Figure 1.
Convolution template of image block in horizontal and vertical directions.
Citation: Somisetti V. Sambasivarao, David M. Granum, Hua Wang, C. Mark Maupin. Identifying the Enzymatic Mode of Action for Cellulase Enzymes by Means of Docking Calculations and a Machine Learning Algorithm[J]. AIMS Molecular Science, 2014, 1(1): 59-80. doi: 10.3934/molsci.2014.1.59
| [1] | Yanyan Zhang, Jingjing Sun . An improved BM3D algorithm based on anisotropic diffusion equation. Mathematical Biosciences and Engineering, 2020, 17(5): 4970-4989. doi: 10.3934/mbe.2020269 |
| [2] | Fangrong Zhou, Gang Wen, Yi Ma, Yutang Ma, Hao Pan, Hao Geng, Jun Cao, Yitong Fu, Shunzhen Zhou, Kaizheng Wang . A two-branch cloud detection algorithm based on the fusion of a feature enhancement module and Gaussian mixture model. Mathematical Biosciences and Engineering, 2023, 20(12): 21588-21610. doi: 10.3934/mbe.2023955 |
| [3] | Yong Tian, Tian Zhang, Qingchao Zhang, Yong Li, Zhaodong Wang . Feature fusion–based preprocessing for steel plate surface defect recognition. Mathematical Biosciences and Engineering, 2020, 17(5): 5672-5685. doi: 10.3934/mbe.2020305 |
| [4] | Xiao Wang, Jianbiao Zhang, Ai Zhang, Jinchang Ren . TKRD: Trusted kernel rootkit detection for cybersecurity of VMs based on machine learning and memory forensic analysis. Mathematical Biosciences and Engineering, 2019, 16(4): 2650-2667. doi: 10.3934/mbe.2019132 |
| [5] | Hongyan Xu . Digital media zero watermark copyright protection algorithm based on embedded intelligent edge computing detection. Mathematical Biosciences and Engineering, 2021, 18(5): 6771-6789. doi: 10.3934/mbe.2021336 |
| [6] | Yingying Xu, Chunhe Song, Chu Wang . Few-shot bearing fault detection based on multi-dimensional convolution and attention mechanism. Mathematical Biosciences and Engineering, 2024, 21(4): 4886-4907. doi: 10.3934/mbe.2024216 |
| [7] | Xinlin Liu, Viktor Krylov, Su Jun, Natalya Volkova, Anatoliy Sachenko, Galina Shcherbakova, Jacek Woloszyn . Segmentation and identification of spectral and statistical textures for computer medical diagnostics in dermatology. Mathematical Biosciences and Engineering, 2022, 19(7): 6923-6939. doi: 10.3934/mbe.2022326 |
| [8] | Yugui Jiang, Qifang Luo, Yuanfei Wei, Laith Abualigah, Yongquan Zhou . An efficient binary Gradient-based optimizer for feature selection. Mathematical Biosciences and Engineering, 2021, 18(4): 3813-3854. doi: 10.3934/mbe.2021192 |
| [9] | Kelum Gajamannage, Erik M. Bollt . Detecting phase transitions in collective behavior using manifold's curvature. Mathematical Biosciences and Engineering, 2017, 14(2): 437-453. doi: 10.3934/mbe.2017027 |
| [10] | Zhenwu Xiang, Qi Mao, Jintao Wang, Yi Tian, Yan Zhang, Wenfeng Wang . Dmbg-Net: Dilated multiresidual boundary guidance network for COVID-19 infection segmentation. Mathematical Biosciences and Engineering, 2023, 20(11): 20135-20154. doi: 10.3934/mbe.2023892 |
Image segmentation technology plays a very important role in the field of machine vision [1–5], and it is the basis of subsequent image processing work. Image edge detection technology is the most important part of image segmentation technology [6]. Edge is an area in which the local gray level changes significantly [7,8]. It mainly exists between different objects, objects and backgrounds, and different regions. How to improve the accuracy of edge detection is an active topic in the field of machine vision [9,10]. For image signals, drastically changing parts, such as edges and contours, carry important feature information. Edge detection can find the boundary contours of objects to achieve the goal of target recognition [11,12]. Therefore, it has a wide range of applications in image processing, computer vision, fault diagnosis, hydrodynamics, seismic signal analysis, data compression, etc. [13]. Gradient-based edge detection operators are actually high-pass filters used to enhance edge points in images, such as Roberts [14], Sobel [15] and Prewitt operators [16]. Classical edge detection operators are very effective for high SNR image processing, but because they use a small template to convolute with the image, the effect of image processing with noise is not good [17]. The standard wavelet transform studied by Mallat and Zhong is also a representative gradient method [18]. However, when the detected image contains noise, the detection effect of the wavelet edge detection operator is greatly reduced. Many scholars have proposed various improved methods for wavelet edge detection, such as applying New Wavelet to traditional wavelet edge detection [19], and combining wavelet with other methods [20]. However, most of the above methods aim at non-noisy image edge detection, which can achieve good detection results, but the effect for noisy image is not good [21]. In this paper, singular value decomposition is introduced into edge detection. Local gradient singular value decomposition is applied in gradient field. The calculation methods of gradient modulus and gradient direction are improved. The gradient modulus defined by singular value can enhance image edge features and suppress noise. This method can not only extract weak edges and detect clear and complete single edges in noiseless images, but also can extract ideal edges in the presence of noise interference.
The remainder of the paper is organized as follows. In Section 2, basic principles of image gradient and Obel operator are introduced. Then we extend the Sobel gradient template to other directions. Section 3 designs an image edge detection algorithm based on singular value feature vector and gradient operator. The experimental results are given in Section 4. Finally we summarize the full paper in Section 5.
Image gradient is a highly discriminatory feature representation method, which has a certain anti-noise ability [22]. In gray image, gradient is usually used to reflect the gray change at the edge. The gradient of image has been proved to be a highly discriminatory feature representation method, and has a certain degree of noise resistance [23,24].
Let $f$ be a continuous function, so the gradient of $\left({x, y} \right)$ is
| $ ∇f(x,y)=[Px(i,j),Py(i,j)]T=[∂P(i,j)∂x,∂P(i,j)∂y]TM(i,j)=|∇f(x,y)|=(|∂P(i,j)∂x|2+|∂P(i,j)∂y|2)1/2 $ | (1) |
where $\nabla f\left({x, y} \right)$ is the first order differential of $f\left({x, y} \right)$ in different direction. $M\left({i, j} \right)$ is the gradient of $\left({x, y} \right)$. For discrete pixels of gray image, the discrete first-order difference is used to replace the continuous first-order differential operation for gradient calculation.
| $ \left| {\nabla f\left( {x,y} \right)} \right| = {\left\{ [f(x,y)−f(x+1,y)]2+[f(x,y)−f(x,y+1)]2 \right\}^{1/2}} $ | (2) |
where $f\left({x, y} \right)$ is the pixel value located at $\left({x, y} \right)$ in the image $f$.
At present, Roberts operator, Prewitt operator, Kirsch operator and Sobel operator are commonly used to detect image edges by finding the maximum. Laplacian algorithm and its derivative algorithm are used to detect image edges by finding zero-crossing points of second derivative. Sobel algorithm is a very important algorithm in the field of image detection. It plays an irreplaceable role in both machine vision and image processing. It is a discrete first-order difference operator, which is mainly used to calculate the approximation of image gray function under the first-order gradient. Using this algorithm for every point of digital image, different gradient vectors or other vectors can be obtained. Sobel algorithm uses these vectors to get image edge points [25,26].
Generally, Sobel operator contains two sets of matrices, namely, two directional templates, the size of which is 3 × 3. Generally, the principle of edge detection by Sobel operator is convolution, that is, image and directional template are convoluted, and the result can be obtained as
| $ fx(x,y)={f(x+1,y−1)+2f(x+1,y)+f(x+1,y+1)}−{f(x−1y−1)+2f(x−1,y)+f(x−1,y+1)}fy(x,y)={f(x−1,y+1)+2f(x,y+1)+f(x+1,y+1)}−{f(x−1,y−1)+2f(x,y−1)+f(x+1,y−1)} $ | (3) |
So the direction template is also called convolution core. Two commonly used horizontal and vertical templates are as Figure 1.
In edge extraction, each pixel in the image is convoluted with the template separately, and the larger value of the convoluted results is used to replace the pixel value of the corresponding point in the center of the template. If the pixel value of the processed pixel is greater than or equal to the smear value, it can be preliminarily judged that the pixel is an edge point. Since the adjacent pixels of a pixel point in an image are not only in its horizontal and vertical directions, in order to better reflect the gradient of the pixels in each direction, the Sobel operator is extended from horizontal and vertical directions to other directions as Figure 2.
The gradient of the pixels can be obtained by convolution template in eight directions as
| $ s\left( {x,y} \right) = \sqrt {f_{\theta = 0}^2\left( {x,y} \right) + ... + f_{\theta = 315}^2\left( {x,y} \right)} $ | (4) |
where $\theta $ is the gradient direction of Sobel template. $\left({x, y} \right)$ represents the coordinate position of the image pixels. For the boundary pixels of gray image, there may be some incomplete gradient calculation model in some direction. Because of the particularity of the boundary pixels, we can regard the area outside the gray image as the same area as the boundary pixel value, so that the gradient value of the boundary pixels of gray image is only determinated by the pixel within the image.
This section proposed a detailed algorithm for image edge detection. For simplicity, we analyze the singular values of image blocks firstly, then determine the threshold of image pixel gradient based on global and local thresholds, and finally extract edge pixels. The solving process is divided into three stages.
Singular Value Decomposition (SVD) is an important matrix decomposition method in linear algebra. Singular values of images have good characteristics in describing the distribution characteristics of image pixel matrix, and can capture the important basic structure of image data, thus reflecting the essence of image pixel values [27,28]. Singular value decomposition is defined as follows:
Let $Z\left({Z \in R} \right)$ be the image pixel matrix, where $R$ is the real number field. The singular value decomposition of matrix $Z$ is defined as
| $ Z = U\lambda {V^T} $ | (5) |
where $U \in {R^{m \times m}}, V \in {R^{n \times n}}$ are the unitary matrixs, they satisfy the condition $U{U^T} = E, V{V^T} = E$. $T$ represents the transpose of a matrix. $\lambda \in {R_{m \times n}}$ is a diagonal matrix whose elements on the non-diagonal line are non-negative. The element ${\lambda _i}$ on the diagonal line is called the singular value of matrix $Z$. The common practice is to arrange singular values from large to small as ${\lambda _1} \geqslant {\lambda _2} \geqslant... \geqslant {\lambda _i} = {\lambda _{i + 1}} = ... = 0$, then ${\lambda _i}$ can be uniquely determined by $A$.
In order to prove the stability of singular values, the concept of norm is introduced in this section. The norm of image matrix has the following relationship with singular values:
Let $A = US{V^T}$ be the singular value decomposition of matrix $A \in {R^{m \times n}}$, where $S = diag\{ {\sigma _1}, \cdots, {\sigma _p}\} $. Then its 2-norm is as
| $ {\left\| A \right\|_2} = \sqrt {{\lambda _{\max }}({A^T}A)} = {\sigma _1} $ | (6) |
Let $A, B \in {C^{m \times n}}$ be two sets of image blocks, which singular values are${\sigma _1} \geqslant {\sigma _2} \geqslant... \geqslant {\sigma _n} \geqslant 0$, ${\tau _1} \geqslant {\tau _2} \geqslant... \geqslant {\tau _n} \geqslant 0$. Then for each unitary invariant norm$\left\| {} \right\|$, $\left\| {diag\left({{\tau _1} - {\sigma _1}, {\tau _2} - {\sigma _2}, ..., {\tau _n} - {\sigma _n}} \right)} \right\| \leqslant \left\| {B - A} \right\|$. From known conditions we can get${\sigma _1} \geqslant {\sigma _2} \geqslant... \geqslant {\sigma _p} \geqslant 0$, for each unitary invariant norm on ${C^{m \times n}}$, we can get
| $ \left\| {diag\left( {{\tau _1} - {\sigma _1},{\tau _2} - {\sigma _2},...,{\tau _n} - {\sigma _n}} \right)} \right\| \leqslant \left\| {A' - A} \right\| $ | (7) |
Obviously $\left| {{\sigma _1} - {\delta _1}} \right| \leqslant \left\| {diag\left({{\tau _1} - {\sigma _1}, {\tau _2} - {\sigma _2}, ..., {\tau _n} - {\sigma _n}} \right)} \right\|$ and $\left\| {A' - A} \right\| = \left\| {\Delta A} \right\|$, so we can get
| $ \left| {{\sigma _1} - {\delta _1}} \right| \leqslant \left\| {A' - A} \right\| = \left\| {\Delta A} \right\| $ | (8) |
where $\left\| {\Delta A} \right\|$ represents the difference between two matrices. For the gray image in this paper, $A$ can be regarded as the difference between the gradient operator matrices of two adjacent pixels. From the adjacency of the pixels, it can be seen that the difference between the gradient operator matrices of adjacent pixels is small. From the above process, we can see that the maximum singular value of the image pixel matrix has good stability, that is, the maximum singular value of the image pixel matrix changes little after slight noise interference. Moreover, the maximum singular value of a matrix is often much larger than other singular values, and the stability of the matrix is guaranteed without affecting the order of the size of the singular values.
Global threshold refers to the use of only one threshold in all image processing, which is called global threshold. We usually determine the global threshold based on the image histogram. Certainly, it is also necessary to use the distribution of gray space to determine the global threshold. The principle of binarization based on global thresholds is simple. It only needs to compare the gray values of all the pixels in the image with the global thresholds. If the gray values of the pixels are larger than the global thresholds, they are taken as white; otherwise, they are taken as black. It can be seen that the global threshold algorithm is relatively simple to run. Local threshold is a threshold set for each locality, which is called local threshold. That is to say, the local threshold is determined according to the distribution of the pixels in the neighborhood for the pixels in the location. The advantage of local thresholds is that they are flexible. Different thresholds can be determined according to different situations without generalization and specific analysis. However, the design of local threshold has strong pertinence, and there is no general algorithm to realize automatic threshold processing.
Therefore, this paper combines global threshold with local threshold to seek adaptive threshold setting. The adaptive global threshold is based on the method of maximum inter-class variance, and the local threshold is based on Bernsen algorithm.
Suppose the number of gray levels contained by image is $L$, the number of pixels with gray value $i$ is ${N_i}$, and the total number of pixels in the image is $N = {N_0} + {N_1} +... + N{}_{L - 1}$. Then the probability of the point whose gray value is $i$ is
| $ {P_i} = {N_i}/N $ | (9) |
Set a threshold $t$, the whole image can be divided into dark areas $c1\left({0, 1, ..., t} \right)$ and bright areas $c2\left({t + 1, ..., L - 1} \right)$. The global threshold $TM$ can be obtained as
| $ TM=argmax{a1(t)×a2(t)Δu2}s.t.TM=u1−u2σ=a1×a2(u1−u2)2a1=sum(Pi)(0→t),a2=1−a1u1=sum(i×Pi)/a1(0→t),u2=sum(i×Pi)/a2(t+1→L−1) $ | (10) |
Let $f\left({i, j} \right)$ be the gray value of the image, the window size centered on the pixels $\left({i, j} \right)$ is $\left({2\omega + 1} \right) \times \left({2\omega + 1} \right)$, then the local threshold $TL$ of each pixel is
| $ TL\left( {i,j} \right) = 1/2 \times \left( {\max f\left( {i + m,j + m} \right) + \min f\left( {i + m,j + m} \right)} \right) $ | (11) |
The final threshold of this algorithm is determined as the weighting of global and local thresholds. The formula is
| $ T = TM \times \alpha + TL\left( {i,j} \right) \times \left( {1 - \alpha } \right) $ | (12) |
where $\alpha $ represents the weight factor, $TM$ and $TL$ represent the global and local gradient threshold. When $\alpha $ is assigned to an initial value, the final threshold $T$ of the image pixel gradient can be calculated automatically by Eq (12).
Based on the above theoretical basis, this section gives the specific steps of the edge detection algorithm in this paper as follows:
Stage 1 (Image Pixel Gradient Calculation Based on Singular Value). Let $f$ be original image. Firstly, for each pixel, we can find a $3 \times 3$ image block centered on it. For example, for an image pixel $f\left({i, j} \right)$, the set of image blocks is $\sum\limits_{m = i - 1, n = j - 1}^{i + 1, j + 1} {f\left({m, n} \right)} $. For each image block, we decompose it into singular values, and then replace the original pixels with the maximum of the singular values of the image block. The image is divided into $3 \times 3$ image block sets $\sum\limits_{l = 1}^N {\sum\limits_{m = i - 1, n = j - 1}^{i + 1, j + 1} {{f_l}\left({m, n} \right)} } $, where $N$ is the number of the image blocks. Using the eight templates in Figure 2 to convolute each image blocks, we can get the gradient set of each pixel by Eq (4).
Stage 2 (Determination of Adaptive Pixel Gradient Threshold). For the gradient set $E$ in stage 1, we first calculate the global gradient threshold and local gradient threshold of the original image gradient according to Eqs (10) and (11), then assign an initial value to the weight factor $\alpha $, and calculate the final threshold $T$ of the image pixel gradient according to Eq (12). The value of weight factor $\alpha $ can be adjusted according to the final edge information. For example, if the edge information image obtained by this algorithm is too complex for an original gray image, that is, there are more edge pixels, then the value of weight factor $\alpha $ can be reduced and the gradient threshold of the image can be recalculated. Conversely, if the edge information image obtained by this algorithm is not clear for an original gray image, that is, fewer edge pixels can be calculated, the weight factor $\alpha $ can be increased, the gradient threshold of the image is recalculated after the new value of $\alpha $. Repeat this process until the final satisfactory edge information image is obtained.
Stage 3 (Extraction of Image Edge Pixels). On the basis of the first two stages, we determine whether the pixel of an image is an edge point according to the threshold and the gradient value of the pixel. If the gradient of the pixel of an image is greater than the threshold gradient, we determine that the pixel is an edge pixel of the image. If the gradient value of the pixel of an image is less than the threshold gradient, we determine that the pixel is a non-edge pixel of the image. For edge pixels, we use black dots instead of original pixels (let the gray value of the pixel be 0); for non-edge pixels, we use white dots instead of original pixels (let the gray value of the pixel be 255). The formula is
| $ f'\left( {x,y} \right) = \left\{ 0,s(x,y)⩾T255,s(x,y)<T \right. $ | (13) |
where $f'\left({x, y} \right)$ represents the pixel value of the edge information image. We use this method to process each pixel and finally get the edge information image of the original image.
In this section, we tested the performance of our algorithm with images from the UCID test database. All the experiments are performed using MATLAB v7.0 on a Windows XP platform with a CPU at 1.9 GHz and 4 GB memory. The algorithms to be compared include the proposed algorithm, WT algorithm and Curvelet algorithm.
In this paper, we adjust the value of weighting factor $\alpha $ to make the extracted edge information most obvious. The quality of edge information image can be evaluated by imperceptibility. Peak signal-to-noise ratio (PSNR) is used to evaluate the algorithm by comparing the original image with the edge information image and expressing the peak mean square error of the image in logarithmic form. The calculation formula of PSNR is
| $ PSNR = - 10{\log _{10}}\frac{{\sum\limits_{k = 1}^d {\sum\limits_{m = 0}^M {\sum\limits_{n = 0}^N {{{\left[ {{I_k}\left( {m,n} \right) - {I_k}'\left( {m,n} \right)} \right]}^2}} } } }}{{d \times M \times N \times \mathop {\max }\limits_{m,n} \left\{ {I_k^2\left( {m,n} \right)} \right\}}} $ | (14) |
where ${I_k}\left({m, n} \right)$ is the pixel value of the original image, ${I_k}'\left({m, n} \right)$ is the pixel value of an edge image, $d = 3$ represents the image is a color image, $d = 1$ represents image is gray image. $M \times N$ is the size of image, $\mathop {\max }\limits_{m, n} \left\{ {I_k^2\left({m, n} \right)} \right\}$ represents the square of the maximum pixel, and for gray image, $\mathop {\max }\limits_{m, n} \left\{ {I_k^2\left({m, n} \right)} \right\} = {255^2}$.
Figure 3 shows the edge detection results of the algorithm under different noise conditions, where (a) is the original image; (b) is the image after adding salt and pepper noise; the noise intensity $\delta = 0.01$; (c) is the original image after adding Gauss noise, the noise intensity $\delta = 20$; (d) is the edge detection result of the original image; (e) is the edge detection result of the image (b); and (f) is the edge detection result of the original image (a). The edge detection result of image (c) shows that the edge information of image can still be detected by this algorithm after adding salt and pepper or Gauss noise. Experiments show that the proposed algorithm has a certain anti-noise performance.
Figure 4 shows the experimental results of three different edge detection algorithms. Three representative gray-level images Lena, House and Peppers are selected in this paper. The first line are original image, the second are WT detection algorithm, the third are Curvelet algorithm and the fourth behavior our proposed algorithm. From the data in the graph, it can be seen that the edge information extracted by the algorithm in this paper is clearer than that extracted by the other two algorithms. That is to say, the detection effect of the proposed algorithm is better than that of the other two algorithms.
Figure 5 shows the detection results of three detection algorithms for Lena image under different noise conditions. The first column is the detection results of three algorithms for the original image, the second the detection results of three algorithms after adding Gauss noise, and the third the detection results of three algorithms after adding salt and pepper noise. From the information in the graph, it can be seen that the edge information extracted by this algorithm is clearer than that of the other two algorithms after adding Gauss noise, and the edge information extracted by this algorithm is obviously better than that of the other two algorithms after adding salt and pepper noise. The experimental results show that the proposed algorithm is superior to other similar algorithms in anti-jamming.
The experimental test images are 8 images in Figure 6.
Table 1 presents the comparison of PSNR results of three algorithms for image detection time and edge information extracted. From the experimental results in Table 1, we can see that the algorithm in this paper runs faster than the other two algorithms, and the edge information image extracted by this algorithm has higher PSNR value.
| Image | Our method | WT method | Curvelet method | |||
| PSNR | Time (s) | PSNR | Time (s) | PSNR | Time (s) | |
| Barbara | 11.918 | 8.2124 | 8.928 | 16.0680 | 7.917 | 25.0420 |
| Baboon | 11.930 | 6.6189 | 9.491 | 18.7680 | 8.836 | 21.3780 |
| Boat | 11.712 | 8.8901 | 9.908 | 16.9420 | 8.959 | 25.4220 |
| Cartoon | 10.991 | 10.3894 | 8.663 | 16.3340 | 7.900 | 24.6960 |
| Lake | 12.065 | 15.1090 | 9.597 | 15.8810 | 8.926 | 33.4920 |
| House | 11.890 | 9.2783 | 10.910 | 21.2630 | 9.884 | 33.0670 |
| Lena | 10.910 | 8.3820 | 9.652 | 21.2910 | 8.950 | 23.7630 |
| Peppers | 11.790 | 11.2891 | 8.886 | 17.4220 | 8.836 | 36.8600 |
DownLoad:
CSV
In order to test the edge detection accuracy of our proposed algorithm and other algorithms, images with known number of edge pixels are selected as the test images, as shown in Figure 7. Three algorithms are used to detect the edge information, and then according to the ratio of the number of extracted edge pixels to the number of known edge pixels, the edge detection rate of the three algorithms can be obtained.
Three detection algorithms are used to detect the edge of the eight gray-scale images and extract the edge information image. Then the number of black points in the edge information image (i.e. the number of pixels whose pixel value is 0) is calculated. The detection rate of the algorithm is the ratio of the number of black points in the edge information image extracted by the algorithm to the number of known edge pixels.
Figure 8 is a comparison of the detection rates of three algorithms for detecting experimental images. The abscissa is eight different test images, and the ordinate is the percentage of edge pixels detected by the algorithm. From the data in the graph, it can be seen that the detection rate of this algorithm is higher than that of the other two algorithms for different experimental images.
An image edge detection algorithm based on singular value vector and gradient operator is proposed in this paper. The effectiveness and advantages of this method are verified by experiments. In this paper, the gradient operator is extended to eight other directions to make the calculated gradient value more accurate. By analyzing the stability of the image block singular value, the maximum singular value of the image is used to improve the anti-interference ability of the algorithm. The threshold of image gradient is determined adaptively according to global and local image information. Experiments are given to compare the proposed algorithm with other similar algorithms in terms of visual perception, anti jamming and running time of the algorithm. The results show that the algorithm presented in this paper has good performance.
The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group No. RG-1441-331. This work was also supported by the Opening Project of Jiangsu Key Laboratory of Advanced Numerical Control Technology (SYKJ201804), by the Project funded by Jiangsu Postdoctoral Science Foundation (2019K041), by Nanjing Subsidy Project of IUR Cooperation (201722043) and by Changzhou Sci & Tech Program (CE20195030).
The authors declare no conflict of interest.
| [1] |
Bhat MK, Bhat S (1997) Cellulose degrading enzymes and their potential industrial applications. Biotechnol Advances 15: 583-620. doi: 10.1016/S0734-9750(97)00006-2
|
| [2] |
Himmel ME, Ding SY, Johnson DK, et al. (2007) Biomass recalcitrance: Engineering plants and enzymes for biofuels production. Science 315: 804-807. doi: 10.1126/science.1137016
|
| [3] | Himmel ME (2008) Biomass Recalcitrance: Deconstructing the Plant Cell Wall for Bioenergy. Wiley Blackwell. |
| [4] | Updegraff DM (1969) Semimicro determination of cellulose in biological materials. Anal Biochem 420-424. |
| [5] |
Wang LS, Zhang YZ, Gao PJ (2008) A novel function for the cellulose binding module of cellobiohydrolase I. Sci Chin Series C-Life Sci 51: 620-629. doi: 10.1007/s11427-008-0088-3
|
| [6] |
Edgar KJ, Buchanan CM, Debenham JS, et al. (2001) Advances in cellulose ester performance and application. Prog Polym Sci 26: 1605-1688. doi: 10.1016/S0079-6700(01)00027-2
|
| [7] |
Ragauskas AJ, Williams CK, Davison BH, et al. (2006) The path forward for biofuels and biomaterials. Science 311: 484-489. doi: 10.1126/science.1114736
|
| [8] |
Lynd LR, Laser MS, Brandsby D, et al. (2008) How biotech can transform biofuels. Nat Biotechnol 26: 169-172. doi: 10.1038/nbt0208-169
|
| [9] |
Schubert C (2006) Can biofuels finally take center stage? Nat Biotechnol 24: 777-784. doi: 10.1038/nbt0706-777
|
| [10] |
Andre G, Kanchanawong P, Palma R, et al. (2003) Computational and experimental studies of the catalytic mechanism of Thermobifida fusca cellulase Cel6A (E2). Protein Eng 16: 125-134. doi: 10.1093/proeng/gzg017
|
| [11] |
Wolfenden R, Yuan Y (2008) Rates of spontaneous cleavage of glucose, fructose, sucrose, and trehalose in water, and the catalytic proficiencies of invertase and trehalas. J Am Chem Soc 130: 7548. doi: 10.1021/ja802206s
|
| [12] |
Nishiyama Y, Sugiyama J, Chanzy H, et al. (2003) Crystal structure and hydrogen bonding system in cellulose 1(alpha), from synchrotron X-ray and neutron fiber diffraction. J Am Chem Soc 125: 14300-14306. doi: 10.1021/ja037055w
|
| [13] |
CarleUrioste JC, EscobarVera J, ElGogary S, et al. (1997) Cellulase induction in Trichoderma reesei by cellulose requires its own basal expression. J Biol Chem 272: 10169-10174. doi: 10.1074/jbc.272.15.10169
|
| [14] |
Bayer EA, Chanzy H, Lamed R, et al. (1998) Cellulose, cellulases and cellulosomes. Curr Opin Structl Biol 8: 548-557. doi: 10.1016/S0959-440X(98)80143-7
|
| [15] |
Boisset C, Fraschini C, Schulein M, et al. (2000) Imaging the enzymatic digestion of bacterial cellulose ribbons reveals the endo character of the cellobiohydrolase Cel6A from Humicola insolens and its mode of synergy with cellobiohydrolase Cel7A. Appl Environ Microbiol 66: 1444-1452. doi: 10.1128/AEM.66.4.1444-1452.2000
|
| [16] |
Cantarel BL, Coutinho PM, Rancurel C, et al. (2009) The Carbohydrate-Active EnZymes database (CAZy): an expert resource for Glycogenomics. Nucleic Acids Res 37: D233-D238. doi: 10.1093/nar/gkn663
|
| [17] |
Wilson DB (2009) Cellulases and biofuels. Curr Opin Biotechnol 20: 295-299. doi: 10.1016/j.copbio.2009.05.007
|
| [18] |
Davies G, Henrissat B (1995) Structures and mechanisms of glycosyl hydrolases. Structure 3: 853-859. doi: 10.1016/S0969-2126(01)00220-9
|
| [19] |
Henrissat B, Davies G (1997) Structural and sequence-based classification of glycoside hydrolases. Curr Opin Struct Biol 7: 637-644. doi: 10.1016/S0959-440X(97)80072-3
|
| [20] |
Divne C, Stahlberg J, Teeri TT, et al. (1998) High-resolution crystal structures reveal how a cellulose chain is bound in the 50 angstrom long tunnel of cellobiohydrolase I from Trichoderma reesei. J Mol Biol 275: 309-325. doi: 10.1006/jmbi.1997.1437
|
| [21] | Davies GJ, Brzozowski AM, Dauter M, et al. (2000) Structure and function of Humicola insolens family 6 cellulases: structure of the endoglucanase, Cel6B, at 1.6 angstrom resolution. Biochem J 348: 201-207. |
| [22] |
Yang B, Willies DM, Wyman CE (2006) Changes in the enzymatic hydrolysis rate of avicel cellulose with conversion. Biotechnol Bioeng 94: 1122-1128. doi: 10.1002/bit.20942
|
| [23] |
Dashtban M, Maki M, Leung KT, et al. (2010) Cellulase activities in biomass conversion: measurement methods and comparison. Crit Rev Biotechnol 30: 302-309. doi: 10.3109/07388551.2010.490938
|
| [24] |
Teeri TT (1997) Crystalline cellulose degradation: New insight into the function of cellobiohydrolases. Trends Biotechnol 15: 160-167. doi: 10.1016/S0167-7799(97)01032-9
|
| [25] |
Rouvinen J, Bergfors T, Teeri T, et al. (1990) 3-dimensional structure of cellobiohydrolase-II from trichoderma-reesei. Science 249: 380-386. doi: 10.1126/science.2377893
|
| [26] |
Meinke A, Damude HG, Tomme P, et al. (1995) Enhancement of the endo-beta-1,4-glucanase activity of an exocellobiohydrolase by deletion of a surface loop. J Biol Chem 270: 4383-4386. doi: 10.1074/jbc.270.9.4383
|
| [27] |
Kurasin M, Valjamae P (2011) Processivity of Cellobiohydrolases Is Limited by the Substrate. J Biol Chem 286: 169-177. doi: 10.1074/jbc.M110.161059
|
| [28] |
Breyer WA, Matthews BW (2001) A structural basis for processivity. Protein Sci 10: 1699-1711. doi: 10.1110/ps.10301
|
| [29] |
Morris GM, Huey R, Lindstrom W, et al. (2009) AutoDock4 and AutoDockTools4: Automated Docking with Selective Receptor Flexibility. J Comput Chem 30: 2785-2791. doi: 10.1002/jcc.21256
|
| [30] |
Pettersen EF, Goddard TD, Huang CC, et al. (2004) UCSF chimera - A visualization system for exploratory research and analysis. J Comput Chem 25: 1605-1612. doi: 10.1002/jcc.20084
|
| [31] |
Wang H, Nie F, Huang H, et al. (2012) Identifying quantitative trait loci via group-sparse multitask regression and feature selection: an imaging genetics study of the ADNI cohort. Bioinformatics 28: 229-237. doi: 10.1093/bioinformatics/btr649
|
| [32] |
Wang H, Nie F, Huang H, et al. (2012) Identifying disease sensitive and quantitative trait-relevant biomarkers from multidimensional heterogeneous imaging genetics data via sparse multimodal multitask learning. Bioinformatics 28: i127-136. doi: 10.1093/bioinformatics/bts228
|
| [33] | Lee S, Zhu J, Xing EP (2010) Adaptive Multi-Task Lasso: with application to eQTL detection. Adv Neural Informat Process Syst: 1306-1314. |
| [34] |
Puniyani K, Kim S, Xing EP (2010) Multi-population GWA mapping via multi-task regularized regression. Bioinformatics 26: i208-216. doi: 10.1093/bioinformatics/btq191
|
| [35] | Mackenzie LF, Sulzenbacher G, Divne C, et al. (1998) Crystal structure of the family 7 endoglucanase I (Cel7B) from Humicola insolens at 2.2 angstrom resolution and identification of the catalytic nucleophile by trapping of the covalent glycosyl-enzyme intermediate. Biochem J 335: 409-416. |
| [36] |
Zou JY, Kleywegt GJ, Stahlberg J, et al. (1999) Crystallographic evidence for substrate ring distortion and protein conformational changes during catalysis in cellobiohydrolase Cel6A from Trichoderma reesei. Struct Fold Des 7: 1035-1045. doi: 10.1016/S0969-2126(99)80171-3
|
| [37] |
Parkkinen T, Koivula A, Vehmaanpera J, et al. (2008) Crystal structures of Melanocarpus albomyces cellobiohydrolase Ce17B in complex with cello-oligomers show high flexibility in the substrate binding. Protein Sci 17: 1383-1394. doi: 10.1110/ps.034488.108
|
| [38] |
Varrot A, Schulein M, Davies GJ (2000) Insights into ligand-induced conformational change in Cel5A from Bacillus agaradhaerens revealed by a catalytically active crystal form. J Mol Biol 297: 819-828. doi: 10.1006/jmbi.2000.3567
|
| [39] |
Divne C, Stahlberg J, Reinikainen T, et al. (1994) The 3-dimensional crystal-structure of the catalytic core of cellobiohydroase-I from trichoderma-reesei. Science 265: 524-528. doi: 10.1126/science.8036495
|
| [40] |
Grassick A, Murray PG, Thompson R, et al. (2004) Three-dimensional structure of a thermostable native cellobiohydrolase, CBHIB, and molecular characterization of the cel7 gene from the filamentous fungus, Talaromyces emersonii. Eur J Biochem 271: 4495-4506. doi: 10.1111/j.1432-1033.2004.04409.x
|
| [41] |
Momeni MH, Payne CM, Hansson H, et al. (2013) Structural, Biochemical, and Computational Characterization of the Glycoside Hydrolase Family 7 Cellobiohydrolase of the Tree-killing Fungus Heterobasidion irregulare. J Biol Chem 288: 5861-5872. doi: 10.1074/jbc.M112.440891
|
| [42] | Kleywegt GJ, Zou JY, Divne C, et al. (1997) The crystal structure of the catalytic core domain of endoglucanase I from Trichoderma reesei at 3.6 angstrom resolution, and a comparison with related enzymes. J Mol Biol 272: 383-397. |
| [43] | Munoz IG, Ubhayasekera W, Henriksson H, et al. (2001) Family 7 cellobiohydrolases from Phanerochaete chrysosporium: Crystal structure of the catalytic module of Cel7D (CBH58) at 1.32 angstrom resolution and homology models of the isozymes. J Mol Biol 314: 1097-1111. |
| [44] |
Ubhayasekera W, Munoz IG, Vasella A, et al. (2005) Structures of Phanerochaete chrysosporium Cel7D in complex with product and inhibitors. Febs J 272: 1952-1964. doi: 10.1111/j.1742-4658.2005.04625.x
|
| [45] | Varrot A, Hastrup S, Schulein M, et al. (1999) Crystal structure of the catalytic core domain of the family 6 cellobiohydrolase II, Cel6A, from Humicola insolens, at 1.92 angstrom resolution. Biochem J 337: 297-304. |
| [46] |
Varrot A, Frandsen TP, von Ossowski I, et al. (2003) Structural basis for ligand binding and processivity in cellobiohydrolase Cel6A from Humicola insolens. Structure 11: 855-864. doi: 10.1016/S0969-2126(03)00124-2
|
| [47] |
Larsson AM, Bergfors T, Dultz E, et al. (2005) Crystal structure of Thermobifida fusca endoglucanase Cel6A in complex with substrate and inhibitor: The role of tyrosine Y73 in substrate ring distortion. Biochemistry 44: 12915-12922. doi: 10.1021/bi0506730
|
| [48] |
Varrot A, Schulein M, Davies GJ (1999) Structural changes of the active site tunnel of Humicola insolens cellobiohydrolase, Cel6A, upon oligosaccharide binding. Biochemistry 38: 8884-8891. doi: 10.1021/bi9903998
|
| [49] |
Liu Y, Yoshida M, Kurakata Y, et al. (2010) Crystal structure of a glycoside hydrolase family 6 enzyme, CcCel6C, a cellulase constitutively produced by Coprinopsis cinerea. Febs J 277: 1532-1542. doi: 10.1111/j.1742-4658.2010.07582.x
|
| [50] | Davies GJ, Dauter M, Brzozowski AM, et al. (1998) Structure of the Bacillus agaradherans family 5 endoglucanase at 1.6 angstrom and its cellobiose complex at 2.0 angstrom resolution. Biochemistry 37: 1926-1932. |
| [51] |
Wu TH, Huang CH, Ko TP, et al. (2011) Diverse substrate recognition mechanism revealed by Thermotoga maritima Cel5A structures in complex with cellotetraose, cellobiose and mannotriose. Biochim Et Biophys Acta-Proteins and Proteomics 1814: 1832-1840. doi: 10.1016/j.bbapap.2011.07.020
|
| [52] |
Lee TM, Farrow MF, Arnold FH, et al. (2011) A structural study of Hypocrea jecorina Cel5A. Protein Sci 20: 1935-1940. doi: 10.1002/pro.730
|
| [53] |
Pereira JH, Sapra R, Volponi JV, et al. (2009) Structure of endoglucanase Cel9A from the thermoacidophilic Alicyclobacillus acidocaldarius. Acta Crystallogr Sect D-Biological Crystallogr 65: 744-750. doi: 10.1107/S0907444909012773
|
| [54] | Eckert K, Vigouroux A, Lo Leggio L, et al. (2009) Crystal Structures of A. acidocaldarius Endoglucanase Cel9A in Complex with Cello-Oligosaccharides: Strong-1 and-2 Subsites Mimic Cellobiohydrolase Activity. J Mol Biol 394: 61-70. |
| [55] |
Mandelman D, Belaich A, Belaich JP, et al. (2003) X-ray crystal structure of the multidomain endoglucanase Cel9G from Clostridium cellulolyticum complexed with natural and synthetic cello-oligosaccharides. J Bacteriol 185: 4127-4135. doi: 10.1128/JB.185.14.4127-4135.2003
|
| [56] |
Parsiegla G, Belaich A, Belaich JP, et al. (2002) Crystal structure of the cellulase Ce19M enlightens structure/function relationships of the variable catalytic modules in glycoside hydrolases. Biochemistry 41: 11134-11142. doi: 10.1021/bi025816m
|
| [57] |
Sandgren M, Berglund GI, Shaw A, et al. (2004) Crystal complex structures reveal how substrate is bound in the -4 to the +2 binding sites of Humicola grisea cel12A. J Mol Biol 342: 1505-1517. doi: 10.1016/j.jmb.2004.07.098
|
| [58] | Sandgren M, Shaw A, Ropp TH, et al. (2001) The X-ray crystal structure of the Trichoderma reesei family 12 endoglucanase 3, Cel12A, at 1.9 angstrom resolution. J Mol Biol 308: 295-310. |
| [59] | Sandgren M, Gualfetti PJ, Paech C, et al. (2003) The Humicola grisea Cell2A enzyme structure at 1.2 angstrom resolution and the impact of its free cysteine residues on thermal stability. Protein Sci 12: 2782-2793. |
| [60] |
Kitago Y, Karita S, Watanabe N, et al. (2007) Crystal structure of Cel44A, a glycoside hydrolase family 44 endoglucanase from Clostridium thermocellum. J Biol Chem 282: 35703-35711. doi: 10.1074/jbc.M706835200
|
| [61] |
Valjakka J, Rouvinen J (2003) Structure of 20K endoglucanase from Melanocarpus albomyces at 1.8 angstrom resolution. Acta Crystallogr Sect D-Biol Crystallogr 59: 765-768. doi: 10.1107/S0907444903002051
|
| [62] |
Hirvonen M, Papageorgiou AC (2003) Crystal structure of a family 45 endoglucanase from Melanocarpus albomyces: Mechanistic implications based on the free and cellobiose-bound forms. J Mol Biol 329: 403-410. doi: 10.1016/S0022-2836(03)00467-4
|
| [63] |
Parsiegla G, Reverbel-Leroy C, Tardif C, et al. (2000) Crystal structures of the cellulase Ce148F in complex with inhibitors and substrates give insights into its processive action. Biochemistry 39: 11238-11246. doi: 10.1021/bi001139p
|
| [64] |
Sulzenbacher G, Driguez H, Henrissat B, et al. (1996) Structure of the Fusarium oxysporum endoglucanase I with a nonhydrolyzable substrate analogue: Substrate distortion gives rise to the preferred axial orientation for the leaving group. Biochemistry 35: 15280-15287. doi: 10.1021/bi961946h
|
| [65] |
Li JH, Du LK, Wang LS (2010) Glycosidic-Bond Hydrolysis Mechanism Catalyzed by Cellulase Cel7A from Trichoderma reesei: A Comprehensive Theoretical Study by Performing MD, QM, and QM/MM Calculations. J Phys Chem B 114: 15261-15268. doi: 10.1021/jp1064177
|
| [66] |
Mine Y, Fukunaga K, Itoh K, et al. (2003) Enhanced enzyme activity and enantioselectivity of lipases in organic solvents by crown ethers and cyclodextrins. J Biosci Bioeng 95: 441-447. doi: 10.1016/S1389-1723(03)80042-7
|
| [67] |
Payne CM, Bomble Y, Taylor CB, et al. (2011) Multiple Functions of Aromatic-Carbohydrate Interactions in a Processive Cellulase Examined with Molecular Simulation. J Biol Chem 286: 41028-41035. doi: 10.1074/jbc.M111.297713
|
| [68] |
Voutilainen SP, Boer H, Alapuranen M, et al. (2009) Improving the thermostability and activity of Melanocarpus albomyces cellobiohydrolase Cel7B. Appl Microbiol Biotechnol 83: 261-272. doi: 10.1007/s00253-008-1848-9
|
| [69] | Ding H, Xu F (2004) Lignocellulolse Biodegradation, Chapter 9, ACS 154-169. |
| 1. | Run Tian, Guiling Sun, Xiaochao Liu, Bowen Zheng, Sobel Edge Detection Based on Weighted Nuclear Norm Minimization Image Denoising, 2021, 10, 2079-9292, 655, 10.3390/electronics10060655 | |
| 2. | Shikai Wang, Kangjian Sun, Wanying Zhang, Heming Jia, Multilevel thresholding using a modified ant lion optimizer with opposition-based learning for color image segmentation, 2021, 18, 1551-0018, 3092, 10.3934/mbe.2021155 | |
| 3. | Shuping Yuan, Yang Chen, Chengqiong Ye, Mohd Dilshad Ansari, Edge detection using nonlinear structure tensor, 2022, 11, 2192-8029, 331, 10.1515/nleng-2022-0038 | |
| 4. | Daohui Bi, Fangqing Wen, A Motion Image Pose Contour Extraction Method Based on B-Spline Wavelet, 2021, 2021, 1687-5877, 1, 10.1155/2021/4553143 | |
| 5. | Xiuna Yi, Weiwei Xu, Aizhi Li, Muhammad Akhlaq, The Clinical Application of Remimazolam Benzenesulfonate Combined with Esketamine Intravenous Anesthesia in Endoscopic Retrograde Cholangiopancreatography, 2022, 2022, 2314-6141, 1, 10.1155/2022/5628687 | |
| 6. | Viliam Ďuriš, Vladimir I. Semenov, Sergey G. Chumarov, Wavelets and digital filters designed and synthesized in the time and frequency domains, 2022, 19, 1551-0018, 3056, 10.3934/mbe.2022141 | |
| 7. | Fei Hao, Dashuai Xu, Delin Chen, Yuntao Hu, Chaohan Zhu, Sobel operator enhancement based on eight-directional convolution and entropy, 2021, 13, 2511-2104, 1823, 10.1007/s41870-021-00770-3 | |
| 8. | Yuechun Wang, Suzhen Zhang, Shaofang Zhang, C. Venkatesan, Network Data Mining Algorithm of Associated Users Based on Multi-Information Fusion, 2022, 2022, 1939-0122, 1, 10.1155/2022/9656986 | |
| 9. | Gang Li, C. Venkatesan, Research on Smartphone Trojan Detection Based on the Wireless Sensor Network, 2022, 2022, 1939-0122, 1, 10.1155/2022/2455102 | |
| 10. | Jiahao Li, 2021, Study on Automatic Shoreline Extraction Based on Multi-spectral Remote Sensing Images, 9781450385183, 68, 10.1145/3502827.3502830 | |
| 11. | V. Gowthami, K. Bhoopathy Bagan, S. Ewins Pon Pushpa, A novel approach towards high-performance image compression using multilevel wavelet transformation for heterogeneous datasets, 2023, 79, 0920-8542, 2488, 10.1007/s11227-022-04744-5 | |
| 12. | Xiuyan Wang, Xuan Zhou, Lin Li, Cuijie Liu, Enas Abdulhay, Internet of Things-Based Ultrasound-Guided Erector Spinae Plane Block Combined with Edaravone Anesthesia in Thoracoscopic Lobectomy, 2021, 2021, 2040-2309, 1, 10.1155/2021/9510783 | |
| 13. | Nazish Tariq, Rostam Affendi Hamzah, Theam Foo Ng, Shir Li Wang, Haidi Ibrahim, Quality Assessment Methods to Evaluate the Performance of Edge Detection Algorithms for Digital Image: A Systematic Literature Review, 2021, 9, 2169-3536, 87763, 10.1109/ACCESS.2021.3089210 | |
| 14. | Shahzada Fahad, Sami Ur Rahman, Fakhre Alam, Muhammad Yousaf, Faten S. Alamri, Naveed Abbas, Saeed Ali Bahaj, Amjad R. Khan, A Modified Singular Value Decomposition (MSVD) Approach for the Enhancement of CCTV Low-Quality Images, 2024, 12, 2169-3536, 20138, 10.1109/ACCESS.2024.3349477 | |
| 15. | Yaohe Li, Long Jin, Min Liu, Youtang Mo, Weiguang Zheng, Dongyuan Ge, Yindi Bai, Research on Adaptive Edge Detection Method of Part Images Using Selective Processing, 2024, 12, 2227-9717, 2271, 10.3390/pr12102271 | |
| 16. | Fallah H. Najjar, Kifah T. Khudhair, Ali Hussein Abdul Khaleq, Ola N. Kadhim, Firas Abedi, Ibrahim H. Al-Kharsan, 2022, Histogram Features Extraction for Edge Detection Approach, 978-1-6654-7215-9, 373, 10.1109/IICETA54559.2022.9888697 | |
| 17. | Lei Gao, Haolong Hong, Fan Min, Stable first-arrival picking through mathematical morphology and edge detection, 2023, 236, 0956-540X, 14, 10.1093/gji/ggad410 | |
| 18. | Yini Li, Cao Li, Tao Yang, Lingzhi Chen, Mingquan Huang, Lu Yang, Shuxian Zhou, Huaqing Liu, Jizhu Xia, Shijie Wang, Multiview deep learning networks based on automated breast volume scanner images for identifying breast cancer in BI-RADS 4, 2024, 14, 2234-943X, 10.3389/fonc.2024.1399296 | |
| 19. | Lizette Tello-Cifuentes, Johannio Marulanda, Peter Thomson, Detection and classification of pavement damages using wavelet scattering transform, fractal dimension by box-counting method and machine learning algorithms, 2024, 25, 1468-0629, 566, 10.1080/14680629.2023.2219338 |
Figures(11) / Tables(1)
Somisetti V. Sambasivarao, David M. Granum, Hua Wang, C. Mark Maupin. Identifying the Enzymatic Mode of Action for Cellulase Enzymes by Means of Docking Calculations and a Machine Learning Algorithm[J]. AIMS Molecular Science, 2014, 1(1): 59-80. doi: 10.3934/molsci.2014.1.59
| Image | Our method | WT method | Curvelet method | |||
| PSNR | Time (s) | PSNR | Time (s) | PSNR | Time (s) | |
| Barbara | 11.918 | 8.2124 | 8.928 | 16.0680 | 7.917 | 25.0420 |
| Baboon | 11.930 | 6.6189 | 9.491 | 18.7680 | 8.836 | 21.3780 |
| Boat | 11.712 | 8.8901 | 9.908 | 16.9420 | 8.959 | 25.4220 |
| Cartoon | 10.991 | 10.3894 | 8.663 | 16.3340 | 7.900 | 24.6960 |
| Lake | 12.065 | 15.1090 | 9.597 | 15.8810 | 8.926 | 33.4920 |
| House | 11.890 | 9.2783 | 10.910 | 21.2630 | 9.884 | 33.0670 |
| Lena | 10.910 | 8.3820 | 9.652 | 21.2910 | 8.950 | 23.7630 |
| Peppers | 11.790 | 11.2891 | 8.886 | 17.4220 | 8.836 | 36.8600 |
DownLoad:
CSV
| Image | Our method | WT method | Curvelet method | |||
| PSNR | Time (s) | PSNR | Time (s) | PSNR | Time (s) | |
| Barbara | 11.918 | 8.2124 | 8.928 | 16.0680 | 7.917 | 25.0420 |
| Baboon | 11.930 | 6.6189 | 9.491 | 18.7680 | 8.836 | 21.3780 |
| Boat | 11.712 | 8.8901 | 9.908 | 16.9420 | 8.959 | 25.4220 |
| Cartoon | 10.991 | 10.3894 | 8.663 | 16.3340 | 7.900 | 24.6960 |
| Lake | 12.065 | 15.1090 | 9.597 | 15.8810 | 8.926 | 33.4920 |
| House | 11.890 | 9.2783 | 10.910 | 21.2630 | 9.884 | 33.0670 |
| Lena | 10.910 | 8.3820 | 9.652 | 21.2910 | 8.950 | 23.7630 |
| Peppers | 11.790 | 11.2891 | 8.886 | 17.4220 | 8.836 | 36.8600 |
