Detail enhancement for high-dynamic-range infrared images.pdf

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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/264198235 Detail enhancement for high-dynamic-range infrared images based on guided image filter ARTICLE in INFRARED PHYSICS & TECHNOLOGY · NOVEMBER 2014 Impact Factor: 1.55 · DOI: 10.1016/j.infrared.2014.07.013 CITATIONS 3 2 AUTHORS: READS 203 Ning Liu Nanjing University of Posts and Telecomm… Dongxue Zhao Greenville College 17 PUBLICATIONS 14 CITATIONS 17 PUBLICATIONS 10 CITATIONS SEE PROFILE SEE PROFILE All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. Available from: Dongxue Zhao Retrieved on: 11 April 2016

Infrared Physics & Technology 67 (2014) 138–147 Contents lists available at ScienceDirect Infrared Physics & Technology j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i n f r a r e d Detail enhancement for high-dynamic-range infrared images based on guided image ﬁlter Ning Liu a,⇑ , Dongxue Zhao b a Nanjing XiaoZhuang University, College of Physics & Electronics, Nanjing, Jiangsu Province 211171, China b University of Missouri-St. Louis, Department of Physics and Astronomy, St. Louis, MO 63121, United States h i g h l i g h t s New detail enhancement algorithm has been raised in this paper. Greatly simpliﬁed the computation process to the existing methods. Better noise suppression when enhancing the detail of IR images. Effective in enhancing the detail information of IR images. a r t i c l e i n f o a b s t r a c t Article history: Received 18 March 2014 Available online 24 July 2014 Keywords: Detail enhancement Guided image ﬁlter Noise reduction Infrared images High dynamic range Detail enhancement and noise reduction play crucial roles in high dynamic range infrared image process- ing. The main focuses are to compress the high dynamic range images with an effective way to display on lower dynamic range monitors, enhance the perceptibility of small details, and reduce the noises without causing artifacts. In this paper, we propose a new method for detail enhancement and noise reduction of high dynamic range infrared images. We ﬁrst apply a guided image ﬁlter to smooth the input image and separate the image into the base component and the detail component. This process also gives us an adaptive weighting coefﬁcient associated with the details generated by the ﬁlter kernel. After the ﬁltering process, we compress the base component into the display range by our modiﬁed histogram projection and enhance the detail component using the gain mask of the ﬁlter weighting coefﬁcient. At last, we recombine the two parts and quantize the result to 8-bit domain. Our method is signiﬁcantly better than those based on histogram equalization (HE), and it also has better visual effect than bilateral ﬁlter-based methods. Furthermore, our proposed method is much faster, non-approximate and suffers much less gra- dient ﬂipping artifacts compared to the bilateral ﬁlter-based methods because the guided image ﬁlter uses the local linear model. We demonstrate that our method is both effective and efﬁcient in a great variety of applications. Experimental veriﬁcation and detailed analysis are shown in this paper. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction Nowadays, high-quality thermal cameras can detect tempera- ture difference within 0.01 K. They can also accommodate the tem- perature range about 50 K. For these reasons, modern infrared cameras are able to produce images with a wide dynamic range of 14-bit (or more), which exceeds the 8-bit sensitivity of a typical display device. Nevertheless, a human visual system only has the capability of distinguishing 128 gray levels of an image [1]. Hence, we need a procedure to compress the dynamic range of the raw images into a lower range. Thus, it is suitable for the display ⇑ Corresponding author. E-mail address: coolboy006@sohu.com (N. Liu). http://dx.doi.org/10.1016/j.infrared.2014.07.013 1350-4495/Ó 2014 Elsevier B.V. All rights reserved. system and enhances the signiﬁcant details of images during the compressing and then improve the image visual quality. Dynamic-range compression (DRC) has been widely investi- gated and a number of visualization techniques have been pro- posed in literature. Such techniques are applied speciﬁcally in the visible spectral domain and take no account of the characteris- tics of infrared images. Thus, speciﬁc technology must be studied especially for high dynamic range infrared images, which will be useful for adjusting the raw data into a proper range for display and maintaining or even improving objects’ visibility and overall contrast. Traditional gamma correction is a widely used for contrast enhancement owing to its simplicity and the convenience of dis- playing infrared images in real-time system. It improves image

N. Liu, D. Zhao / Infrared Physics & Technology 67 (2014) 138–147 139 contrast through a speciﬁed gamma correction curve [2]. Other widely used methods are automatic gain control (AGC) and histo- gram equalization (HE)-based method [10,15–17]. The AGC method is quite simple. It removes extreme values and linearly compresses the raw data to a display range [18]. Unlike the AGC, HE employs non-linear and non-monotonic transfer functions to map the pixel intensity values between the input and output images. A large number of algorithms derived from HE are aimed to overcome the drawbacks of HE [3,4] such as increasing noises, losing details and washing out effect in some homogeneous areas. Technically, they can be categorized into two types: the global HE (GHE) and the local HE (LHE) [14]. The plateau histogram equaliza- tion (PHE) [21,22] and brightness preserving bi-HE (BPBHE) belong to the traditional GHE. They can suppress the enhancement of homogeneous regions by involving some tuning parameters. Com- pared to the GHE methods, the LHE techniques also act as the same role in display wide dynamic range infrared images. LHE applies histogram equalization in the local region of an image. This makes the image quality superior to GHE but has high computational expense and complexity. Adaptive histogram equalization (AHE) [3] can improve the local contrast and bring out more details of the image by computing the histogram through a local window centered at a given pixel to determine the mapping for this pixel. But it produces signiﬁcant noises during processing. The improved AHE: contrast limited AHE (CLAHE) [4] has more ﬂexibility in choosing the local histogram mapping function, and it can reduce undesired noise ampliﬁcation. A novel contrast enhancement method called partially overlapped sub-block HE (POSHE) [5] has the capability to highlight the local details, and it dramatically reduces the computational time. All in all, these aforementioned HE-based methods could compress the dynamic range of the raw images more effectively than AGC. Given that they just process the images based on histogram information, obviously they cannot do a satisfactory job for detail enhancement. In order to enhancing details while compressing dynamic range, some advanced methods are proposed. The balanced CLAHE and contrast enhancement (BCCE) [6] as well as the bilateral ﬁlter and dynamic range partitioning (BF&DRP) [7] are two methods for visualizing high dynamic range infrared images proposed by Branchitta et al. images are smoothed into the base component and the detail component by a bilateral ﬁlter. The detail component is acquired by subtracting the base component from the input images. Then the two compo- nents are processed independently through a set of tunable param- eters. These parameters should be carefully tuned to adjust the visualization system for the speciﬁc scenario. In the BF&DRP method, input Recently, Zuo et al. [8] proposed a novel method of display and detail enhancement for high-dynamic-range infrared images based on the framework of BF&DRP; here we call it BF&DDE. This approach is clearly superior in detail protection and noise reduc- tion than other methods. It separates the raw image into two com- ponents using a modiﬁed bilateral ﬁlter, and then processes each component independently. The base component is projected to the display range, and the detail component is added back after an adaptive gain control process. Because of the mechanism of the bilateral ﬁlter, the gradient ﬂipping artifacts are produced. The BF&DDE uses an adaptive Gaussian ﬁltering (AGF) to avoid the unwanted artifacts. We found in our experiments that the AGF can suppress the gradient ﬂipping artifacts to a certain extent but could not completely avoid it. In some particular scene with strong edges, the gradient ﬂipping artifacts can be very annoying. Besides, the high computation cost of the bilateral ﬁlter and the AGF makes the actual application of BF&DDE restricted. For these reasons, a new method of display and detail enhancement for high dynamic range infrared images is proposed. We use the guided image ﬁlter (GIF) instead of the bilateral ﬁlter (BF). Its advantages include as follows: ﬁrst, the GIF is a fast and non-approximate lin- ear algorithm, its computational complexity is independent of the ﬁltering kernel size [9]. Second, we use a mask as detail identiﬁer to enhance the detail component adaptively, and set independent tuning parameters during the ﬁltering process. The proposed method can be more ﬂexible to reduce the background noises. This method can achieve the great effect of detail enhancement and noise reduction, and furthermore, works better near strong edges. 2. The principle of the proposed algorithm He et al. [9] has proposed a novel ﬁlter, the guided image ﬁlter (GIF), which is widely applicable in computer vision and graphics. As they said, the GIF not only do a great job in edge-preserving but also can be computed efﬁciently. Inspired by the sensational effect of the BF&DDE [8] in high dynamic range infrared images processing, we design the framework of our method and improve it. We ﬁrst use a GIF to smooth the input image and treat the result as a base layer, which contains the large amplitude variations which must be com- pressed. The subtraction of the input image and the base layer is then determined as the detail layer. The detail layer must be expanded because it contains the small signal variations related to ﬁne texture. We process the two layers respectively and recombine them at last. Fig. 1 illustrates the intact principle scheme. The key assumption of the GIF is a local linear model between the guidance image G and the ﬁltered output Igif. The guidance G can be acquired from the adjacent image or the input image Iin itself. When Iin and G are identiﬁed, the expression of the GIF is for- mulated as follow: Igifði; jÞ ¼ ; j0ÞIin: X W Gði0 ð1Þ ði0;j0Þ2wi;j The notation ði0 ; j0Þ 2 wi;j indicates that ði0 ; j0Þ are pixels in a ﬁl- ter window that centered at the pixel ði; jÞ. W Gði0 ; j0Þ is the kernel weights function which can be used as the weighting coefﬁcient to enhance the details. We regard the ﬁlter output Igif as the base component IB. Then, the detail component ID is merely obtained as: IDði; jÞ ¼ Iinði; jÞ IBði; jÞ: ð2Þ We process the two components separately. The base layer is mapped into the proper range using modiﬁed histogram projection with a threshold and a displacement factor, then we get the result IBP. Meanwhile the detail layer is enhanced using the adaptive gain control method and we get the result IDP. Finally, the two layers are recombined and regulated linearly to the proper range for display: ð3Þ Iout ¼ IBP þ IDP; The detail layer only has a small range, we can just compress the base layer to a lower range in case that when the detail layer is added back, the results would not overﬂow. Here the process is quite ﬂexible and diverse. 3. Guided image ﬁltering techniques 3.1. Filtering process The GIF [9] is a linear translation-variant ﬁlter and Eq. (1) is its general expression. In Eq. (1), the kernel weights can be explicitly expressed by: ;j0Þ¼ 1 jwj2 ! ;j0Þli0;j0Þ ;j00Þli0;j0ÞðIinði0 ri0;j0 þe 1þðIinði00 X W Gði0 ; ði00 ði00 ;j00Þ2 wi;j; ;j00Þ2 wi0;j0 ð4Þ

140 N. Liu, D. Zhao / Infrared Physics & Technology 67 (2014) 138–147 Fig. 1. Flowchart of our algorithm. The blue arrows indicate that these modules are controlled or can be adjusted by the parameters or the ﬁlter kernel weights. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.) X where w is the number of pixels in the window wi;j, a square win- dow of a radius r, li0;j0 and ri0;j0 are the mean and variance of Iin in wi0;j0 . e is a regularization parameter to describe the smoothing level of the ﬁlter. The linear model of this ﬁlter output can be shown as follows: Igifði; jÞ ¼ 1 j wj X Here, aði0 ;j0Þ and bði0 ;j0Þ are linear coefﬁcients assumed to be con- stant in wi0;j0 . They can be given by: ; j0Þ þ bði0 ; j0ÞIinði0 ði0;j0Þ2wi;j ; j0ÞÞ: ðaði0 ð5Þ 1 wj j ði0;j0Þ2wi;j aði; jÞ ¼ Iinði0 ; j0ÞGði0 ; j0Þ li;jIinði0 ; j0Þ ri;j þ e : ð6Þ bði; jÞ ¼ Iinði0 ; j0Þ aði; jÞli;j: ð7Þ From Eqs. (5)–(7), we can get the output value of the GIF. As He et al. [9] mentioned that because of the linear coefﬁcients are vary- ing spatially, rIgif is no longer the scaling of rIin. Since the linear coefﬁcients are the output of an average ﬁlter, their gradients should be much smaller than those of Iin near strong edges. In this situation we can still have rIgif arIin. It means that abrupt intensity changes in Iin can be mostly maintained in Igif. The edge-preserving property can be seen from the equations above: if a pixel is in the middle of a ‘‘high variance’’ area, its value will be unchanged. Meanwhile, if it is in the middle of a ‘‘ﬂat patch’’ area, its value becomes the average of the pixels nearby. The parameter e becomes the criterion of ‘‘ﬂat patch’’ and ‘‘high vari- ance’’. When the patches’ variance ðr2Þ is much smaller than e, they will be smoothed. On the contrary, those with variance much larger than e are preserved. The parameter e and the window size determine the capability of detail extraction. Fig. 2 shows this capability with different values. Unlike the visible images, infrared images often have the characteristic of edge blur. Since the smoothing effect increases when the size of the ﬁlter window is getting larger, the radius r should not be a large value in case of the blurred images become more blurry. When e is set to a small value like 100, the detail layer consists of small details such as background noises and tiny structures. A large window size with a large e will ignore some textures and pay much attention to strong edges. As for our application in infrared images, a small win- dow size with a large e will give us a satisﬁed detail layer. 3.2. Filter kernel weights analysis The ability of the edge-preserving can be understood by inves- tigating the ﬁlter kernel. Eq. (4) shows the property. When the two pixels Iinði00 ; j0Þ are on the same side of an edge, the terms Iinði00 ; j0Þ li0;j0 have the same signs (±). Otherwise, they have opposite signs. Therefore, the term ; j00Þ and Iinði0 ; j00Þ li0 ;j0 and Iinði0 1 þ ðIinði00 ; j0Þ li0;j0ÞðIinði0 ri0;j0 þ e ; j0Þ li0;j0Þ is much smaller when two pixels are on different sides than on the same sides [9,11]. For ‘‘ﬂat patch’’ with small scale textures, the ﬁl- ter acts like a low-pass ﬁlter. However, when pixels across an edge, the kernel assigns nearly zero weights to those on the opposite sides, they are almost not averaged together [12]. A good advantage of guided ﬁlter compared to bilateral ﬁlter is that it avoids the gradient ﬂipping artifacts. We choose a real cap- tured frame and conduct the two ﬁlter separately. The plots show the ﬁltering effect of them. The red1 line in Fig. 3(a) indicates the sampling column. The process result by these two ﬁlter are shown in Fig. 3(c–f). The data in selected region of Fig. 3(b) are processed and shown in Fig. 3(c–f). We can see that for the bilateral ﬁlter, the base layer is not consistent with input signal at the edge pixels because few pixels around them have similar gray levels and the Gaussian weighted average has little statistical data and becomes unreliable. This causes great ﬂuctuations in detail layer, and the recombined signal has reversed gradients. For guided ﬁlter, the gra- dient of the base layer is nearly linear around the edge, so it pre- serves the gradient information better. The shape of the edge is well maintained in the recombined layer (see Fig. 3). Most detail enhancement processing based on GIF are merely for visible images which contain little noises. For infrared images, simply enhance the detail component will inescapably lead to an unacceptable ampliﬁcation of the noise in homogeneous region of the image. In order to obtain visually optimal results, the prop- erties of the visual system should be incorporated into the enhancement algorithm. 3.3. Gain mask technique Zuo et al. proposed an adaptive gain control method for detail component in his BF&DDE in Ref. [8]. They simply employed the nor- malized weighting coefﬁcient of the bilateral ﬁlter to act as the mask to enhance the detail layer. In the smooth region of the image, the gain of the detail is set low to avoid the over ampliﬁcation of the noise. Otherwise, in the high spatial active area, the gain of the detail is set high to enhance the image’s visual effect. Usually the gain range is set from 1 to 2.5. The background, like the sky region, has the values of gain near 1, which prevents ampliﬁcation of noise. Here we propose a new method to identify the details and background. We noticed that the kernel of the GIF somehow reﬂects the spatial detail of the image. We simplify the kernel as follows: Wði; jÞ ¼ 1 wj j ðIði; jÞ lm;nÞ2 X ! ð8Þ m;n þ e0 r2 : ðm;nÞ2wi;j 1 For interpretation of color in Fig. 2, the reader is referred to the web version of this article.

N. Liu, D. Zhao / Infrared Physics & Technology 67 (2014) 138–147 141 Fig. 2. Detail extraction of guided image ﬁlter. The input image is 14-bit raw data. This ﬁgure shows the different window size and parameter e of GIF determine the capability of detail extraction. Here we set the window size of wi;j to 3 3. The parameter e0 in Eq. (8) differs from which in Eq. (6). In this equation, the parameter e0 can modify the masking function, which makes the detail enhancement more controllable. It determines whether the pixels are in the background or not, just like we discussed before. Fig. 4 shows the gain mask of an image with different value of e0. For a small value of e0, the enhancing region is much bigger and the noise in background may be identiﬁed as details and then enhanced by mistake. A large parameter shrinks the enhancing region, this may suppress noise but also details. A proper value of about 500 may be satisﬁed for our application. The parameter e0 determines exactly which parts of the image should be enhanced and which should be restrained. With this tech- nique we are able to enhance the detail region as much as we need. Meanwhile, the background like the sky is clean and fresh. 4. Processing of base and detail component Since the GIF has an excellent effect of separating the images into two component and involving the gain masking function as a detail indicator, we then have to deal the two components prop- erly and recombine them to get the ﬁnal result. 4.1. Histogram projection for base component The property of the base component is smoothness and has wide dynamic range [13]. Hence we can compress it without DðxÞ ¼ x ¼ 0 ; ; other ð10Þ HðyÞ x1 y¼0 nvalid worrying about losing details and noise ampliﬁcation. As Zuo et al. [8] mentioned in the BF&DDE, in order to guarantee that the histogram of the image has a quasi-uniform distribution in its dynamic range, histogram projection is very suitable for this sit- uation [19,20]. The key point of the histogram projection is that the output range is the sum of each valid gray level present, regardless of how many pixels occupy that level. Whether the gray level is valid depends on the share of the number of pixels in this level. The histogram of the base layer is binarized by a threshold T. If the number of pixels in the gray level surpasses T, it will be identiﬁed as valid. Conversely, if the number is less than T, it will be identiﬁed as invalid. Here is the binarized histogram of IB: HðxÞ ¼ 0; nx < T 1; nx > T ð9Þ ; nx is the number of pixels sharing the gray level x. The threshold T can improve the overall contrast and dramatically change the global intensity of the display. When T is chosen as 0.1% of the total number of the pixels, the output of the histogram projection will have a proper visual effect. The cumulative distribution function is deﬁned as: 8< : P 0;

142 N. Liu, D. Zhao / Infrared Physics & Technology 67 (2014) 138–147 Fig. 3. 1-D illustration for detail enhancement for BF and GIF. (a) Input image with selected column; (b) 1-D data of the selected column; (c) BF smoothing effect illustration; (d) BF detail extraction illustration; (e) GIF smoothing effect illustration; and (f) GIF detail extraction illustration. Zuo et al. mapped the level x into RD(x) and change the maxi- mum range of output image R as: R ¼ minðnvalid; DÞ; ð11Þ where nvalid denotes the total number of the valid gray levels and D is the dynamic range of a monitor. Here we improve it and make it more suitable for all possible scenarios. When the dynamic range of the input is not necessarily higher than the display range, the origi- nal should not simply be mapped into the output dynamic range D. When the camera faces a uniform background, like a uniform wall or the cloudless sky, the number of valid gray level can be a very small value, perhaps less than 10. In this case, the output of original histogram projection is mapped into the 8-bit domain, the image will be distorted and full of noise. For Zuo et al. proposed histogram

N. Liu, D. Zhao / Infrared Physics & Technology 67 (2014) 138–147 143 Fig. 4. Gain mask for different e, (a) input raw image with 14-bit displayed by AGC, (b)–(f) are different gain mask with different kernel weighting parameter e, (b) e ¼ 100, (c) e ¼ 200, (d) e ¼ 500, (e) e ¼ 1000, and (f) e ¼ 2000. Bright region means enhancing and dark region means suppressing. projection method, the BF&DDE can move the histogram into the middle of the whole display range, which shows in Ref. [8]. Here we focus on how to raise the output value in a better and more effective way, the histogram projection output modiﬁed as follows: IBP ¼ ðD RÞ P þ D IB½ R; ð12Þ P is a controllable parameter for ﬁne tuning the output bright- ness. From this equation we can see that with the decreasing of the valid gray level, the output range R is shrinking when nvalid < D. The output image would suits the display range better when the adjustable factor ðDRÞ is increasing. P visibility in the complex background [14]. In Section 3 we have involved the weighting coefﬁcient W(i, j) to tell us which part of the image should be enhanced. Here we will approach how much each part should be enhanced. For a completely ﬂat region, the value of W(i, j) is near 0. It will increase when the ﬂuctuation of pixels gets more and more obvious. Most of the values are under 1. If W(i, j) exceed 1.2, we assign them to 1.2. Then, IDP is derived from the following formula: IDP ¼ ID ðWði; jÞ a þ bÞ; ð13Þ 4.2. Gain mask enhancement for detail component We have discussed the compression of the base component, we now focus on the enhancement of the detail layer. Experiments have conﬁrmed that noise in ﬂat regions of the image will give rise to spurious or texture for the observer. The masking effect of the human visual system results in lower noise Here a and b are the coefﬁcients which are linearly mapping the gain to a proper value. Our experiment shows that with a set value of a = 2.5 and b = 0.2 we can get a satisfactory result. Fig. 5 gives an example to demonstrate the effect of the adaptive gain control for an image of a building with a clean background. Since b is set to 0.2, the gains of the sky is far below 1, hence this part is suppressed signiﬁcantly. Meanwhile, the detail regions like the buildings and the crane have the gains near 3 to ensure better enhancement.

144 N. Liu, D. Zhao / Infrared Physics & Technology 67 (2014) 138–147 5. Experimental results We have three sets of raw image data containing different scenarios to complete our tests. Those raw data are captured by two infrared cameras: a 3–5-lm-HgCdTe-IRFPA with 16-bit output raw data and a 8–14-lm-HgCdTe-IRFPA with 14-bit out- put raw data, both of them are 320 256. As a comparison, we focus on the current best effect method, the BF&DDE. We use the code provided by the author and the parameters are set as default. We focus on the subjective feeling and the calculation speed of these two methods. We process the captured raw image data and choose 3 different representative samples presented in Figs. 6–8. Our ﬁrst choice is a scenario with abundant details. We choose it to inspect the ability of detail enhancement of our algorithm. Fig. 6 shows the results. The output of the (a) is just linear com- press the gray level to the display range without doing any enhancement of contrast adjustment. The histogram equalization can change the overall contrast to a certain extent, but it may lose some details and produces some annoying artifacts. The BF&DDE method achieves an outstanding performance in this full detail scene without any strong edges just as our proposed method does. We can see that the wire lines and the fences are seen clearly. The hazy feeling of the original image has disappeared and the output image becomes sharper. For further testing, we choose a scene with bushes, buildings, electric wires and a large background area. As is shown is Fig. 7, both of the two algorithms can signiﬁcantly enhance the bushes, the wire and the lines of the buildings. Though the BF&DDE uses an adaptive Gaussian ﬁlter to restrain the gradient ﬂipping arti- facts, it cannot make them die away completely. As we can see that the BF&DDE manufactures a line between the roof of the building and the sky unauthorized. Our method works better in this situation. Fig. 8 illustrates a real high dynamic range situation: less details background with a soldering iron. The raw data of the iron region can reach up to about 2000 while the background is just near 9500. Obviously, the histogram method cannot be a proper manner to deal such situation. Considering our method and the BF&DDE, both of them can enhance the details and improve the overall contrast. The BF&DDE creates some borderlines unfounded in the original images to make the details more visible. Though we can see the details among the iron region more clearly, those artifacts cannot veritably reﬂect the range of the temperature in this scenario. Some hotter areas have much lower gray levels. This can be seen intuitively from the pseudo-color of Rainbow-code images in (d). The point a in the center of the iron, it seems to has a lower tem- perature than point b aside of the iron for the arbitrary created bor- derlines. Our approach is more respect for the information of the original image. It enhances the details and improves the contrast without involving any artifacts. As an application of temperature measurement, our method is more suitable than the BF&DDE. To further demonstrate the advantages of our algorithm, we experiment the running time in MATLAB of our methods and the BF&DDE. We choose the algorithm shown in Ref. [8] to compare the processing speed of BF and the GIF. It must be pointed out that, the one in Ref. [8] is the brute-force implementation of BF. Although there are several fast algorithms for BF, we choose the one Zuo et al. used to make a precise comparison. In Ref. [11], It is said that the GIF has an O(N) time exact algorithm which means that the time complexity is independent of the window size and we can use arbitrary kernel sizes as we wanted. Since we discussed that the kernel size should not be a larger value, our method uses the 3 3 window for our GIF. As for the bilateral ﬁlter, things change. Larger kernel size performs good visual effect, and also increases computational complexity a lot. Here the BF&DDE uses a 7 7 kernel size of the bilateral ﬁlter and for simplicity a 3 3 Gaussian ﬁlter is used to suppression the gradient reversal artifacts Fig. 5. Gain mask enhancement for detail layer. (a) Input raw image with 14-bit displayed by AGC. (b) Detail enhanced without gain mask. (c) Gain Mask obtained by ﬁlter kernel. (d) Detail enhanced with gain mask (a = 2.5, b = 0.2). The background is quite clean.

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