Adaptive weighted guided image filtering for image denoising based on artificial swarm optimization

Abstract

To solve the shortcomings of traditional guided image filtering (GIF) in edge preservation and denoising performance, this study describes a novel generalized guided image filtering method, which integrates an artificial swarm optimization algorithm. A locally adaptive weighting based on monogenic phase congruency and chaotic swarm optimization is used to produce a more robust method. Since the fixed regularization parameter cannot adapt to the grayscale difference between flat and edge patches, the box filter radius and regularization parameter of guided image filtering have significant influences on image-denoising effects. The chaotic swarm optimization algorithm, which is an improved optimization algorithm with a self-adapting search space, is adopted to find their optimal values for the best denoising effects. Compared with traditional guided image filtering for image denoising and other state-of-the-art methods with image quality as a performance metric, experimental results showed that the proposed denoising algorithm can not only remove noise efficiently and reduce halo artifacts, but can also preserve the edge texture well.

Keywords

Image denoising adaptive weighted guided image filter artificial swarm optimization parameter selection

1 Introduction

Digital images are often subjected to noise in image acquisition, transmission, or storage. For this reason, the presence of noise usually decreases the accuracy of various applications in image processing; therefore, image denoising is one of the important steps in image processing and analysis. A wide range of techniques have been developed to improve the quality of images by human vision in image restoration-enhancement applications. However, denoising is an ill-conditioned problem. Noise reduction and edge preservation are the two main metrics for measuring the effectiveness image-denoising algorithms. Creating an algorithm that simultaneously performs well for both remains a challenge.

Many image-denoising methods have been proposed in [1 –3]. Generally, there are two types of edge-preserving, image-smoothing techniques to reconstruct images via spatial or frequency domain. The algorithms with Gaussian filters have a good smoothing effect for Gaussian noise, but image structure and edge are severely destroyed. On the other hand, algorithms with anisotropic diffusion filters excel at preserving edge; however, halo artifacts emerge.

Recently, a novel filtering method denoted guided image filtering (GIF) was proposed [4]. GIF is a both an effective and efficient linear translation-invariant filter for image denoising, and it fulfills the requirements of edge preservation and low complexity for noise reduction by means of a guidance image. It is an edge-preserving smoothing algorithm for simultaneous sharpening and denoising. Owing to GIF’s superior performance, it has been applied to the fields of computational photography and image processing. Typical examples include image sharpening [5], image fusion [6], and single image haze removal [7]. Unlike the popular bilateral filter [8], independent of window radius and intensity range, GIF is one of the fastest edge-preserving filtering methods for image denoising. In a general way, a noisy input image is also used as the reference image for GIF’s method of weight calculation, which can transfer the structures of the guidance image to the filtering output. Unfortunately, it is possible for the structure of the noisy image to be lost, which causes low accuracy in the denoising output and suffers from halo artifacts.

In order to address the above problems, an edge-aware weighting using local variances of all pixels in a 3×3 window was used in Ref. [9] to penalize the fixed regularization parameter to produce a more robust method. A gradient-domain guided image filter was proposed by Fei et al. [10] using an explicit first-order, edge-aware constraint to prevent the loss of texture and edge information. However, local variances and a first-order gradient in image noise cannot objectively represent the information of edge and texture area that changes greatly and that is disturbed by noise. The edge-aware weighting factor using local variances or first-order gradients in image noise is inaccurate. Therefore, it is sensible to seek a method that is efficient in precision edge detection and noise suppression to penalize the fixed regularization parameter.

Swarm intelligence methods comprise an area of bionic, intelligent technology that is seeing wide use in image processing and that has attracted the attention of researchers [29 –33]. With the development of many methods using a swarm intelligence algorithm, image processing, is more effective; for example multiwavelet image denoising based on the artificial bee colony algorithm [28]. This type of method mainly includes the particle swarm optimization (PSO) algorithm, the fish Swarm optimization, ant colony optimization algorithms, the swarm algorithm, etc. In recent years, the artificial colony algorithm simulates the process of honey bees using local optimization and one-worker individual behavior, and highlights the global optimal value. The artificial swarm optimization algorithm has the advantages of high precision and fast search convergence, which can effectively avoid local minima problems. As a result, the artificial colony algorithm can be used for parameter selections in guided image filtering for further optimization.

Phase congruency measures the significance of feature invariance to contrast, such as edge and corner features. However, an impediment to applying phase congruency to the detection of image features has been its sensitivity to noise. Monogenic phase congruency, which is an improved version of phase congruency that overcomes noise sensitivity, was introduced to construct the structure similarity feature in Ref. [11]. As the regularization parameter of GIF uses the fixed value regardless of the image structure, halo artifacts appear in the image’s edge patch. A novel weighted guided image filtering algorithm using edge-aware weighting by monogenic phase congruency that takes edge and texture information into consideration is proposed in this paper. The proposed filter also has a linear computational cost, which is the same as that of GIF [4]. Experimental results for image denoising show that the proposed denoising algorithm has visual quality and removes noise efficiently.

The traditional GIF result relies on the choice of parameters when GIF is used for image denoising. In order to reduce difficulties in parameter selection, the chaotic swarm optimization algorithm is adopted to adaptively find the optimal parameter values.

The chaotic swarm optimization algorithm is an efficient, simple, and versatile optimization algorithm. It has already been applied to many of the optimization problems in science and engineering, e.g., individualized modeling, project scheduling, optimization of oil- and gas-field development planning, and image segmentation for determining thresholds.

The rest of this paper is organized as follows. Related works and techniques on the GIF are summarized in Section 2. Section 3 includes details on adaptive weighted (AW) GIF using monogenic phase congruency and parameter selections optimization with artificial colony algorithm. Experimental results and analysis of AWGIF are given in Section 4. Concluding remarks are provided in Section 5.

2 Related works on GIF

The guided image filter discussed in Ref. [4] uses a linear transform of the guidance image to preserve preferable edges independent of the filter radius and the range of gray values, and it outperforms the bilateral filter [8]. Guided by different guided images, GIF has been widely applied to the fields of image processing and computer vision, including enhancing image sharpness without noise amplification, high-dynamic-range compression, image matting or feathering, dehazing, and image fusion.

The guided filter is a general linear translation-variant filter. It is assumed that the output image is a linear transform of a guidance image and a filtering input image. The filtering output ${\hat{f}}_{i}$ at a pixel i is given as ${\hat{f}}_{i} = \sum_{j} W_{ij} (G) f_{j},$ (1) where f is the filtering input image, G is a guidance image independent of the filtering input image, ${\hat{f}}_{i}$ is the output image, and the filter kernel W_ij (G) is a function of the guide image G, but is independent of f. Note that the W_ij are normalized weights; that is, ∑_jW_ij (G) =1.

It is assumed that $\bar{Z}$ is a linear transform of G_k in a window w_i centered at a pixel i. A linear transform $\bar{Z}$ of G in the window w_i is expressed by $\bar{Z} (i) = a_{i} G_{k} + b_{i}, \forall k \in w_{i},$ (2) where a_i and b_i are two constants in the window w_i, (a_i, b_i) are linear coefficients, and w_i is a square window centered at the pixel i of radius r.

Obtaining two coefficients a_i and b_i requires a solution that minimizes the following cost function E (a_i, b_i) in the window w_i using the linear ridge regression model: $E (a_{i}, b_{i}) = \sum_{i = 1}^{N} [a_{i} G_{k} + b_{i} - f_{i}]^{2} + λ a_{i}^{2},$ (3)

Here, N is the total number of pixels in the window w_i, and λ is a regularization parameter penalizing a large a_i. The solution of Equation (3) is given by ${\begin{matrix} a_{i} = \frac{\frac{1}{N} \sum_{i = 1}^{N} f_{i} G_{i} - \bar{f_{k}} μ_{k}}{σ_{k}^{2} + λ} \\ b_{i} = \bar{f_{i}} - a_{i} μ_{k} \end{matrix},$ (4) where μ_k and σ_k are the mean and variance of G in the window w_i, respectively, and $\bar{f_{k}}$ is the mean of f_i in the window w_i. Having obtained the coefficients (a, b) by Equation (4) for all windows of the image, the averaging strategy is used to compute the coefficients of the entire image. Therefore, finally, Equation (2) with the average coefficients computed by taking the average of all overlapping windows is modified by $\bar{Z} (i) = \bar{a_{i}} G_{i} + \bar{b_{i}},$ (5) where $\bar{a_{i}} = \frac{1}{N} \sum_{i = 1}^{N} a_{i}$ and $\bar{b_{i}} = \frac{1}{N} \sum_{i = 1}^{N} b_{i}$ are the average coefficients of all windows overlapping i.

For the same reason, it was proven in Ref. [4] that GIF is also a weighted averaging filter, and the weighting kernel function W_ij can be explicitly written as

$\begin{matrix} W_{ij} (G) & = & \frac{1}{{| w |}^{2}} \sum_{k : (i, j) \in w_{k}} \\ (1 + \frac{(G_{i} - u_{k}) (G_{j} - u_{k})}{σ_{k}^{2} + λ}), \end{matrix}$ (6) where |w| is the total number of pixels in a window w_k, λ is a global smoothing parameter, and u_k and σ² are the mean and variance of G in w_k, respectively.

The guided filter approach has an edge-preserving smoothing capability and low computational complexity. It has been widely applied to enhance the sharpness of, and reduce the noise of, blurred, noisy images [12], in real-time local stereo matching [13], and in interactive computation of global illumination [14].

It is well known that the guided-filter kernel weights can flexibly recognize underlying geometric structures in accordance with the performance of the guide image. Unfortunately, although GIF has numerous advantages for computer vision and graphics applications, the fixed regularization global smoothing parameter λ cannot adapt to the grayscale difference between flat and edge patches. Specifically, it performs poorly in image denoising of low signal-to-noise (SNR) images. It is difficult for it to find the noiseless image of the input image as the guide image, and it also lacks the ability to select optimal; parameters, which seriously affects its practicality. In general, the guide image in GIF for image denoising is identical to the input image. Therefore, the performance of the restored image is seriously affected.

To overcome the flaws of the GIF parameters and obtain an excellent result, integrating the shift-variant technique and a Laplacian of Gaussian (LOG) filter response output for pixel classification into the guided filter results was proposed in Ref. [12] to avoid halo artifacts or noise amplification.

In Ref. [4], the regularization parameter λ is a constant, and thus halo artifacts near the edge are caused without distinguishing differences in the image structure. To solve this problem, in Ref. [9] the regularization parameter of weighted GIF (WGIF) is defined by another function that is an edge-aware weighting. The regularization parameter λ (i) = λ/Γ_G (i) is defined by a weighted factor using local variances of all pixels in the 3×3 window, which is expressed by $Γ_{G} (i) = \frac{1}{N} \sum_{i^{'} = 1}^{N} \frac{σ_{G, 1}^{2} (i) + γ_{σ}}{σ_{G, 1}^{2} (i^{'}) + γ_{σ}},$ (7) where σ_G,1 (i) is the local variance of a 3×3 square window centered at a pixel i of the guidance image and γ_σ is a small constant and its value is selected as (0.001×L)2, where L is the dynamic range of the input image. λ (i) in Equation (7) can preferably reflect the change in image detail. Clearly, large weights are assigned to pixels at edges, but small weights of those pixels in flat areas are close to 0 using the weighting of Equation (7). The weighting function of WGIF in Ref. [9] conforms to one feature of the human visual system, namely that the pixels of sharp edges are usually more significant than those in flat areas. WGIF can be applied to reduce halo artifacts, but the local-variance linear model cannot exactly represent the image near some edges. To be precise, the more accurately the edges are detected, the better fine details are enhanced by the proposed weighting. However, edge-preserving methods using the local variance cannot preserve edges preferably in some cases in Ref. [9].

Recently, gradient-domain GIF was proposed in Ref. [17] that uses an edge-aware weighting-defining variable window to measure the importance of some pixels with respect to the entire guidance image. Through a reasonable analysis of the filter’s window size, the proposed filter handles images with better visual appearance than the existing guided-filter-based algorithms, especially around edges. However, the definition of the filter’s window size for different images is inextricable.

In the next section, a novel adaptive weighted GIF, which includes an explicit monogenic phase congruency, weighted for an edge-aware constraint to remove noise while preserving the detail information, is introduced. The new constraint using monogenic phase congruency can preferably detect the edge and be seamlessly integrated into the GIF. The monogenic phase congruency described in Ref. [11] not only captures the edge exactly, but also detects perceptually significant image features.

3 AWGIF using chaotic swarm optimization

In this section, a novel measure of phase congruency called monogenic phase congruency, which uses the monogenic signal to construct phase congruency is first introduced, followed by proposal of a new edge-aware weighting that is incorporated into GIF in Ref. [4] to form AWGIF. The optimal parameters using artificial swarm optimization are approached in parallel via the division of labor, cooperation, and information sharing of employed bees, onlookers, and scouts.

3.1 Monogenic phase congruency

Phase congruency (PC) is a perceptually significant image-feature-detection method and reflects the behavior of the image in the frequency domain. It is applied to construct an edge-detection method that is particularly robust against changes in illumination and contrast. The phases in the frequency domain have maximal congruency at the edges, which corresponds to the human-perceived edges in an image where there are sharp changes between light and dark areas.

The monogenic signal was introduced in Ref. [16] and is considered to be a multidimensional extension of the Riesz transform. The monogenic signal f_m of an image f (x) is defined by $f_{m} (x) = {f (x), R_{x_{1}} * f (x), R_{x_{2}} * f (x)} .$ (8)

Monogenic phase congruency (MPC) can be expressed as $MPC (x) = \frac{⌊ 1 - ξ \times acos (\frac{\sqrt{{fs}^{2} + {fr}_{x_{1}}^{2} + {fr}_{x_{2}}^{2}}}{\sum_{s = 1}^{N} A_{s} (x)}) ⌋}{1 + exp (γ (s - c (x)))} P (x),$ (9) where

${\begin{matrix} f_{s} = \sum_{s} f_{s} (x) \\ {fr}_{x_{1}} = \sum_{s} (R_{x_{1}} * f (x)) \\ {fr}_{x_{2}} = \sum_{s} (R_{x_{2}} * f (x)) \end{matrix}, P (x) = \frac{⌊ \sqrt{{fs}^{2} + {fr}_{x_{1}}^{2} + {fr}_{x_{2}}^{2}} - T ⌋}{\sum_{s = 1}^{N} A_{s} (x) + ɛ}$ ,γ is a gain factor for the sharpness of the cutoff, s is the cutoff value of the filter response spread, and c (x) is a fractional measure of spread. The value of c (x) is obtained by taking the sum of the amplitudes of the responses and dividing by the highest individual response; namely, c (x) = A′ (x)/(N * (A_max (x) + ɛ)), where N is the total number of scales, and ɛ is a gain factor approximately from 1 to 2. T compensates for the influence of noise, and is set at a fixed threshold according to empirical estimation.

MPC is fast and possesses greatly reduced memory requirements compared to the other phase-congruency model. Using T to compensate for the influence of noise, the MPC response is not sensitive to noise. From Fig. 1, it is not difficult to find that MPC correlates well with the human vision system (HVS) and provides good localization of features similar to human vision perception. The image called Harbour in Fig. 1(a) is from the LIVE image database and the Harbour image in Fig. 1(d) is from the A57 image database. Therefore, edge detection by MPC is a good choice for edge-aware weighting.

3.2 A new edge-aware weighting

Instead of local variance, a new edge-aware weighting using monogenic-phase-congruency-based edge-detection methods is proposed. The proposed edge-aware weighting $Γ_{G}^{'} (i)$ is defined by using the monogenic phase congruency of 3×3 windows of all pixels as follows: $Γ_{G}^{'} (i) = \frac{1}{N} \sum_{i^{'} = 1}^{N} \frac{| MPC (i) | + γ^{'} (i)}{| MPC (i^{'}) | + γ^{'} (i)},$ (10) where MPC (i) is the value of the monogenic phase congruency at the center pixel i, i′ is the index of the windows, and γ′ is a small constant | · | is the expression of absolute values.

3.3 Optimal parameters using artificial swarm optimization

Artificial swarm optimization is an optimization algorithm based on the intelligent foraging behavior of honey bee swarms, proposed by Karaboga in 2005. Since the box filter radius r and regularization parameter λ have a significant impact on image denoising performance, in order to make GIF achieve its best effect, a chaotic swarm optimization algorithm is introduced to the box filter radius and the regularization-parameter optimization. Based on the product of the local contrast and sharpness as the fitness function for evaluation, the optimal parameter values are obtained by use of an improved chaotic mutation swarm optimization algorithm.

The fitness function F is defined by

$F = \frac{\sum_{i = 1}^{m} \sum_{j = 1}^{n} [(I_{D} (i, j) - I_{D} (i - 1, j))^{2} + (I_{D} (i, j) - I_{D} (i, j - 1))^{2}]^{1 / 2}}{\sum_{i = 1}^{m} \sum_{j = 1}^{n} [(I_{O} (i, j) - I_{O} (i - 1, j))^{2} + (I_{O} (i, j) - I_{O} (i, j - 1))^{2}]^{1 / 2}}$ (11)

An artificial swarm optimization algorithm consists of three groups of bees; namely, employed bees, onlookers, and scouts. In other words, the number of employed bees in the colony is equal to the number of food sources around the hive. The optimum GIF parameters are found by searching for the best food source location via loop iteration.

The complete steps of the algorithm are as follows.

Step 1: The total number of swarms is set to 40. The largest loop number is set to 20 and the search dimension is 2. The search ranges of the box filter radius r and regularization parameter λ, respectively, are from 2 to 30 and from 0.01 to 1. The next step is to produce initial food sources for all employed bees.

Step 2: The leading bee corresponding to the position of the food source is initialized; namely, the initial value of r and λ. The fitness value of the current food source is used to evaluate denoising image quality by the fitness function F.

Step 3: Each of the leading bees in the surrounding area randomly search for another food source and the fitness value F is calculated according to Step 2. If the food source is more superior, the leading bees will move to a new food source.

Step 4: On the basis of the superiority of each leading bee’s food source, the observed bees choose a leading bee, and randomly search in the surrounding area of a food source. If a food source that the observed bees found is better, that information is fed back to the leading bees, and the leading bees will follow to the same place.

Step 5: At the end of a loop, the current global optimal solution is recorded, and loop variable C increases by 1.

Step 6: When C reaches the maximum of 20 loops, the global optimal solution comprises the best parameter values. Otherwise, go back to to Step 3 and continue to search for the global optimal solution.

4 Experimental results and analysis

In this section, in order to test and compare the performance of our proposed algorithm with other algorithms in the literature, we conducted experiments on 10 512×512-pixel images from Ref. [18] that are widely available, such as Baboon, Barbara, Peppers, House, etc. The noise we use is normal, with standard deviation σ = 10, 15, 20, 25, 30, 35, and 40.

4.1 Image-quality evaluation

For the comparison we used both qualitative and quantitative evaluations to compare our proposed AWGIF method with other methods. Quantitative evaluations were performed using structural similarity (SSIM) [19] and peak signal-to-noise ratio (PSNR) for full-reference cases in which original high-quality images on large benchmark datasets are available. SSIM is a new criterion of image-quality evaluation that considers the image-structure information. It is easy to calculate and applicable to various image-processing applications. The image-quality index of SSIM is defined as $SSIM (x, y) = \frac{(2 μ_{x} μ_{y} + A_{1}) (2 σ_{xy} + A_{2})}{(μ_{x}^{2} + μ_{y}^{2} + A_{1}) (σ_{x}^{2} + σ_{y}^{2} + A_{2})},$ (12) where μ_x, σ_x, and σ_xy denote, respectively, the mean of image x, the variance of image x, and the covariance of images x and y. A₁ and A₂ are small constant positive numbers for the divisor in a division operation to prevent zero A₁ = 0.01 and A₂ = 0.03 in our experiments. μ_x and σ_x measure how similar the contrast and luminance of the images are. σ_xy measures how close the structures of images x and y are. The values range from 0 to 1 for estimating the two images’ similarity index, where the best value, 1, is achieved if and only if σ_x = σ_y.

We compared our proposed AW GIF to the other five different filtering methods: the non-local means algorithm (NLM) [1], median filtering (MF) [21], bilateral filtering (BF) [22], the original GIF [4], and gradient-domain GIF (GD GIF) [17]. GD GIF is representative of the improved version of GIF and gives excellent performance. All algorithms in the experiments were implemented using MATLAB 2010b software, and all the simulations were carried out on an Intel Core 2 Duo T5850 processor with a frequency of 2.16 GHz and 4 GB of DDRII memory running the Windows 7 operating system.

4.2 Results and analysis

The performance of different algorithms were measured quantitatively using PSNR and SSIM. Figures 2 and 3 list the denoising performance of the different methods for comparison.

First, the original GIF, our proposed GIF, and GDGIF produced outputs of reasonable quality for images with low noise levels from PSNR and SSIM indexes. However, when the noise level increased, the performance of both the original GIF and GDGIF deteriorated drastically. GD GIF performed better than the original GIF because of its better edge-preserving capability. Our proposed GIF did not suffer from noise amplification, and its performance was better than that of the original GIF and GDGIF when the noise level increased. Our proposed GIF outputs were comparable to those obtained using BF and superior to those obtained using any of the other algorithms. Although GDGIF produced images with slightly higher PSNR indexes than our proposed GIF did, our proposed GIF outperformed GDGIF in terms of SSIM indexes. We will discuss these characteristics in more detail from the perspectives of detail comparison and execution time.

From the detail shown in Fig. 4, it is seen that the result of our proposed GIF is better than that achieved using MF and the NLM algorithm. There are more edges in the detail region of our proposed GIF than in the others.

Finally, we compare execution times. Comparison of the computation times of our proposed GIF, GDGIF, the NLM algorithm, and BF are shown in Table 1 using three images, each of different size. The table shows that the processing times of our proposed GIF are very low. This is due to the measure of phase congruency based on the monogenic signal and the reduction of orientation and the noise threshold calculation, and the avoidance of dot and cross products. The execution time for phase congruency of our proposed GIF is lower than that of GDGIF for edge detection. BF is fast, however, as the image size increases; the execution time of BF is significantly longer than GIF.

5 Conclusions

A novel denoising algorithm based on the guided image filter is proposed. The novel weighted guided image filter based on monogenic signal theory and a chaotic swarm optimization algorithm is introduced in this paper. The adaptive regularization parameter of GIF can adapt to the grayscale differences between flat and edge patches to avoid halo artifacts for image denoising. The chaotic swarm optimization algorithm is adopted to find the optimal values for the best denoising effects in the proposed method. The usefulness of chaotic swarm algorithm optimizing parameters can effectively remove Gaussian white noise, and provide a good denoising effect. The improved GIF version can not only can keep the image edge and texture, but can also improve the adaptability of the algorithm in dealing with different images, as it chooses the optimal parameters automatically to achieve the best effect. Compared to the existing state-of-the-art approaches, the proposed method exhibited improved performance in terms of PSNR and SSIM indexes. The method also demonstrated better generalization performance and lower execution time than its nearest competitors.

Footnotes

Acknowledgments

This work is partially supported by the doctoral development Foundation of Panzhihua University and scientific Foundation of department of education of sichuan province under grant No. 15ZB0425.

References

Buades

, Coll

and Morel

J.M.

, A review of image denoising algorithms, with a new one, Multiscale Modeling & Simulation4(2) (2005), 490–530.

Elad

and Aharon

, Image denoising via sparse and redundant representations over learned dictionaries, IEEE Transactions on Image Processing15(12) (2006), 3736–3745.

Orchard

, Ebrahimi

and Wong

, Efficient nonlocal-means denoising using the SVD, Proceedings of IEEE International Conference on Image Processing, 2008, pp. 1732–1735.

, Sun

and Tang

, Guided image filtering, IEEE Transactions on Pattern Analysis and Machine Intelligence35(6) (2013), 1397–1409.

Pham

C.C.

and Jeon

J.W.

, Efficient image sharpening and denoising using adaptive guided image filtering, Iet Image Processing9(1) (2014), 71–79.

, Kang

and Hu

, Image fusion with guided filtering, IEEE Transactions on Image Processing22(7) (2013), 2864–2875.

, Sun

and Tang

, Single image haze removal using dark channel prior, IEEE Transactions on Pattern Analysis and Machine Intelligence33(12) (2011), 2341–2353.

Tomasi

and Manduchi

, Bilateral Filtering for Gray and Color Images, Proceedings of the 1998 IEEE International Conference on Computer Vision, Bombay, India.

Zhengguo

, Jinghong

, Zijian

et al., Weighted guided image filtering, IEEE Transactions on Image Processing24(1) (2015), 120–129.

10.

Fei

, Chen

, Wen

et al., Gradient domain guided image filtering, IEEE Transactions on Image Processing24(11) (2015), 4528–4539.

11.

Luo

X.G.

, Wang

H.J.

and Wang

, Monogenic signal theory based feature similarity index for image quality assessment, AEU - International Journal of Electronics and Communications69(1) (2015), 75–81.

12.

Pham

C.C.

and Jeon

J.W.

, Efficient image sharpening and denoising using adaptive guided image filtering, Iet Image Processing9(1) (2014), 71–79.

13.

Hosni

, Bleyer

, Rhemann

et al., REal-time local stereo matching using guided image filtering, IEEE International Conference on Multimedia & Expo (2011), 1–6.

14.

Bauszat

, Eisemann

and Magnor

, Guided image filtering for interactive high-quality global illumination, Computer Graphics Forum30(4) (2011), 1361–1368.

15.

Morrone

M.C.

and Owens

R.A.

, Feature detection from local energy, Pattern Recognition Letters6(5) (1987), 303–313.

16.

Felsberg

and Sommer

, The monogenic signal, IEEE Transactions on Signal Processing49(12) (2001), 3136–3144.

17.

Fei

, Chen

, Wen

et al., Gradient domain guided image filtering, IEEE Transactions on Image Processing24(11) (2015), 4528–4539.

18.

Buades

, Coll

and Morel

J.M.

, A review of image denoising algorithms, with a new one, Multiscale Modeling & Simulation4(2) (2005), 490–530.

19.

Wang

, Bovik

A.-C.

, Sheikh

H.-R.

and Simoncelli

E.-P.

, Image quality assessment: Form error visibility to structural similarity, IEEE Transactions on Image Processing13(4) (2004), 600–612.

20.

Narvekar

N.D.

and Karam

L.J.

, A no-reference image blur metric based on the cumulative probability of blur detection (CPBD), IEEE Transactions on Image Processing20(9) (2011), 2678–2683.

21.

Ito

and Xiong

, Gaussian filters for nonlinear filtering problems, IEEE Transactions on Automatic Control45(5) (2000), 910–927.

22.

Tomasi

and Manduchi

, Bilateral filtering for gray and color images, Proceedings of the Sixth International Conference on Computer Vision, 1998, pp. 839–846.

23.

, Duan

and Liu

, Chaotic artificial bee colony approach to Uninhabited Combat Air Vehicle (UCAV) path planning, Aerospace Science & Technology14(8) (2010), 535–541.

24.

Wen

Y.E.

, Deng-Wu

M.A.

and Fan

H.D.

, Algorithm for low altitude penetration aircraft path planning with improved ant colony algorithm, Chinese Journal of Aeronautics18(4) (2005), 304–309.

25.

Dasgupta

, Das

, Abraham

et al., Adaptive computational chemotaxis in bacterial foraging optimization: An analysis, IEEE Transactions on Evolutionary Computation13(4) (2009), 919–941.

26.

Alatas

, Chaotic bee colony algorithms for global numerical optimization, Expert Systems with Applications37(8) (2010), 5682–5687.

27.

Karaboga

and Basturk

, On the performance of Artificial Bee Colony(ABC)algorithm, Applied Soft Computing8(1) (2008), 687–697.

28.

Lin

, Zhijun

and Shengqian

, Multi-wavelet adaptive method based on genetic algorithm, Infrared and Millimeter Waves28(1) (2009), 77–80.

29.

and Zheng

, A measure of similarity between trajectories of vessels, Journal of Engineering Science and Technology Review9(1) (2016), 17–22.

30.

and Zheng

, Trajectory prediction of vessels based on data mining and machine learning, Journal of Digital Information Management14(1) (2016), 33–40.

31.

Krolczyk

J.B.

, Homogeneity assessment of multi-element heterogeneous granular mixtures by using Multivariate Analysis of Variance, Technical Gazette23(2) (2016), 383–388.

32.

Aydemir

and Koruca

H.I.

, A new production scheduling module using priority-rule based genetic algorithm, International Journal of Simulation Modelling14(3) (2015), 450–462.

33.

Cai

, Yang

, Ning

, Ou

and Zeng

, An automatic algorithm for distinguishing optical navigation markers used during surgery, DYNA90(2) (2015), 203–209.