0 引言

數(shù)字圖像因具有易于獲取、便于傳輸?shù)奶攸c(diǎn)，得到了廣泛的應(yīng)用[1-2]。雖然數(shù)字圖像獲取變得簡(jiǎn)單，但是受制于成像設(shè)備的技術(shù)及環(huán)境的限制，不能一次性獲取具有多個(gè)聚焦的圖像[3-4]。因此，為了獲取具有良好視覺(jué)效果的多聚焦圖像，就需要對(duì)不同聚焦的圖像進(jìn)行多聚焦圖像融合。

對(duì)此，本文將非下采樣Contourlet變換引入多聚焦圖像融合，利用其對(duì)圖像進(jìn)行分解，獲取圖像系數(shù)信息。通過(guò)低頻系數(shù)的區(qū)域能量特征，構(gòu)造低頻系數(shù)融合函數(shù)，獲取融合低頻系數(shù)。通過(guò)高頻系數(shù)的平均梯度特征，構(gòu)建近似度規(guī)則，獲取融合高頻系數(shù)。結(jié)果顯示，所提算法融合的圖像具有較好的空間特性，視覺(jué)效果較好。所提算法的主要貢獻(xiàn)在于：1）通過(guò)低頻系數(shù)的區(qū)域能量特征，構(gòu)造低頻系數(shù)融合函數(shù)，獲取融合低頻系數(shù)，避免了比值取大法帶來(lái)的融合弊端；2）利用高頻系數(shù)的平均梯度，建立相似度規(guī)則，從平均梯度差值出發(fā)，設(shè)計(jì)不同的高頻系數(shù)融合規(guī)則，獲取融合高頻系數(shù)，使得融合高頻系數(shù)能夠包含源圖的更多細(xì)節(jié)信息。

1 本文圖像融合算法設(shè)計(jì)

本文所提多聚焦圖像融合算法的流程圖如圖1所示。從圖1可見(jiàn)，所提算法首先通過(guò)非下采樣Contourlet變換對(duì)源圖像進(jìn)行精細(xì)的分解，使得獲取的高、低頻系數(shù)中能夠包含更多的源圖信息，以助于改善融合圖像的清晰度。通過(guò)低頻系數(shù)的區(qū)域能量特征，建立低頻系數(shù)融合函數(shù)，使得融合的低頻系數(shù)能夠包含更多的源圖能量，以提高融合圖像的質(zhì)量。最后通過(guò)高頻系數(shù)的平均梯度特征，建立近似度規(guī)則，對(duì)高頻系數(shù)進(jìn)行融合，使得融合高頻系數(shù)具有豐富的源圖邊緣等信息，進(jìn)一步提高了融合圖像的質(zhì)量。

圖1 本文多聚焦圖像融合算法的流程

1.1 非下采樣Contourlet變換

非下采樣Contourlet變換是依靠非下采樣塔式分解(Nonsubsampled Pyramid, NSP)與非下采樣濾波器組(Nonsubsampled Pyramid, Directional Filter Bank, NSDFB)對(duì)圖像進(jìn)行分解[12]。非下采樣contourlet變換對(duì)源圖分解過(guò)程示意圖如圖2所示[13]，依圖可見(jiàn)，源圖經(jīng)過(guò)NSP變換進(jìn)行多尺度分解獲取子圖后，再經(jīng)過(guò)NSDFB對(duì)高頻子圖進(jìn)行多方向分解，獲取分解系數(shù)。

圖2 非下采樣Contourlet變換的示意圖

1.2 低頻系數(shù)融合

低頻系數(shù)包含了源圖的主要能量，反應(yīng)了源圖的主要圖像信息[14]。圖像的區(qū)域能量能夠較好地表述不同低頻系數(shù)所含圖像信息的大小，區(qū)域能量越大表示低頻系數(shù)所含圖像信息越多，其越有優(yōu)勢(shì)。在此，將借助低頻系數(shù)的區(qū)域能量來(lái)完成低頻系數(shù)的融合。

1.3 高頻系數(shù)融合

通過(guò)近似度規(guī)則，可利用（5）式和（6）完成高頻系數(shù)的融合，從而輸出融合圖像。

2 實(shí)驗(yàn)結(jié)果

圖3 不同方法的融合結(jié)果

圖4 不同方法的融合結(jié)果

圖5 不同方法對(duì)亮度差異圖像的融合結(jié)果

（8）式中，p表示灰度級(jí)為的像素點(diǎn)所占的幾率[21]。

表1 圖3中不同方法融合圖像的量化測(cè)試結(jié)果

表2 圖4中不同方法融合圖像的量化測(cè)試結(jié)果

3 結(jié)論

本文將非下采樣Contourlet變換引入多聚焦圖像的融合，設(shè)計(jì)了非下采樣Contourlet變換耦合近似度規(guī)則的多聚焦圖像融合算法。利用具有平移不變性的非下采樣Contourlet變換，對(duì)源圖進(jìn)行多尺度、多方向的精細(xì)分解，獲取包含豐富源圖信息的高、低頻系數(shù)，提高了融合圖像所包含源圖信息的豐富度。通過(guò)區(qū)域能量特征獲取低頻融合系數(shù)，使得融合低頻系數(shù)能夠包含更多的源圖能量。利用高頻系數(shù)的平均梯度，建立相似度規(guī)則，從平均梯度差值出發(fā)，設(shè)計(jì)不同的高頻系數(shù)融合規(guī)則，獲取融合高頻系數(shù)，使得融合高頻系數(shù)能夠包含源圖的更多細(xì)節(jié)信息，提高了融合圖像的視覺(jué)效果。

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Multi Focus Image Fusion Algorithm Based on Nonsubsampled Contourlet Transform Coupling Approximation Rule

BAI Tao-tao1, WANG Xi-juan2

(1. Anhui radio and Television University, Chuzhou branch, Chuzhou, Anhui, 239000,China ; 2. Jinggangshan University, Ji’an Jiangxi, 343009, China)

Currently, most of the focus image fusion algorithms mainly use a single ratio to maximize the fusion of high-frequency coefficients, which ignores the approximation among different high-frequency coefficients, resulting in fuzziness and blocking effects in the fusion image. In this paper, a multi-focus image fusion algorithm based on the coupling approximation rule of non-downward contourlet transform is proposed. The non-downsampling contourlet transform is used to decompose the image in multi-scale and multi-direction to obtain the high and low frequency decomposition coefficients. The information of low-frequency coefficients is measured by the region energy of the image, and the fusion function of low-frequency coefficients is constructed for the fusion of low-frequency coefficients. The difference of different high frequency coefficients is measured by the mean gradient difference of the image, and the approximation rule is established. Different fusion methods are used according to the approximation of different high frequency coefficients to complete the fusion of high frequency coefficients. The fusion coefficients are acquired by the non - down sampling inverse transform to get the final fused image. Experimental results show that the proposed method has better image quality than the current multi-focus image fusion method.

image fusion;nonsubsampled contourlet transform; region energy; average gradient; approximation rule

1674-8085(2019)01-0039-06

TP391

A

10.3969/j.issn.1674-8085.2019.01.009

2018-11-07；

2018-12-19

江西省教育廳科學(xué)技術(shù)研究項(xiàng)目(GJJ160750)

柏濤濤(1982-)，男，安徽鳳陽(yáng)人，講師，碩士，主要從事圖像處理、計(jì)算機(jī)應(yīng)用技術(shù)、大數(shù)據(jù)技術(shù)等方面的研究(E-mail:AnhuiddBotaotao@126.com);

王茜娟(1976-)，女，江西吉安人，副教授，碩士，主要從事圖像處理、模式識(shí)別等方面的研究( E-mail: wxj1976@sina.com);

*譚云蘭(1972-)，女，江西新干人，副教授，博士，主要從事圖像處理、模式識(shí)別等方面的研究( E-mail: tanyunlan@163.com).