sensors Article

Improved Wallis Dodging Algorithm for Large-Scale Super-Resolution Reconstruction Remote Sensing Images Chong Fan 1,2 , Xushuai Chen 1, *, Lei Zhong 1 , Min Zhou 1,3 , Yun Shi 4 and Yulin Duan 4, * 1 2 3 4

*

School of Geoscience & Info-Physics, Central South University, Changsha 410083, China; [email protected] (C.F.); [email protected] (L.Z.); [email protected] (M.Z.) State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China Geomatics Engineering Investigation of China Gezhouba Group Co., Ltd., Yichang 443000, China Institute of Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100083, China; [email protected] Correspondence: [email protected] (X.C.); [email protected] (Y.D.); Tel.: +86-185-6953-8834 (X.C.); +86-188-1052-1973 (Y.D.)

Academic Editor: Assefa M. Melesse Received: 5 December 2016; Accepted: 16 March 2017; Published: 18 March 2017

Abstract: A sub-block algorithm is usually applied in the super-resolution (SR) reconstruction of images because of limitations in computer memory. However, the sub-block SR images can hardly achieve a seamless image mosaicking because of the uneven distribution of brightness and contrast among these sub-blocks. An effectively improved weighted Wallis dodging algorithm is proposed, aiming at the characteristic that SR reconstructed images are gray images with the same size and overlapping region. This algorithm can achieve consistency of image brightness and contrast. Meanwhile, a weighted adjustment sequence is presented to avoid the spatial propagation and accumulation of errors and the loss of image information caused by excessive computation. A seam line elimination method can share the partial dislocation in the seam line to the entire overlapping region with a smooth transition effect. Subsequently, the improved method is employed to remove the uneven illumination for 900 SR reconstructed images of ZY-3. Then, the overlapping image mosaic method is adopted to accomplish a seamless image mosaic based on the optimal seam line. Keywords: super-resolution reconstruction; large-scale image; Wallis dodging; overlapping region; optimal seam line; seam elimination

1. Introduction Remote sensing (RS) images are increasingly being used in agriculture, mainly in the monitoring of crops, resources, and disasters. In particular, high-resolution RS images play a significant role in agriculture, aiding with the development of agricultural production and research into the fine and quantitative stage. However, high-resolution images are generally quite expensive. Super-resolution (SR) image reconstruction is a technique that recovers a high-resolution image from several low-resolution images using the non-redundant information among them [1,2]. A sub-block algorithm is usually used in the SR reconstruction of images to improve the operation efficiency and reduce the consumption of computer memory. The continuity and correlation between blocks are ignored, particularly at the block junctions. The gray-level distribution will always be discontinuous, resulting in inconsistent color of the large-scale mosaic image. In other words, the brightness and contrast distribution of images are uneven and an obvious seam line is observed [3]. Therefore, the color differences among images should be diminished before image mosaicking. Sensors 2017, 17, 623; doi:10.3390/s17030623

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The uneven illumination phenomenon of RS images, which directly affects the quality of images and leads the mosaic result to exhibit obvious differences in luminance or color [4], is a significant problem in image processing. To date, two kinds of dodging processing algorithms exist, depending on the number of images involved. Mask dodging [5,6], retinex uniform light [7,8], and homomorphic filtering dodging [9,10] ensure color balance inside a single image, whereas histogram matching, dodging based on information entropy, and Wallis filter-based dodging deal with the color difference between images. Histogram matching [11–14] is able to reduce the difference in brightness and hue among image objects by correcting the shape of the histogram. However, this method adjusts the mean and variance to fit both the reference and target images by directly changing the histogram shape. Different internal features of images reflect the differences in the histogram shape of the image. Thus, if the difference is large, histogram matching may change the relative distance between gray levels, leading to color deviation of an image with different internal features. The dodging method based on information entropy eliminates or weakens the color difference through entropy mapping, whose theory is that two images have the same amount of information in the overlapping region. The Wallis filter is usually used to adjust the gray mean and variance of images to a given level, as its effectiveness and many improvements are put forward by researchers. Zhang Li investigated the principles and characteristics of the Wallis filter and determined that the Wallis filter, which has a local adaptive function, can enhance the contrast of images while suppressing noise [15]. On this basis, Li De-ren proposed a dodging approach for multiple images with the Wallis filter by adjusting the mean and variance of the image, which relies on the linear transfer relationship and causes color deviation of images that are far from the reference image [6]. Aiming at the characteristics of a large-scale seamless image database, an improved color balance method, which considers local and global information according to the Wallis adaptive filter, was proposed by Wang Mi. Not only can this method solve the color balance problem effectively, but it can also preserve radiometric resolution easily [16]. Zhang Deng-rong employed a whole-image color adjustment based on the Wallis transformation in the color adjustment step, and separately adopted a weighted smoothing method based on the optimal seam line and a compulsion correction method according to the size of the overlap area [17]. Zhou Li-ya presented a single image based on the Wallis filter-based dodging algorithm, which achieved single-image dodging through reasonable blocking and automatically achieving the statistics of the mean and variance [18]. Wang Ye and Zhang Han-song selected the Wallis filter parameters using the optimal index factor, and improved the Wallis dodging algorithm based on the moment matching balancing algorithm [19]. Chen Ke obtained large-scale seamless DOM (digital orthophoto map) data and disposed of the problem of consistency by using two algorithms. One is the dodging method for a single image based on the Gaussian filter, the other is the uniform color for multiple images based on the Wallis filter [20]. Luo Si proposed an improved dodging algorithm based on the Wallis principle, which can achieve illumination consistency and contrast effectively [21]. Tian Jin-yan developed a seam elimination approach for unmanned aerial vehicle images based on Wallis dodging, which was introduced to adjust the difference of brightness between the matched images and Gaussian distance weight enhancement that can fuse the two matched images in the overlapping region [22]. The existing Wallis dodging algorithm is only suitable for keeping the color and brightness consistency between two images or a few images, whose parameters usually depend on the selected standard image from the original images, which has many different criteria. However, for large format images, the uneven distribution of brightness and contrast cannot be removed completely because of the propagation of errors. In view of the aforementioned problems, this study proposes an innovative color adjustment and smoothness transition method, which successfully achieves color consistency processing and a seamless image mosaic. The improved Wallis dodging algorithm mainly has two improvements: (1) A weighted method is used to calculate the Wallis filter parameters for each image. (2) A new method of weighted iteration of adjacent images is proposed to eliminate the spatial transfer error caused during large-scale image adjustment.

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2. Methodology 2.1. Super-Resolution Reconstruction Image SR reconstruction, which was first proposed by Harris and Goodman in the 1960s, is the process of producing one or a series of high-resolution image(s) by exploiting hidden information from one or a sequence of low-resolution original image(s). Generally, SR methods can be divided into two categories, namely, frequency domain method and spatial domain method [23,24]. A classical approach of minimizing a regularized energy function, which is invulnerable to noise, is adopted in this study [25]. The complete energy function with four terms takes the following form: K

E ( f , h) =

∑ ||DHk f − gk ||2 + αQ(f) + β1 R(h) + β2 Q(h)

(1)

k=1

The first term measures fidelity to the data. The remaining three terms, i.e., α, β 1 , and β 2 , are regularization terms with positive weighting constants that attract the minimum of E to an admissible set of solutions. Q(f) is a smoothing term used to suppress noise in low-resolution images. The point spread function regularization term R(h) directly follows from the conclusions of the previous section. Q(h) assumes that the fuzzy function is a smooth variation. 2.2. Wallis Dodging The Wallis filter is actually a local image transform, which ensures that the standard deviations and means of the image at different locations are approximately equal. This phenomenon produces good local contrast throughout the image, while reducing the overall contrast between bright and dark areas. The small amount of gray information of the image is enhanced [18], which ensures that the Wallis filter has a special effect on images with low contrast. The Wallis dodging algorithm can be used to modify the brightness and contrast of multiple images. According to the statistical mean and variance of the selected reference image, the linear distribution of the gray level of the target image is adjusted by the Wallis filter using Equation (2): f ( x, y) = (k( x, y) − mk )α + β

(2)

where k ( x, y) is the gray value of the target image, f ( x, y) is the gray value of the results of Wallis dodging, and α and β are multiplicative and additive coefficients, which can be calculated using Equation (3): ( c sf α = c s +(1− c)s f k (3) β = bm f + (1 − b)mk where mk and sk are the mean and standard deviation of the target image, m f and s f are the mean and standard deviation of the reference image, c ∈ [0,1] is the expansion coefficient for the variance value, and b ∈ [0,1] is the luminance coefficient for the mean value. The mean of the image is close to m f when b tends to 1, whereas the mean is close to mk when b tends to 0. The equation of the classical Wallis transform is expressed in Equation (4), where the parameters (b and c) are equal to 1: f ( x, y) = (k( x, y) − mk ) ×

sf + mf sk

(4)

In general, Wallis dodging involves two images (i.e., the reference and target images). When several images are obtained, the images should be dealt with individually. Four processing sequences are mainly used to adjust the color of multiple images, as shown in Figure 1. Each image is adjusted based on its adjacent left or upper image, as shown in Figure 1a,b. Another method is shown in Figure 1c. The images, except those located on the boundary of the block images, are adjusted twice. An adjustment method based on the four-fork tree is proposed according to the idea

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of quadtree coding [26]. Four adjacent images are defined as child nodes. Four child nodes form 2017, 17, 623 4 of 19 the parentSensors node. Then, four parent nodes are calculated to complete the entire image processing. The correlation between adjacent images is considered in this method, and the suture four parent nodes are calculated to complete the entire image processing. The correlation between transition images is considered in this method, and the suture transition processingresults method of [27,28] processingadjacent method [27,28] is used for color images. Although the processing the is method are images. Although the processing results of methodby arethe unaffected by the unaffectedused by for thecolor processing order [29], this method is the limited number of processing images. The small order [29], this method is limited by the number of images. The small block may lose a considerable block may lose a considerable amount of gray-level information because of multiple computations. amount of gray-level information because of multiple computations.

(a)

(b)

(c)

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Figure 1. Schematic diagram of the sequence of image adjustment: (a) left image benchmark; (b) above

Figure 1. Schematic diagram of image the sequence adjustment: (a) left image benchmark; (b) above image benchmark; (c) left cross; and of (d)image quadtree. image benchmark; (c) left image cross; and (d) quadtree. 2.3. Seam Elimination

2.3. Seam Elimination Seam lines are often apparent between parts when RS images are combined in image mosaicking. The seam lines are caused by gray-level differences because of the different conditions

Seamunder lines which are often apparent between when RS differences images are inamong imagethe mosaicking. the parts were recorded. In parts this study, slight arecombined still observed thecaused overlapping region of the adjacent images after the Wallis dodging conditions processing. As a The seam tones lines in are by gray-level differences because of the different under which result, an obvious stitching line of the image mosaicking result, which reduces the visual quality and the parts were recorded. In this study, slight differences are still observed among the tones in the application value of the image, is observed. Thus, seam line removal is indispensable to ensure a overlapping region of the adjacent images after the Wallis dodging processing. As a result, an obvious smooth gray-level transition in the overlapping region of two adjacent images. Two categories of stitching line theremoval imagemethods mosaicking result,one which reduces thetransform visual quality andtheapplication value seamofline are available: is based on wavelet [30,31] and other is basedison overlappingThus, imageseam [32]. The theory of the is seam line removal method baseda on waveletgray-level of the image, observed. line removal indispensable to ensure smooth is rigorous. However, methodimages. is difficultTwo and the requirement computer transition transform in the overlapping regionachieving of two this adjacent categories ofofseam line removal memory is high. The seam line removal method based on overlapping image is simple and widely methods are available: one is based on wavelet transform [30,31] and the other is based on overlapping used to achieve smooth transition in the overlapping region. In this method, the gray value of each image [32]. The theory of of the line removalaccording methodto based wavelet transform is rigorous. pixel at the two sides theseam seam line is corrected the grayon difference between two pixels at the same position at a certain extent ofand the overlapping areas, asofshown in Equation (7). The closer The seam However, achieving this method is difficult the requirement computer memory is high. the pixel is to the seam line, the larger the correction is. line removal method based on overlapping image value is simple and widely used to achieve smooth (𝐼𝐵𝑖 − 𝐼𝐴𝑖the ) × Kgray 𝐼𝑖 = 𝐼𝐴𝑖 + transition in the overlapping region. In this method, value of each pixel at the two sides of i the seam line is corrected according to the gray difference between two pixels at the same(7)position at i Ki = 0≦i≦W−1 W a certain extent of the overlapping areas, as shown in Equation (5). The closer the pixel is to the seam wherethe 𝐼𝑖 denotes the gray valueis.of the pixel after processing; 𝐼𝐴𝑖 and 𝐼𝐵𝑖 are the pixel gray values line, the larger correction value of the two-scene image mosaicking in the overlapping area; W is the gray smooth width, which is less Ii = I Aiarea; + ( IB I Athe Ki which shows a linear inverse than the width of the image overlapping and K is weight, i− i) × (5) variation in the smooth range. i Ki = 0 5 i how 5 Weffectively −1 The location of the seam line critically influences any two data sets can be W merged. The bisector of the overlapping area can be used as the seam line. However, its effect is not ideal. Thus, searching for a curve as the optimal seam line in the overlapping twopixel adjacent where Ii denotes the gray value of the pixel after processing; I Ai andarea, IBi where are the gray values images have the mosaicking minimum difference, usually necessary. seam line searching of the two-scene image in the is overlapping area;Many W is optimal the gray smooth width, which is methods have developed in the literature, Dijkstra’s algorithm-based methods [33– inverse less than the width of been the image overlapping area;including and K is the weight, which shows a linear 35], dynamic programming-based methods [36–38], and graph-cuts-based methods [39,40]. Ancillary variation in the smooth range. data is also applied to detect the seam line in some algorithms, such as digital surface model, vector The location of the seam critically how effectively any two data can be roads, building map, and line lidar point cloudsinfluences [41–43]. In this study, a minimum connected path sets is sought by certain based on the difference of images. This createdline. by theHowever, differences of merged. The bisector ofcriteria the overlapping area can be used aspath theisseam its effect is gray searching values in thefor overlapping not ideal. the Thus, a curvearea. as the optimal seam line in the overlapping area, where two

adjacent images have the minimum difference, is usually necessary. Many optimal seam line searching methods have been developed in the literature, including Dijkstra’s algorithm-based methods [33–35], dynamic programming-based methods [36–38], and graph-cuts-based methods [39,40]. Ancillary data is also applied to detect the seam line in some algorithms, such as digital surface model, vector roads, building map, and lidar point clouds [41–43]. In this study, a minimum connected path is sought by certain criteria based on the difference of images. This path is created by the differences of the gray values in the overlapping area.

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An experiment with two images which exhibit significant gray-level difference,5 ofas Sensors 2017, 17, 623 19 shown in Figure 2a,b, is conducted to verify the effect of the stitching algorithm. The gray-level difference of An 17, experiment two images which exhibit significant gray-level difference, as shown in Sensors 2017, 623 5 of 19 image the mosaicking position iswith relatively significant, such that an obvious seam line in the direct Figure 2a,b, is conducted to verify the effect of the stitching algorithm. The gray-level difference of mosaicking exists, as shown in Figure 2c. The result shown Figureseam 2d is spliced at theimage bisector of the theAn mosaicking position relatively such that aninobvious in the direct experiment with istwo imagessignificant, which exhibit significant gray-levelline difference, as shown in overlapping region, in which the seam line is not eliminated completely. The result of removing the mosaicking as shown in Figure Theofresult shown inalgorithm. Figure 2d isThe spliced at the bisector of of Figure 2a,b, isexists, conducted to verify the 2c. effect the stitching gray-level difference the overlapping region, in which the seam line is not eliminated completely. The result of removing seam line on theposition overlapping areasignificant, with an optimal line isseam shown 2e.image The smooth thebased mosaicking is relatively such thatseam an obvious linein inFigure the direct the seam line based on the overlapping area with an optimal seam line is shown in Figure 2e. The mosaicking exists, as shown inand Figure 2c. The result 2d is spliced at the bisector of transition is natural in panorama, a perfect visualshown effectinisFigure achieved. smooth transition is natural in panorama, and a perfect visual effect is achieved.

the overlapping region, in which the seam line is not eliminated completely. The result of removing the seam line based on the overlapping area with an optimal seam line is shown in Figure 2e. The smooth transition is natural in panorama, and a perfect visual effect is achieved.

(a)

(b)

(c)

(d)

(e)

Figure 2. Image mosaicking results: (a) original left image; (b) original right image; (c) image

Figure 2. mosaicked Image mosaicking results: (a) with original left image; (b) original image; directly; (d) image mosaicked the bisector of the overlapping region right as the seam line; (c) image (a) (b) (c) with (d)the overlapping region (e) as the seam mosaicked directly; imagewith mosaicked and (e) image(d) mosaicked the optimal seam the line. bisector of line; andFigure (e) image mosaicked with the optimal seamleft line. 2. Image mosaicking results: (a) original image; (b) original right image; (c) image

3. Improved Wallis Dodging mosaicked directly; (d) image mosaicked with the bisector of the overlapping region as the seam line; The Wallis dodging is only (e) existing image mosaicked with thealgorithm optimal seam line. suitable for keeping the color and brightness 3. Improvedand Wallis Dodging consistency between two images or a few images. The adjustment order and parameter calculation methods are improved to ensurealgorithm that the Wallis method isfor suitable for color balance large-brightness The3. existing Wallis dodging is dodging only suitable keeping the colorofand Improved Wallis Dodging scale SR images. Theimages processing procedure of the proposed algorithm is that theand imageparameter in the middlecalculation consistency between two or a few images. The adjustment order The existing dodging algorithm is images only suitable keeping color gradually, and brightness is selected as theWallis first standard image and other in four for directions arethe adjusted as methods are improved to ensure that the Wallis dodging method is suitable for calculation color balance of consistency between two images or a few images. The adjustment order and parameter shown in Figure 3. The images at the same line or column as the first image are modified based on a methods are improved ensure that procedure the Wallison dodging is suitable for color of image large- in the large-scale SR images. The processing of two themethod proposed algorithm is balance that the contiguous image. Theto other images are based its adjacent images.

scale SR images. The processing procedure of the proposed algorithm that the image the middle middle is selected as the first standard image and other images in fourisdirections are in adjusted gradually, is selected as the first standard image and other images in four directions are adjusted gradually, as as shown in Figure 3. The images at the same line or column as the first image are modified based on shown in Figure 3. The images at the same line or column as the first image are modified based on a a contiguous image. The other images are based on its two adjacent images. contiguous image. The other images are based on its two adjacent images.

Figure 3. Weighted adjustment sequence.

The traditional Wallis dodging algorithm generally involves a reference image and a target image. However, the target image may be adjusted according to two target images in the proposed method. In this study, two adjacent images are defined as a and b. Their overlapping areas in the Weighted adjustment horizontal direction are a rightFigure and b 3. left, as shown in Figuresequence. 4a, whereas their overlapping areas in Figure 3. Weighted adjustment sequence. the vertical direction are a bottom and b top, as shown in Figure 4b. If the image to be processed and Wallisare dodging algorithm involves a reference and𝑠𝑓a are target theThe firsttraditional standard image at the same line orgenerally column, the parameters 𝑚𝑘 , 𝑚𝑓image , 𝑠𝑘 , and image. However, the target image may be adjusted according to two target images in the proposed calculated according to the overlapping region of the target image and its adjacent image. Otherwise, The traditional Wallis dodging algorithm generally involves a reference image and a target two abutting be considered. For image a andb.right image b1 below areas b2 the method. In this study, two adjacent areexample, defined as a and Their overlapping in image. However, theimages targetshould image mayimages be adjusted according to two target imagesimage in the proposed are contiguous, as are shown in Figure The , 𝑚𝑓1 , 𝑚 and 𝑚𝑓2their and overlapping the variancesareas 𝑆𝑘1 , in horizontal direction a right and b 4. left, asmeans shown𝑚in 4a, 𝑘1Figure 𝑘2 ,whereas

method. In this study, two adjacent images are defined as a and b. Their overlapping areas in the the vertical direction are a bottom and b top, as shown in Figure 4b. If the image to be processed and horizontal direction areimage a right b left, shown in Figure 4a, whereas the first standard areand at the sameas line or column, the parameters 𝑚𝑘 , their 𝑚𝑓 , 𝑠𝑘overlapping , and 𝑠𝑓 are areas in the vertical direction are a bottom and region b top,ofasthe shown in Figure 4b. If the image. imageOtherwise, to be processed calculated according to the overlapping target image and its adjacent images should considered. example, image athe andparameters right image b1mbelow b2 s f are and thetwo firstabutting standard image arebeat the sameFor line or column, , m , sk , and k f image are contiguous, as shown in Figure 4. The means 𝑚 , 𝑚 , 𝑚 , and 𝑚 and the variances 𝑆 𝑘1 𝑓1image 𝑘2 and its 𝑓2 adjacent image. Otherwise, 𝑘1 , calculated according to the overlapping region of the target two abutting images should be considered. For example, image a and right image b1 below image b2 are contiguous, as shown in Figure 4. The means mk1 , m f 1 , mk2 , and m f 2 and the variances Sk1 , S f 1 ,

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Sk2 , and S f 2 are computed based on the overlapping area of three images. Then, the parameters are Sensors 2017, 17, 623 6 of 19 formulated, as expressed in Equation (6): 𝑆𝑓1 , 𝑆𝑘2 , and 𝑆𝑓2 are computed based on the overlapping area of three images. Then, the parameters mk =(5): P1 × mk1 + P2 × mk2 are formulated, as expressed in Equation

m f = P1 × m f 1 + P2 × m f 2 m𝑘 = P1 × m𝑘1 + P2 × m𝑘2

(6)

sk m= P 2× k1 ++PP =1P××Sm ×S mk2 𝑓

1

𝑓1

2

𝑓2

(5)

s f = P1 × Sf1 + P2 × Sf2 s𝑘 = P1 × Sk1 + P2 × Sk2

where P1 and P2 denote the weighting coefficients, s𝑓 = P1 × Sf1which + P2 × are Sf2 related to the difference of the means of the target and reference images. The purpose of the Wallis filter is to adjust the mean of the target where 𝑃 and 𝑃 denote the weighting coefficients, which are related to the difference of the means image to the 1level of2the reference image. The difference reflects the degree of adjustment. Accordingly, of the target and reference images. The purpose of the Wallis filter is to adjust the mean of the target the parameters arelevel calculated Equation (7)The to ensure that reflects the graythe values of the adjusted image image to the of theusing reference image. difference degree of adjustment. are closest to the value of the adjacent two images: Accordingly, the parameters are calculated using Equation (6) to ensure that the gray values of the adjusted image are closest to the value ofthe adjacenttwo images:

Pi =

ABSABS mki − m f i  (m𝑘i−m𝑓𝑖)  (i = 1, = 1, 2) (i2) ABS )+ABS(m𝑘2 −m𝑓2 ) 𝑓1 ABS mk1 −(mm𝑘1f−m + ABS m − m 1 k2 f2 P i =

(a)

(6)

(7)

(b)

Figure 4. Parameter calculation: (a) left and right overlapping diagram and (b) upper and lower

Figure 4. Parameter calculation: (a) left and right overlapping diagram and (b) upper and lower overlapping diagram. overlapping diagram.

4. Experimental Results and Discussion

4. Experimental Results and Discussion

ZY-3 is the first civilian high-resolution optical transmission mapping satellite in China, which

is equipped withcivilian four sets of optical cameras, including a panchromatic CCD camera with a ZY-3 is the first high-resolution optical transmission mappingTDI satellite in China, which is groundwith resolution of 2.1of m,optical two setscameras, of panchromatic TDI CCD cameras with aTDI resolution of 3.6 m, with equipped four sets including a panchromatic CCD camera and aresolution multispectral camera withsets a ground resolution ofTDI 5.8 m. ZY-3 images with ofof 3.63.6 m, a ground of 2.1 m, two of panchromatic CCD cameras withaaresolution resolution m are divided into sub-blocks to verify the validity of the proposed algorithm. Then, SR reconstructed and a multispectral camera with a ground resolution of 5.8 m. ZY-3 images with a resolution of 3.6 m images with a resolution of 1.8 m are obtained by the blind SR reconstruction algorithm. The size of are divided into sub-blocks to verify the validity of the proposed algorithm. Then, SR reconstructed these images, which are overlapped 50 pixels, is 1024 × 1024 pixels. The traditional and improved images withdodging a resolution of are 1.8 applied m are obtained the images. blind SR algorithm. size of Wallis methods to processby these Allreconstruction the experiments are realizedThe with theseMATLAB images, which are overlapped 50 pixels, is 1024 × 1024 pixels. The traditional and improved in this study. The results of the experiments are analyzed in this section. Wallis dodging methods are applied to process these images. All the experiments are realized with 4.1. Image SR study. Reconstruction MATLAB in this The results of the experiments are analyzed in this section. In order to prove the effect and significance of SR reconstruction algorithm, ZY-3 forward and backward panchromatic images with a resolution of 3.6 m, as shown in Figure 5a,b, are reconstructed by order the blind SR reconstruction algorithm. The reconstructed image and its details ZY-3 are shown in and In to prove the effect and significance of SR reconstruction algorithm, forward Figure 5d. The edges of the building and road in the reconstructed image are much clearer and more backward panchromatic images with a resolution of 3.6 m, as shown in Figure 5a,b, are reconstructed distinct than that in the original images. Moreover, the result is also better than the image shown in by the blind SR reconstruction algorithm. The reconstructed image and its details are shown in Figure 5c, which is obtained by the bicubic interpolation method. The nominal values of metric 𝑄 of Figure 5d. The edges of the building and road in the reconstructed image are much clearer and more two reconstructed images are shown in Table 1. The metric 𝑄 of the image based on the blind SR distinct than that inalgorithm the original images. Moreover, result is also better algorithm than the image shown in reconstruction is high, showing that the the blind SR reconstruction has a good Figure 5c, which is obtained by the bicubic interpolation nominal values of metric Q visual performance and detail preservation. In summary, method. Image SR The reconstruction can effectively of two reconstructed images are shown in images. Table 1. The metric Q of the image based on the blind SR produce robust and clear high-resolution

4.1. Image SR Reconstruction

reconstruction algorithm is high, showing that the blind SR reconstruction algorithm has a good visual

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performance and detail preservation. In summary, Image SR reconstruction can effectively produce robust and clear high-resolution images. Sensors 2017, 17, 623

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(d) Figure 5. Results of the experiments using two methods: (a) original forward image; (b) original

Figure 5. Results of the experiments using two methods: (a) original forward image; (b) original backward image; (c) image based on the bicubic interpolation algorithm; (d) image based on the blind backward image; (c) image based on the bicubic interpolation algorithm; (d) image based on the blind SR reconstruction algorithm. SR reconstruction algorithm.

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Table 1. The nominal values of metric Q of two reconstructed images. Table 1. The nominal values of metric 𝑄 of two reconstructed images. Image Reconstructed by Different Algorithms The Value of Q Image Reconstructed by Different Algorithms The Value of Q The 20.6348 The blind blind SR SR reconstruction reconstruction algorithm algorithm 20.6348 The bicubic interpolation algorithm 13.0267 The bicubic interpolation algorithm 13.0267

4.2. Experiments Experiments of of Different Different Dodging Dodging Algorithms 4.2. Algorithms All the of of different dodging algorithms are affected by the processing sequence. sequence. Therefore, All theresults results different dodging algorithms are affected by the processing two images with large contrast are processed to verify the effect of different dodging algorithms, Therefore, two images with large contrast are processed to verify the effect of different dodging as shown inasFigure An obvious line seam in theline image mosaicking without any dodging algorithms, shown6a,b. in Figure 6a,b. Anseam obvious in the image mosaicking without any processing can be observed, as shown in Figure 6c. Although the method based on histogram matching dodging processing can be observed, as shown in Figure 6c. Although the method based on weakens difference of the original imagesof in the brightness contrast, the seam and line contrast, in the image histogramthe matching weakens the difference originaland images in brightness the mosaicking also bemosaicking easily observed, as be shown Figure 6d.asFurthermore, the 6d. relative distance seam line in can the image can also easilyinobserved, shown in Figure Furthermore, between gray levels in the processed rightinimage is changed, resulting color deviation of the the relative distance between gray levels the processed right image in is the changed, resulting in the image with different internal features. The effect of the method based on information entropy is color deviation of the image with different internal features. The effect of the method based on worse than that based histogram matching. seam line in the image mosaicking shown in information entropy is on worse than that based onThe histogram matching. The seam line in the image Figure 6e almost does not achieve any improvement. The effect of the Wallis dodging method is the mosaicking shown in Figure 6e almost does not achieve any improvement. The effect of the Wallis best, andmethod the image mosaicking consistent color withoutconsistent a visible seam as shown in dodging is the best, andachieves the image mosaicking achieves color line, without a visible Figure 6f. In summary, the results shown in Figure 6 indicate that the Wallis filter has the strongest seam line, as shown in Figure 6f. In summary, the results shown in Figure 6 indicate that the Wallis abilityhas to the achieve consistency andofcontrast. filter strongest ability of to image achievebrightness consistency image brightness and contrast.

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(f) Figure 6. Comparison of different dodging algorithms: (a) original left image; (b) original right image;

Figure 6. Comparison of different dodging algorithms: (a) original left image; (b) original right image; (c) image mosaicking of original images; (d) image mosaicking of two images after dodging based on (c) image mosaicking of original images; (d) image mosaicking of two images afteron dodging based on histogram matching; (e) image mosaicking of two images after dodging based information histogram matching; image mosaicking of two after dodging based filter. on information entropy; entropy; (f) image(e) mosaicking of two images afterimages dodging based on the Wallis (f) image mosaicking of two images after dodging based on the Wallis filter. In addition, average gradient, information entropy and peak signal-to-noise ratio (PSNR) are considered to average estimate the effect of information different dodging algorithms on image quality. Average In addition, gradient, entropy and peak signal-to-noise ratiogradient, (PSNR) are which reflects the ability of image detail contrast expression, is the image definition. Information considered to estimate the effect of different dodging algorithms on image quality. Average gradient, entropy represents the amount of image information. PSNR is usually used as an image quality metric which reflects the ability of image detail contrast expression, is the image definition. Information for evaluating image processing algorithms. A high PSNR value provides a high image quality. At entropy represents of image PSNRhigh is usually used as an image quality the other end ofthe the amount scale, a small value information. of the PSNR implies numerical differences between metric for evaluating image processing algorithms. A high indicators, PSNR value high image quality. images. From the perspective of image quality assessment theprovides details of athe performance At thecomparisons other end of the the three scale,methods a smallare value of the PSNR highgradient, numerical differences between shown in Table 2. implies The average information entropy andFrom PSNRthe of the image afterofdodging based onassessment the Wallis filter are highest, that the images. perspective image quality indicators, the which detailsindicates of the performance Wallis dodging method gives the abundant amount information and the highest definition. comparisons of the three methods aremost shown in Table 2. Theofaverage gradient, information entropy and

PSNR of the image after dodging based on the Wallis filter are highest, which indicates that the Wallis dodging method gives the most abundant amount of information and the highest definition. Hence,

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the Wallis dodging method is the most widely used method for dealing with the color differences between images. Table 2. The quality evaluation of images processed by different algorithms.

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Hence, the Wallis dodging method is the most widely used Average method for Information dealing with the color PSNR Different Image Gradient Entropy differences between images.

Original right image 3.0945 5.8662 Table 2. The quality evaluation of images processed by different algorithms. Right image after dodging based on histogram matching 7.252 5.5439 Right image after dodging based on information entropy Average 2.8257 5.7266 Information Different Image Gradient Entropy Right image after dodging based on Wallis filter 3.9136 5.8812

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Original right image Right image after dodging based on histogram matching Comparative Experiment on 64 Images Right image after dodging based on information entropy Right image after dodging based on Wallis filter

3.0945 7.252 2.8257 3.9136

5.8662 5.5439 5.7266 5.8812

42.8714 43.0832 PSNR 67.2056 42.8714 43.0832 67.2056

A total of 64 images with large contrast were selected for the comparative experiment and analysis to assess the effect ofExperiment the proposed algorithm on image quality. Average gradient and information 4.3. Comparative on 64 Images entropy areAconsidered to estimate the specific methods of image dodging. The results of different total of 64 images with large contrast were selected for the comparative experiment and methods are shown in Figure the performance comparisons the five methods analysis to assess the effect7.ofThe the details proposedofalgorithm on image quality. Averageofgradient and from the perspective of image quality to assessment are shown indodging. Figure The 8. The SR image information entropy are considered estimate theindicators specific methods of image results different are amount shown in of Figure 7. The details the highest performance comparisons of theoffive exhibitsofthe most methods abundant information andofthe definition because radiation methods from the perspective of image quality assessment indicators are shown in Figure The SR Thus, distortion. However, the sub-blocks exhibit the largest difference in brightness and 8.contrast. image exhibits the most abundant amount of information and the highest definition because of the image mosaicking in Figure 7a exhibits a poor visual effect with obvious seam lines. All these radiation distortion. However, the sub-blocks exhibit the largest difference in brightness and contrast. dodgingThus, methods decrease the average the image. Thewith leftobvious image seam crosslines. method the image mosaicking in Figure gradient 7a exhibitsof a poor visual effect All is the best, whereas the quadtree method is the worst, and the proposed method is at a moderate these dodging methods decrease the average gradient of the image. The left image cross method is level. the best, whereas the reduces quadtree the method is the of worst, andinformation the proposed method is atto a moderate level. results Image dodging generally amount image according the statistical Image dodging generally amount of image according shows to the statistical results of information entropy. The reduces result the based on the left information image benchmark the most abundant entropy. The result based on the left image benchmark shows the most abundant amountofofinformation information, and the proposed method follows. The result based on the quadtree method amount of information, and the proposed method follows. The result based on the quadtree method has the has most loss of image information because of excessive computation. the most loss of image information because of excessive computation.

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Figure 7. Results of different methods: (a) original image; (b) result based on left image benchmark;

Figure 7. Results of different methods: (a) original image; (b) result based on left image benchmark; (c) result based on above image benchmark; (d) result based on left image cross; (e) result based on (c) result based image (d)method. result based on left image cross; (e) result based on quadtree; on andabove (f) result basedbenchmark; on the proposed quadtree; and (f) result based on the proposed method.

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8 7 6 5 4 3 2 1 0

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7.07 7.01 6.84 6.88 7.07 7.01 6.84 6.886.73 6.78 6.73 6.78

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3.64 3.64 2.57 2.43 2.58 2.57 2.43 2.582.17 2.51 2.51 2.17

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information entropy information entropy Original image left image Original image left image left image cross Quadtree left image cross Quadtree

average gradient average gradient above image above image proposed method proposed method

Figure 8. Average gradient information entropy of the processed results of different methods. Figure 8. Average gradient andand information entropy of the processed results of different methods. Figure 8. Average gradient and information entropy of the processed results of different methods.

TheThe mean value andand standard deviation of each sub-block image processed by different dodging value standard deviation of each each sub-block image processed by different different dodging The mean mean value and standard deviation of sub-block image processed by dodging methods are computed. The distribution maps are also protracted to estimate the effectiveness of the methods are computed. The distribution maps are also protracted to estimate the effectiveness methods are computed. The distribution maps are also protracted to estimate the effectiveness of of the the improved Wallis dodging algorithm, as shown in Figure 9. The distribution curve of the left image improved improved Wallis Wallis dodging dodging algorithm, algorithm, as as shown shown in in Figure Figure 9. 9. The The distribution distribution curve curve of of the the left left image image benchmark method changes most dramatically and thethe quadtree method follows. TheThe distribution benchmark benchmark method method changes changes most most dramatically dramatically and and the quadtree quadtree method method follows. follows. The distribution distribution curve of the left or above image benchmark method is periodic. The variation trend of the distribution curve the left left or or above above image image benchmark benchmark method method is periodic. The The variation variation trend trend of of the the distribution distribution curve of of the is periodic. curve of the proposed method is relatively stable. This phenomenon indicates that the improved curve indicates that that the curve of of the the proposed proposed method method is is relatively relatively stable. stable. This This phenomenon phenomenon indicates the improved improved weighted Wallis algorithm is suitable forfor thethe color balance of of large-scale SRSR reconstructed images. weighted Wallis algorithm is suitable color balance large-scale reconstructed images. weighted Wallis algorithm is suitable for the color balance of large-scale SR reconstructed images.

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Figure 9. Cont.

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(b) Figure 9. Distribution curve of the mean value and standard deviation of each sub-block image: (a) Figure 9. Distribution curve of the mean value and standard deviation of each sub-block image: distribution curve of the mean value of each sub-block image; (b) distribution curve of the standard (a) distribution curve of the mean value of each sub-block image; (b) distribution curve of the standard (b) deviation of of each each sub-block sub-block image. image. deviation

Figure 9. Distribution curve of the mean value and standard deviation of each sub-block image: (a) distribution of the mean value of each sub-block image; (b) distribution curve of the standard 4.4. Experiment on 900curve Images 4.4. Experiment on 900 Images deviation of each sub-block image.

A total of 900 images are processed with the five methods for another comparative experiment A total of 900 images are processed with the five methods for another comparative experiment 4.4. illustrate Experiment on 900 Images to further the effectiveness of the improved Wallis dodging algorithm for large-scale SR to further illustrate the effectiveness of the improved Wallis dodging algorithm for large-scale SR total of 900 methods images areshown processed with the1a,b, five methods for another comparative between experiment images. TheAprocessing in Figure which ignore the correlation different images. toThe processing methods shown of in the Figure 1a,b, which ignore the correlation betweenSRdifferent further illustrate the effectiveness improved Wallis dodging algorithm for large-scale rows (columns), are simply suitable for the color balance of a few images. These methods will lead to rows (columns), simplymethods suitableshown for the color 1a,b, balance ofignore a fewtheimages. These methods will lead images. Theare correlation different a belt-form imageprocessing for large-scale images,inasFigure shown inwhich Figure 10a,b. In areas between with a relatively large to a belt-form image for images, shown in of Figure 10a,b. In areas with will a relatively rows (columns), arelarge-scale simply suitable for theas color balance a few images. These methods lead to large difference of object reflectivity, the phenomenon of exposure will occur, resulting in serious a belt-form for large-scale images, as shown in Figure will 10a,b. In areas with a relatively large difference of objectimage reflectivity, the phenomenon of exposure occur, resulting in serious distortion distortion of the image. processing shown in Figure 1c,occur, in which the reference difference of processing objectThe reflectivity, the methods phenomenon of exposure serious images of the image. The methods shown in Figure 1c, in will which the resulting referencein images of one of one distortion target image its The leftprocessing and upper adjacent loss images of gray-level of the are image. methods shownimages, in Figuremay 1c, incause which partial the reference target image are its left and upper adjacent images, may cause partial loss of gray-level information. of oneThis targetphenomenon image are its may left and upper adjacent images,ofmay cause partial of gray-level information. also make the contrast adjacent imagesloss obvious, as shown in This phenomenon may also make the contrast ofthe adjacent images obvious, as shown in Figure information. This phenomenon may also make contrast of adjacent images obvious, as shown in 10c. Figure 10c. In order to reduce the spatial transfer and accumulation of error, the small sub-blocks are adjusted In Figure order10c. to reduce the spatial transfer and accumulation of error, the small sub-blocks are and then each of thetofour adjacent blocks are adjusted as a blockofinerror, the method based on theare four-fork In order reduce the spatial transfer and accumulation the small sub-blocks adjusted and then each of the four adjacent blocks areadjusted adjusted asblock a block in the method based on the adjustedin and then each theconsistency four adjacentof blocks arebrightness as aand in the method the tree, as shown Figure 1d. of The image contrast can bebased wellon achieved for four-fork tree, as shown in Figure 1d. The consistency of image brightness and contrast can be well four-fork tree, as shown in Figure 1d. The consistency of image brightness and contrast can be well 64 images, as shown in Figure 11a,d. Block effect and loss of gray-level information are observed with achieved for 64 for images, as shown in in Figure Blockeffect effect and of gray-level information are achieved 64 images, as shown Figure11a,d. 11a,d. Block and lossloss of gray-level information are the increase in the number of images, as shown in Figure 11e,f. observed with the increase in the number of images, as shown in Figure 11e,f. observed with the increase in the number of images, as shown in Figure 11e,f.

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Figure 10. Cont.

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(c) Figure 10. Results based on different sequences: (a) result based on left image benchmark; (b) result

Figure 10. Results based on different sequences: (c) (a) result based on left image benchmark; (b) result based on above image benchmark; and (c) result based on left image cross. based on image benchmark; and (c) result based on left image cross. Figure 10.above Results based on different sequences: (a) result based on left image benchmark; (b) result

based on above image benchmark; and (c) result based on left image cross.

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Figure 11. Results of the quadtree method: (a) 64 images; (b) 64 images; (c) 64 images; (d) 64 images; (e) 256 images; and (f) 576 images.

The overall color of the original image is dark. The phenomenon of non-uniform brightness and contrast is serious. After image dodging by the improved weighted Wallis dodging method, the (e) images exhibit a consistent brightness and contrast, as shown in Figure 12.(f) The mean value and standard deviation of the original images and processed images using the Wallis dodging method Figure 11. Results of the quadtree method: (a) 64 images; (b) 64 images; (c) 64 images; (d) 64 images; Figure 11. Results of the quadtree method: (a) 64 images; (b) 64 images; 64 images; (d)dodging 64 images; are inputted to the statistical analysis to evaluate the effectiveness of the (c) improved Wallis (e) 256 images; and (f) 576 images. (e) algorithm 256 images; and (f) 576 images. quantitatively. The distribution curves are plotted in Figure 13. The mean value and standard deviation of the original images are scattered and changed dramatically, as shown in Figure The13.overall color the of the original image is dark. The phenomenon non-uniform brightness and By contrast, mean value and standard deviation of the images of processed using the Wallis The overall color of the original image is dark. The phenomenon of non-uniform brightness and contrastdodging is serious. After image dodging improved Wallis method, the method change more slowly. by Thethe change intervalweighted is low. This result dodging proves that the contrastproposed is serious. After image dodging improved dodging method, images exhibits the abilityby ofthe brightness and contrast images exhibit aapproach consistent brightness and contrast, asweighted shownhomogenization. inWallis Figure 12. The mean the value and

exhibit a consistent brightness andimages contrast, shown in images Figure 12. The mean value and standard standard deviation of the original andasprocessed using the Wallis dodging method deviation of the original images and processed images using the Wallis dodging method are inputted are inputted to the statistical analysis to evaluate the effectiveness of the improved Wallis dodging to the statistical analysis to evaluate the effectiveness of the improved dodging algorithm algorithm quantitatively. The distribution curves are plotted in Figure Wallis 13. The mean value and quantitatively. The distribution curves are plotted in Figure 13. The mean value and standard standard deviation of the original images are scattered and changed dramatically, as shown deviation in Figure of the are value scattered changed dramatically, shown in Figureusing 13. By 13. By original contrast,images the mean andand standard deviation of the as images processed thecontrast, Wallis the mean value and standard deviation of the images processed using the Wallis dodging method dodging method change more slowly. The change interval is low. This result proves that the change more slowly. The change interval is low. This result proves that the proposed approach exhibits proposed approach exhibits the ability of brightness and contrast homogenization. the ability of brightness and contrast homogenization.

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Figure 12. The result result and and its its local local amplification amplification effect effect of of the the images images after after image image dodging dodging by by the the Figure 12. The improved method. method. improved

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Figure 13. Distribution curve of the mean and standard deviation of the original images and those Figure 13. Distribution curve of the mean and standard deviation of the original images and those processed dodging method: method: (a) processed using using the the Wallis Wallis dodging (a) mean mean of of the the original original images; images; (b) (b) mean mean of of the the images images processed using the Wallis dodging method; (c) standard deviation of the original images; processed using the Wallis dodging method; (c) standard deviation of the original images; and and (d) (d) standard processed using using the the Wallis Wallis dodging dodging method. method. standard deviation deviation of of the the images images processed

After image dodging by the improved weighted Wallis dodging method, the brightness and After image dodging by the improved weighted Wallis dodging method, the brightness and contrast of the images are basically the same or close together. The image mosaicking shown in Figure contrast of the images are basically the same or close together. The image mosaicking shown in 12 exhibits a good visual effect. However, slight differences are still observed among the tones in the sectional overlapping region of the adjacent images. This phenomenon leads to seam lines, as shown

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Figure 12 exhibits a good visual effect. However, slight differences are still observed among the tones Sensors 2017, 17, 623 15 of 19 in the sectional overlapping region of the adjacent images. This phenomenon leads to seam lines, as Figure 14a. Finally, the smooth transition of adjacent images is well achievedby bythe the seam in shown Figurein14a. Finally, the smooth transition of adjacent images is well achieved seam elimination method, which can share the partial dislocation in the seam line to the entire overlapping elimination method, which can share the partial dislocation in the seam line to the entire overlapping region. region. A A homogeneous homogeneous image image exhibiting exhibiting aa perfect perfect visual visual effect effect is is obtained obtained successfully, successfully, as as shown shown in in Figure Figure 14b. 14b.

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(b) Figure 14. Final results: (a) mosaicking result without seam elimination and its local amplification Figure 14. Final results: (a) mosaicking result without seam elimination and its local amplification effect on on the the images images after after image image dodging dodging by by the the improved improved method method and and (b) (b) final final mosaicking mosaicking result result effect with seam elimination and its local amplification effect of the images after image dodging by the with seam elimination and its local amplification effect of the images after image dodging by the improved method. method. improved

In summary, the resolution of original ZY-3 forward and backward images shown in Figure In summary, the resolution of original ZY-3 forward and backward images shown in Figure 15a,b 15a,b is enhanced by the blind SR reconstruction algorithm. Then, the difference in brightness and is enhanced by the blind SR reconstruction algorithm. Then, the difference in brightness and contrast contrast among sub-block SR reconstructed images is eliminated using the improved Wallis dodging algorithm. Finally, a high-resolution image mosaicking without a seam line is obtained, as shown in Figure 15c. As we can see from Figure 15, the building and road in the two original images are fuzzy, while the edges of the building and road in the final image are clear and distinct, with more details.

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among sub-block SR reconstructed images is eliminated using the improved Wallis dodging algorithm. Finally, a high-resolution image mosaicking without a seam line is obtained, as shown in Figure 15c. As we can see from Figure 15, the building and road in the two original images are fuzzy, while the edges of the building and road in the final image are clear and distinct, with more details. Sensors 2017, 17, 623

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(c) Figure 15. Comparison of the original image and the final result: (a) original forward image and its

Figure 15. Comparison of the original image and the final result: (a) original forward image and its local amplification (b) original backward image and its local amplification (c) the final result and its local local amplification (b) original backward image and its local amplification (c) the final result and its amplification. local amplification.

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5. Conclusions The Wallis dodging algorithm can remove the non-homogeneity of the brightness and contrast of multiple images. However, the existing algorithms cannot be applied to large-scale SR images. An efficient, improved weighted Wallis algorithm is proposed in this study. This algorithm uses a novel sequence of adjustment to avoid spatial transfer and accumulation of errors. A total of 900 SR images have been successfully tested by this method. The proposed method can effectively adjust the brightness and contrast differences among large-scale SR images and achieve a seamless image mosaicking with good visual effects compared with four other methods. This method is also suitable for color balance and storage of a large-scale image database. In the experiment, large-scale waters and mists have a significant influence on the results and should be removed in advance. Therefore, investigating and exploring how to detect these special areas efficiently and accurately are necessary. An objective and effective assessment method should also be presented. This method is able to evaluate the precision and accuracy of our algorithm effectively. Acknowledgments: We acknowledge financial support from China Postdoctoral Science Foundation Funded Project (20100471127) and National Key Research and Development Plan (No. 2016YFD0300602). The authors are deeply indebted to the reviewers and editors for the thoughtful and constructive comments on improving the manuscript. Author Contributions: Xushuai Chen wrote the paper, proposed the improved weighted Wallis dodging method and performed the analyses. Min Zhou wrote the code of different methods and performed the experiments. Lei Zhong and Yun Shi completed the experiment and analysis of image SR Reconstruction. Chong Fan and Yulin Duan provided the theoretical guidance for the subject study and design of experiments, and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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