A new image spatial color gamut mapping algorithm

Abstract

Spatial color gamut mapping algorithm is researched to improve the mapping quality by solving halo artifacts and to improve its efficiency. This paper firstly uses guide filtering to filter L channel and get base layer of L channel, and then use the difference between original L channel value with base layer, to get detail layer of L channel. At the same time, makes statistics on distance relationship between each pixel point with target and source color gamut boundary, according to the statistical data to find out the best threshold value. Make the part of detail layer larger than the threshold value compensates to original image. The experiment proved that efficiency of single mapping operation is higher than conventional two-level mapping algorithm and for most of the images, processing effect is better. What’s more, halo artifact is also solved.

Keywords

Spatial color gamut mapping algorithm details compensation halo artifacts guided filter

1. Introduction

Color gamut mapping is an important part of color accurately transferring between different devices. The study on color gamut mapping algorithm has developed from color gamut mapping algorithm of device to device to color gamut mapping algorithm of image to device. Traditional color gamut mapping algorithm only pursuits accurate delivery of color, ensures the color difference as small as possible before and after image processing, however, in subsequent study finds that the human eye vision system more sensitive than spatial relationship of the color values [1], so the color gamut mapping algorithm of image to device derives branch of spatial color gamut mapping algorithm.

Spatial color gamut mapping algorithm considers the spatial characteristic of image pixel, for the two points of same color value, due to the different position, affected by surrounding pixel, algorithm is also different for processing between the two, so the computing values also exist difference. This kind of algorithm is proposed by Meyer and Barth early [2]. The algorithm firstly divides brightness channel of source image into low-pass brightness part and high-pass brightness part, and maps the brightness of original image to brightness range of target color gamut in frequency field, and then along the equal lightness line adopts piecewise linear function for color mapping within equal color phase, finally uses cutting algorithm mapping handle color point outside color gamut. Bala et al. [3], Kasson [4], Morovic et al. [5], Zolliker et al. [6] and Ming et al. [7] propose the algorithm of secondary mapping, which firstly maps image to the smallest point within color gamut in equal color phase, then high-pass filtering brightness error image before and after mapping, makes detail of getting overlay on the image after mapping, and then uses CUSP cutting algorithm processing to handle, in order to protect image detail. Nakauchi [8], McCann [9], Kimmel et al. [10] and Alsam et al. [11, 12] propose optimization algorithm, which firstly has initial mapping for input image, and then calculates error before and after mapping, if error less than the threshold value range that human eye can recognize, then the mapping completes, otherwise the gamut mapped image is merged with the error image, and the above operation will not repeat until the error is less than the threshold value range that human eye can recognize. Ali Alsam and Ivar Farup propose that using anisotropic diffusion to solve the halo problem in iterative algorithm, and the method iteration 10 $\sim$ 20 can get better mapping effect, and small computational complexity is less.

In the traditional spatial color gamut mapping algorithm, the mapping effect of optimization algorithm is comparatively excellent, but its computational complexity is large and computing efficiency is low. The mapping effect of compensation algorithm is not as good as optimization algorithm, although the computing speed is faster than optimization algorithm, mapping mechanism of two mappings leads that its efficiency is lower, and the traditional spatial color gamut mapping algorithm commonly exists halo artifacts, so needs to improve existing algorithm. This paper firstly breaks algorithm architecture of secondary mapping, only one mapping, in order to improve computing efficiency, secondly uses guide filtering of better layer effect to divide original image into base layer and detail layer, which can effectively avoid the occurrence of halo, finally adopts the method of partial compression, not only ensures color is not changed in most color gamut, and partly protects the mutual relationship between colors outside color gamut, the image visual effect after mapping is closer to original image.

2. Algorithm design

Optimization algorithm using iterative mechanism, the problem of algorithm efficiency cannot have bigger improvement. So this paper mainly starts with compensation algorithm. The root cause of detail loss is the loss of local contrast, but the sensitive degree of human eye is much higher than chroma difference on brightness difference, so it can compensate image detail through compensating high frequency brightness [3]. Traditional spatial color gamut mapping algorithm structure of compensation type is shown in Fig. 1a, also is two-level algorithm proposed by Bala and others. Firstly, it has initial mapping of original image, and then obtains the difference value of L layer before and after mapping, and adds back to image after initial mapping to have secondary mapping. Two-level algorithm effectively enhances the image detail after mapping [6], but the structure of two mappings greatly increases the computation time, and the halo artifacts are unable to avoid. In view of the above problems, this paper proposes new algorithm process as shown in Fig. 1b.

Figure 1.

Flowchart of algorithms, (a) the two-level algorithms and (b) the proposed algorithms.

This paper firstly uses guide filtering to filter L channel and get base layer of L channel, and then use the difference between original L channel value with base layer, to get detail layer of L channel. At the same time, makes statistics on distance relationship between each pixel point with target and source color gamut boundary, according to the statistical data to find out the best threshold value. Make the part of detail layer larger than the threshold value compensates to original image. Finally, the part of image less than the threshold value remains the same, the part larger than the threshold value compresses to threshold value in target color gamut boundary according to the CUSP compression algorithm. This paper only maps one time, the computing efficiency is higher than common algorithm, and this algorithm uses guide filtering to extract the image detail, which makes the halo phenomenon have obviously improved [10, 11].

2.1 The reason of halo occurring

Halo phenomenon is the main artifact of spatial color gamut mapping algorithm, it often occurs in sharp boundary of image. Figure 2 is sketch figure of halo occurring, from top to bottom respectively are original input signal, signal after initial mapping, difference value signal between original input signal and signal after initial mapping, base layer signal of difference value image, detail layer signal of the interpolation image and final output signal of mapping. Figure 2a is color gamut mapping image signal change sketch figure of not occurring halo artifacts and Fig. 2b is color gamut mapping image signal change sketch figure of occurring halo artifacts. The difference between the two is mainly in stratified step of difference value signal. In the Fig. 2b, when filtering difference value image, not only filters detail, and also filters border. When compensating detail layer (the 5 ${}^{\text{th}}$ signal) of containing boundary information to mapping image, which occurs halo (part of convex in the 6 ${}^{\text{th}}$ signal).

Figure 2.

The principle of halo-artifacts.

In order to more visually illustrate, taking the example of Gaussian low-pass filter, the principle can be as Eqs (1) and (2), where ( $u$ , $v$ ) represents pixel coordinate, r is fuzzy radius, $\sigma$ is the standard deviation of normal distribution and its essence is to do weighted average for pixel value in the field. In a certain field, the influence weight of surrounding pixel to center pixel is only related with distance between pixels. Figure 3 is enlarged view of local image boundary, A and B respectively are two regions of image and the value of B area is larger than A area. When the Gaussian low-pass filter filterring pixel of position b, the pixel of region A will have larger influence weight on pixel of b, equally, pixel of position a is also affected by region B, which directly causes value of image got bigger after filtering near the border of region A, the value decreased near the border of region B (the 4 ${}^{\text{th}}$ signal in Fig. 2b), and detail layer also changes correspondingly (the 5 ${}^{\text{th}}$ signal in Fig. 2b). When compensating detail on unfilter image, which can occur halo. This paper uses the guide filtering to get detail layer of image, because of the characteristic of guided filtering protecting image gradient, ideal layered effect, can effectively avoid the occurrence of halo, sets forth the principle of guide filtering in Section 2.2.

$\displaystyle G(u,v)=\frac{1}{2\pi\sigma^{2}}e^{-r^{2}/(2\sigma^{2})}$ (1) $\displaystyle r=\sqrt{u^{2}+v^{2}}$ (2)

Figure 3.

Enlarged view of local image boundary.

2.2 The principle of guide filtering

Guide filtering is a kind of edge protection filter proposed by He [13] and others. It can be expressed as weighted average, as shown in Eq. (3):

$\displaystyle q_{i}=\sum\limits_{j}{W_{ij}(I)p_{j}}$ (3)

$I$ and $j$ represent the position of pixel, $P$ is input image, $I$ is guide image used to establish filter core $W_{ij}$ . Set forth derivation process of $W_{ij}$ according to literature [9].

Assume that $q_{i}$ and $I_{i}$ meet the linear relationship as shown in Eq. (4):

$\displaystyle q_{i}=a_{k}I_{i}+b_{k},\forall i\in\omega_{k}$ (4)

$a_{k}$ and $b_{k}$ are constant coefficient in window $\omega_{k}$ . The value of coefficient should ensure the minimize difference between input image $p_{i}$ and output image $q_{i}$ , thus the minimum value of the Eq. (5) will be computed:

$\displaystyle E(a_{k},b_{k})=\sum\limits_{i\in\omega_{k}}{((a_{k}I_{i}+b_{k}-p% _{i})^{2}+\varepsilon a_{k}^{2})}$ (5)

Compute through the linear regression Eqs (6) and (7):

$\displaystyle a_{k}=\frac{\frac{1}{\left|\omega\right|}\sum\nolimits_{i\in% \omega_{k}}{I_{i}p_{i}-\mu_{k}\bar{p}_{k}}}{\sigma_{k}^{2}+\varepsilon}$ (6) $\displaystyle b_{k}=\bar{p}_{k}-a_{k}\mu_{k}$ (7)

$\omega_{k}$ is the size of filter window, $\omega$ is the total quantity of pixel in window, $\mu_{k}$ is the pixel value’s average value of guide image $I$ in window, $\sigma_{k}^{2}$ is the pixel value’s variance of guide image $I$ in window, $\bar{p}_{k}$ is pixel value’s average value of input image $p$ in window. As for pixel $i$ , the $q_{i}$ obtained in different windows $\omega_{k}$ are different, and it can obtain the final value by computing the average value on all $q_{i}$ , thus obtain the following by applying this linear model into the whole image, as shown in Eq. (8).

$\displaystyle q_{i}=\frac{1}{\left|\omega\right|}\sum\limits_{k:i\in\omega{}_{% k}}{(a_{k}I_{i}+b_{k})}=\overline{a}_{i}I_{i}+\overline{b}_{i}$ (8) $\displaystyle\overline{a}_{i}=\frac{1}{\left|\omega\right|}\sum\nolimits_{k\in% \omega{}_{i}}{a_{k}},\overline{b}_{i}=\frac{1}{\left|\omega\right|}\sum% \nolimits_{k\in\omega{}_{i}}{b_{k}}$

Because p and q are linear relation, therefore we have $W_{ij}=\frac{\partial q_{i}}{\partial p_{i}}$ . And we can get Eq. (9) by inserting the Eq. (7) into the Eq. (8):

$\displaystyle q_{i}=\frac{1}{\left|\omega\right|}\sum\limits_{k\in\omega{}_{i}% }{(a_{k}(I_{i}-\mu_{k})+\bar{p}_{k})}$ (9)

We can make derivation on both sides and get Eq. (10):

$\displaystyle\frac{\partial q_{i}}{\partial p_{i}}=\frac{1}{\left|\omega\right% |}\sum\limits_{k\in\omega{}_{i}}\left({\frac{\partial a_{k}}{\partial p_{j}}(I% _{i}-\mu_{k})+\frac{\partial\bar{p}_{k}}{\partial p_{j}}}\right)$ (10)

In this equation:

$\displaystyle\frac{\partial\bar{p}_{k}}{\partial p_{j}}=\frac{1}{\left|\omega% \right|}\delta_{j\in\omega_{k}}=\frac{1}{\left|\omega\right|}\delta_{k\in% \omega_{j}}$ (11)

When j is in window $\omega_{k}$ , $\delta_{j\in\omega_{k}}$ is 1 or 0. According to Eq. (6), $\frac{\partial a_{k}}{\partial p_{j}}$ is computed:

$\displaystyle\frac{\partial a_{k}}{\partial p_{j}}=\frac{1}{\sigma_{k}^{2}+% \varepsilon}\left({\frac{1}{\left|\omega\right|}\sum\limits_{k\in\omega{}_{i}}% {\frac{\partial p_{i}}{\partial p_{j}}I_{i}-\frac{\partial\bar{p}_{k}}{% \partial p{}_{j}}\mu_{k}}}\right)=\frac{1}{\sigma_{k}^{2}+\varepsilon}\left({% \frac{1}{\left|\omega\right|}I_{j}-\frac{1}{\left|\omega\right|}\mu_{k}}\right% )\delta_{k\in\omega_{j}}$ (12)

By inserting Eqs (11) and (12) into Eq. (10), we can get the guided filter kernel $W_{ij}$ as shown in Eq. (13):

$\displaystyle W_{ij}(I)=\frac{\partial q_{i}}{\partial p_{j}}=\frac{1}{\left|% \omega\right|^{2}}\sum\limits_{k:(i,j)\in\omega{}_{k}}\left({1+\frac{(I_{i}-% \mu_{k})(I_{j}-\mu_{k})}{\sigma_{k}^{2}+\varepsilon}}\right)$ (13)

During the derivation of filter core, an important precondition is to assume that $q_{i}$ and $I_{i}$ meet the linear relation. Such as Eq. (2), in each window $\omega_{k}$ , $\nabla q=a\nabla I$ . As for the whole figure, such as Eq. (6), both $\overline{a}_{i}$ and $\overline{b}_{i}$ are $\nabla q$ and $\nabla I$ of spatial variation, which are not proportional. While both $\overline{a}_{i}$ and $\overline{b}_{i}$ are obtained by computing average value, in the sharp edge of image, their variation is far smaller than $\nabla I$ , which can be ignored, thus $\nabla q\approx a\nabla I$ . This means $q_{i}$ is also the edge as long as $I_{i}$ is edge. When guide image is the same with original image, the filter of guide filtering can protect the edge of original image so as to avoid the occurrence of halo.

In order to verify the effect of guide filtering for detail extraction, this paper makes the simple test image. The size of test image is 100*50 pixel, which is constituted by yellow and blue, adding into 8% Gaussian noise, so that Gaussian low-pass filter and guide filtering can respectively extract detail. Extract a line of pixel, the result is showed in Fig. 4a. It can be seen that in the position of about the 50 ${}^{\text{th}}$ pixel, there is obvious mutation (edge information) in the detail extracted by Gaussian filter as shown in Fig. 4c, while the detail extracted by guide filtering is almost unchanged as shown in Fig. 4d. It proves that guide filtering can better protect the edge of image indeed.

Figure 4.

The effect of guide filtering for detail extraction.

2.3 Color mapping

The algorithm in this paper only conducts one time mapping, it requires selecting proper algorithm. Cutting algorithm is easy to cause different colors point that out of color gamut mapped to a same point, and cause detail loss, however though the compression algorithm can better maintain the relative relationship of pixel, thus most of the image pixel value all change, thus this paper adopts the partial compression method, to ensure that the color in vast majority of color gamut unchanged, other colors are compressed within a range that close to target color gamut boundary. Considering that nearby the endpoint of lightness axis, because it almost parallels to the lightness axis compression, variation of lightness axis is larger, and human eye is more sensitive to lightness changing in bright tone and dark tone, therefore adopting CUSP cutting to conduct mapping for the colors which lightness value is greater than 90 and less than 10.

2.3.1 The determination of threshold value proportion

Referencing from the compression way of SGCK (Chorma-dependent Sigmoidal Lightness Mapping and Cusp Knee Scaling) algorithm, this paper also adopts the partial compression method, this method can not only ensure most of colors unchanged, also can protect the relationship between image pixels to some extent. However SGCK uniformly compresses the colors that beyond 90% of the target color gamut into between 90% and 100% of the target color gamut, and does not consider the characteristic of the image itself. The proposed algorithm firstly sorts the relationship of image color in target color gamut, according to the detail layer that the filter separates out before, seeking out the location of the details, thus can obtain the detail numbers in and out of color gamut, if the details are all distributed within color gamut, mapping shall not effect rendering of detail, the optimal proportion is naturally 1. Otherwise, computing the distance $\textit{Dis}\tan ce_{po\;\text{int}}$ from color point of detail place in color gamut to the mapping center, and the distance $\textit{Dis}\tan ce_{t\arg et}$ from intersection point between connection line and target color gamut to mapping center, among them, the connection line is between color point and mapping center, and applying the proportion $\text{Proportion}_{\text{distance}}=\frac{\textit{Dis}\tan ce_{po\;\text{int}}% }{\textit{Dis}\tan ce_{t\arg et}}$ of the two to represent the place that color point of detail place in color gamut located in target color gamut. In SGCK, setting the distance that from mapping center point to 90% of target color gamut boundary as core area, essentially still is to ensure 90% of point unchanged, therefore require finding a threshold value proportion, make the number of color point smaller than that threshold value in all the detail position larger than 90% of the total number of color point in detail position of target color gamut, this threshold value is the optimal proportion $\text{Proportion}_{\text{best}}$ to be found.

Figure 5.

The relationship between the Distance ${}_{\text{point}}$ and Distance ${}_{\text{target}}$ .

2.3.2 Modification of CUSP algorithm

After obtaining the optimal threshold value, compress the color point outside proportion into remaining region of the target color gamut, consider that CUSP algorithm can better preserve the luminance information of original image while protecting the chroma [3], here select CUSP compression as the compression method. Firstly, CUSP algorithm finds out CUSP point in the target color gamut, which is the biggest chroma point in the target color gamut of equal color phase plane, then select the point with equal lightness of CUSP point in lightness axle as mapping center. After this, according to the distance relation between connection line and intersection point, among them, the connection line is between the color point to be mapped and mapping center, the intersection point is between the target color gamut and original color gamut, and then map color point to be mapped to the interior of target color gamut [11], then apply them into the algorithm of this paper, as shown in the following formulas:

$\displaystyle L_{\textit{mapped}}=(L_{\text{original}}-L_{t\arg et\_\text{% intersection}})\times\left({\frac{\textit{Dis}\tan ce_{t\arg et}\times(1-\text% {Proportion}_{\text{best}})}{\textit{Dis}\tan ce_{\textit{original}}-\textit{% Dis}\tan ce_{t\arg et}\times\text{Proportion}_{\text{best}}}}\right)$ (14) $\displaystyle C_{\textit{mapped}}=(C_{\text{original}}-C_{t\arg et\_\text{% intersection}})\times\left({\frac{\textit{Dis}\tan ce_{t\arg et}\times(1-\text% {Proportion}_{\text{best}})}{\textit{Dis}\tan ce_{\textit{original}}-\textit{% Dis}\tan ce_{t\arg et}\times\text{Proportion}_{\text{best}}}}\right)$ (15)

In the formulas above, $L_{\textit{mapped}}$ and $C_{\textit{mapped}}$ are respectively the lightness value and chroma value to be mapped, $L_{t\arg et\_\text{intersection}}$ and $C_{t\arg et\_\text{intersection}}$ are respectively the lightness value and chroma value of intersection point between the connection line and the target color gamut, among them, the connection line is between the color point to be mapped and mapping center, Proportion ${}_{\text{best}}$ is the optimal proportion computed in Section 2.3.1, $\textit{Dis}\tan ce_{t\arg et}$ and $\textit{Dis}\tan ce_{\textit{original}}$ are respectively the distance from intersection point between connection line, target color gamut and original color gamut to mapping center, among them, the connection line is between color point to be mapped and mapping center.

Figure 6.

The problem of CUSP algorithm. Green line is boundary of device color gamut, red line is boundary of image color gamut and the blue line is attachment of mapping center and mapping point.

The default preconditions of CUSP algorithm are that: firstly, the points with equal lightness of CUSP point in lightness axle are in the target color gamut; secondly, it must exist in the intersection point between connection line, target color gamut and original color gamut, among them, the connection line is between color point to be mapped and mapping center. But in the actual application, the edge of target color gamut is not very regular, probably the two intersection points in lightness axle are not the lightness extreme value points in equal color phase plane, as shown in Fig. 3a, thus it may emerge the situation that points in lightness axle with equal lightness of CUSP point are not in the target color gamut. Besides, when apply CUSP algorithm into the color gamut mapping of “image-device”, because the description precision of color gamut edge is limited, then it is more likely to emerge the situation that the color points of image are not included in the described edge, if this mapping is also not in original color gamut as shown in Fig. 3b, thus the intersection point between connection line and original color gamut is not existed, among them, the connection line is between color point to be mapped and mapping center. Both the two problems above will cause that the algorithm mapping cannot be conducted, thus this paper make the following modifications:

Find out the corresponding point of colorfulness maximum point in equal color phase plane of the target color gamut in lightness axle.

Judge whether this point is in target color gamut, if yes then take this point as mapping center, if no then search for it in remaining point, until satisfies the condition of judgment.

Compute the intersection point of connection line, original color gamut and target color gamut, among them, the connection line is between color input point and mapping center.

Judge whether there is interaction point with original color gamut, if the intersection point is existent then conduct step 5, If the intersection point is nonexistent, thus set color input point as the intersection point of connection line, original color gamut and target color gamut, among them, the connection line is between color input point and mapping center.

Conduct mapping according to the rules of compression algorithm.

3. Evaluation of the proposed algorithm

Ten images in TID 2008 image database are selected as test images. ICC of Eizo CG221 monitor is used to transform the test images from RGB to CIELAB color space. The gamut of test images and HP z3200 inkjet printer are extracted as source and target gamut by applying Segment Maxima Gamut Boundary Descriptor (SMGBD). Respectively adopting HpMinDE (Hue Perceived Minimum Color Difference Error) algorithm, Two-Level algorithm that proposed by Bala et al., a classical iterative optimization SGMA (Alsam and Farup), a classical detail-preservation SGMA (P. Zolliker and K. Simon) and the proposed algorithm to conduct mapping processing on test images.

3.1 Objective evaluation

Compare spatial color gamut mapping algorithm with common pixel-level algorithm, the biggest difference is considering the spatial characteristic of pixel, the embodiment in image is clearer detail reduction. Therefore, this paper relatively evaluates algorithm from color reduction and detail reduction. Color evaluation is to compute color difference by applying S-CIELAB model, the smaller the color difference proves the more accurate color reduction. Detail evaluation is to compute structure similarity by applying SSIM (structural similarity index measurement) model, the greater the value proves the more similar the mapped image with structure of original image, the better the detail reduction [14, 15, 16].

Table 1
Color difference of image

	I01	I02	I03	I04	I05	I06	I07	I08	I09	I10
HpMinDE	0.999	1.106	1.538	3.477	2.157	2.016	1.529	1.395	2.460	8.831
Zolliker	0.926	0.913	1.669	3.125	2.099	1.922	0.986	1.217	2.903	4.933
Alsam	0.886	0.929	1.383	3.941	2.139	1.920	0.963	1.094	2.442	5.165
Two_Level	1.020	1.147	1.510	3.662	1.750	2.366	1.563	1.406	2.245	6.730
Proposed	0.693	0.759	1.159	3.221	2.307	1.608	0.772	1.055	2.137	3.334

What the Table 1 shows is the image color difference of the mapped image and original image that computed by applying S-CIELAB model, in the selection of 10 test images, after mapped by applying with the algorithm that proposed by this paper, there are 8 images which color difference is smallest compared with original image. Data shows that, the color gamut mapping algorithm that proposed by this paper has a certain advantage on the accurate transmission of color.

Table 2

Structural similarity by SSIM model

	I01	I02	I03	I04	I05	I06	I07	I08	I09	I10
HpMinDE	0.986	0.951	0.990	0.990	0.887	0.887	0.980	0.985	0.966	0.940
Zolliker	0.988	0.958	0.989	0.985	0.891	0.902	0.972	0.937	0.953	0.952
Alsam	0.980	0.960	0.981	0.921	0.910	0.909	0.933	0.984	0.962	0.965
Two_Level	0.982	0.955	0.985	0.937	0.946	0.926	0.975	0.972	0.952	0.952
Proposed	0.985	0.980	0.989	0.947	0.978	0.945	0.984	0.987	0.972	0.966

What the Table 2 shows is the structural similarity of mapped image and original image that computed by applying SSIM model, in the selection of 10 test images, after mapped by applying with the algorithm that proposed by this paper, there are 7 images which structural similarity is highest compared with original image. Data shows that, the color gamut mapping algorithm that proposed by this paper is more excellent on detail reduction.

3.2 Subjective evaluation

The subjective evaluation of this paper adopts absolute evaluation method, means number the images that have been mapped with five algorithms according to random sequence, compared with original image, let observer sort [17] it according to its proximity with original image. Experiment invites 10 people who have professional knowledge of color and 10 people who without to participate in evaluation, experiment environment is darkroom, experimental equipment is the corrected eizo CG221 professional displayer. Before experiment proper starts, displayer is required to be preheated for 1 hour, observer adapts image for half an hour, after completing experiment, compute approval rating on algorithm of each image. The experimental results are as follows Fig. 7. It can be seen that the performance of the proposed SGMA is best from Fig. 7. The performance of the HpMinDE is worst because it is belong to pointwise GMA and this may cause image detail loss.

Figure 7.

Experimental result of subjective evaluation.

In this Fig. 7, it sorts different algorithms mapped images which are selected as the frequency that closest to original image, blue color is statistical result of HPMinDE algorithm, red color is statistical result of Two-Level algorithm, green color is statistical result of the proposed algorithm. It is not hard to see, the detail compensation color gamut mapping algorithm that based on Guided filter is closer to human eye visual experience, and this is also more consistent with objective evaluation data.

3.3 Halo test

Figure 8.

The test of halo artifacts (a) and (b) are respectively results of the secondary algorithm and the proposed algorithm.

The reason of halo problem has been analyzed in Section 2.1, it mainly occurs at edge of image, thus for more distinct effect, this paper refers to the test picture in literature to conduct test. This picture is composed of color block with distinct edges, including pure black, pure white, neutral grey high saturation of red, green, yellow and blue. The result of mapping is as shown in Fig. 8, taking center junction of four colors, magnifies to 400 times, can clearly see that there is a halo at junction of each two colors in picture a, yet does not exist in b. Combined with the signal contrast of detail layer in Section 2.2, can obtain conclusions, the proposed algorithm can effectively avoid emergence of halo.

3.4 Operating efficiency comparison

Pixel-level algorithm T (n) $=$ O (n ${}^{\wedge}$ 2), Two-Level algorithm T (n) $=$ n ${}^{\wedge}$ 2 $+$ n ${}^{\wedge}$ 2 $=$ O (n ${}^{\wedge}$ 2), the proposed algorithm T (n) $=$ n ${}^{\wedge}$ 2 $+$ log 2n $=$ O (n ${}^{\wedge}$ 2). Though time complexity of Two-Level algorithm and the proposed algorithm are all O (n ${}^{\wedge}$ 2), yet the constitution of frequency count is different, the computing efficiency of the proposed algorithm is higher than Two-Level algorithm. By applying MATLAB software to implement three algorithms on the same computer. The computing times spent on the gamut mapping processes for 10 original images are shown in Table 3. Because the pointwise GMA (HPMinDE) performs pointwise gamut mapping only once, it’s running time is shortest. The proposed SGMA have a longer running time than HPMinDE. The two_Level SGMA needs the longest running time, because it must perform the pointwise gamut mapping twice.

Table 3
Computing times of the three different algorithms (second)

	I01	I02	I03	I04	I05	I06	I07	I08	I09	I10
HPMinDE	49	47	58	46	48	43	46	54	55	57
Two_Level SGMA	93	79	82	98	96	86	104	103	84	98
The proposed SGMA	59	64	76	62	70	53	83	77	59	64

4. Conclusions

This paper utilizes the excellent edge protection effect of Guide filter, solves halo problem of compensation algorithm, and the structure of signal mapping, reduces computing complexity, greatly increases computing efficiency, adopts the method according to threshold value compression, protects the color in most color gamut unchanged, compresses the color that out of threshold value into a small range that close to target color gamut boundary, it not only ensures the reduction of color, also stores the relationship between pixels. Experiment proves that the image quality that obtained by the proposed algorithm mapping is relatively excellent.

References

Bonnier

Schmitt

Hull

and Leynadier

, Spatial and Color Adaptive Gamut Mapping: A Mathematical Framework and Two New Algorithms, in: Proc. IS&T’s 15th Color Imaging Conference (IS&T, Springfield, VA 2007), pp. 267–272.

Meyer

and Barth

, Color gamut matching for hard copy, Proc Sid Dig 86 (1989).

Balasubramanian

Dequeiroz

Eschbach

and Wu

, Gamut mapping to preserve spatial luminance variations, in: Proc. IS&T’s 8th Color Imaging Conference (IS&T, Springfield, VA 2000), pp. 122–128.

Kasson

J.M.

, Color Image Gamut-Mapping System with Chroma Enhancement at Human-Insensitive Spatial Frequencies, US Patent 5450216 (1995).

Morovic

and Wang

, A multi-resolution, full-colour spatial gamut mapping algorithm, in: Proc. IS&T’s 11th Color Imaging Conference (IS&T, Springfield, VA 2003), pp. 282–287.

Zolliker

and Simon

, Adding local contrast to global gamut mapping algorithms, in: Proc. IS&T’s Conference on Colour in Graphics, Imaging, and Vision (IS&T, Springfield, VA 2006), pp. 257–261.

Zhu

Hardeberg

J.Y.

Wang

and Sun

B.Y.

, Spatial Gamut Mapping based on Guided Filter, in: Proc. IS&T’s International Symposium on Electronic Imaging Science and Technology, Color Imaging XXI: Displaying, Processing, Hardcopy, and Applications (IS&T, Springfield, VA 2016), pp. 1–4.

Nakauchi

Hatanaka

and Usui

, Color gamut mapping based on a perceptual image difference measure, Color Research and Application 24(280) (1999).

McCann

J.J.

, Color gamut mapping using spatial comparisons, Proc. SPIE 4300(126) (2001).

10.

Kimmel

Shaked

Elad

and Sobel

, Space dependent color gamut mapping: A variational approach, IEEE Transactions on image processing 14(796) (2005).

11.

Alsam

and Farup

, Spatial Colour Gamut Mapping by Orthogonal Projection of Gradients onto Constant Hue Lines, Advances in Visual Computing, LNCS 7431(556) (2012).

12.

Alsam

and Farup

, Spatial Colour Gamut Mapping by Means of Anisotropic Diffusion, Computational Color Imaging, LNCS 6626(113) (2011).

13.

Sun

and Tang

, Guided image filtering, IEEE Transactions on Pattern Analysis and Machine Intelligence 35(1397) (2013).

14.

Kuang

Johnson

G.M.

and Fairchild

M.D.

, iCAM06: A refined image appearance model for HDR image rendering, Journal of Visual Communication and Image Representation 18(406) (2007).

15.

Wandell

B.A.

and Zhang

, A spatial extension of CIELAB for digital color-image reproduction, Journal of the Society for Information Display 61(5) (1997).

16.

Wang

Bovik

A.C.

Sheikh

H.R.

and Simoncelli

E.P.

, Image quality assessment: from error visibility to structural similarity, IEEE Transactions on Image Processing 13(600) (2004).

17.

Larson

E.C.

and Chandler

D.M.

, Most Apparent Distortion: Full-Reference Image Quality Assessment and the Role of Strategy, Journal of Electronic Imaging 19(143) (2010).