Ex) Article Title, Author, Keywords
Current Optics
and Photonics
Ex) Article Title, Author, Keywords
Curr. Opt. Photon. 2023; 7(4): 408-418
Published online August 25, 2023 https://doi.org/10.3807/COPP.2023.7.4.408
Copyright © Optical Society of Korea.
Hongfei Song, Kehang Zhang , Wen Tan, Fei Guo, Xinren Zhang, Wenxiao Cao
Corresponding author: ^{*}cust_zkh123@163.com, ORCID 0000-0002-6744-666X
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Due to the technological limitations of infrared thermography, infrared focal plane array (IFPA) imaging exhibits stripe non-uniformity, which is typically fixed pattern noise that changes over time and temperature on top of existing non-uniformities. This paper proposes a stripe non-uniformity correction algorithm based on scene-adaptive nonlinear filtering. The algorithm first uses a nonlinear filter to remove single-column non-uniformities and calculates the actual residual with respect to the original image. Then, the current residual is obtained by using the predicted residual from the previous frame and the actual residual. Finally, we adaptively calculate the gain and bias coefficients according to global motion parameters to reduce artifacts. Experimental results show that the proposed algorithm protects image edges to a certain extent, converges fast, has high quality, and effectively removes column stripes and non-uniform random noise compared to other adaptive correction algorithms.
Keywords: Adaptive correction, Nonlinear filter, Non-uniformity correction, Residual estimation
OCIS codes: (110.2650) Fringe analysis; (110.3080) Infrared imaging; (110.4155) Multiframe image processing; (110.4280) Noise in imaging systems
As a main development direction of infrared thermal imaging, the infrared focal plane array (IFPA) has been widely employed in military, aerospace, civil, and other fields due to its high sensitivity, strong detection capability, and strong adaptability to harsh climate conditions [1]. However, due to the limitations of non-uniformity correction technology, different pixels in the focal plane array (FPA) have different response rates, resulting in fixed-pattern noise that seriously affects the imaging quality of the infrared system. In particular, pixels in the same column of the (FPA share the same integral readout circuit, resulting in column stripe noise in the imaging. Moreover, because the fixed noise will shift with temperature and time, it cannot be accurately calibrated [2].
There are currently two directions for non-uniformity correction algorithms: calibration-based and scene-based. The former includes typical methods such as the two-point correction method, multi-point correction method, and baffle correction method, which rely on the periodic use of radiation sources or baffles to provide uniform scenes for calibration [3]. The advantage of this method is its simplicity and obvious correction effect. However, in practical applications, periodic loss of targets may occur. The latter direction, scene-based correction, includes representative methods such as the generative adversarial network method proposed by Mou
Figure 1 is a comparison of infrared image before and after correction by non-uniform correction algorithm.
In this paper, a scene-based non-uniform correction (NUC) algorithm is proposed for removing column stripes and random noise caused by non-uniformity in infrared (IR) imaging systems. IR non-uniformity is often considered fixed pattern noise, which varies with time and temperature, and has a significant impact on image quality. Traditional methods ignore the characteristics of non-uniformity, and changes in scene details may be incorrectly identified as non-uniformity and filtered out. Based on the characteristics of visible light imaging, where adjacent pixels of a target pixel have a Gaussian distribution of mutual influence, it is assumed that the mutual influence between the target column pixel and adjacent column pixels in an IR image also follows a Gaussian distribution. Additionally, pixels in the same column of a FPA share the same integration readout circuit, and the impact of fixed noise between different columns can be ignored. Therefore, it is assumed that a single column contains sufficient imaging information, and the impact of fixed noise between column elements can be ignored. The proposed method uses a nonlinear filtering approach to remove non-uniformity and random noise from a single column, obtaining a single frame NUC image, and calculates the actual residual between the NUC image and the original image. Then, the current residual is obtained using the predicted residual from the previous frame and the actual residual. Finally, the algorithm adaptively calculates the gain and offset coefficients based on global motion parameters to reduce artifacts. Compared with other adaptive correction methods, this method can protect image edges to some extent and has a faster convergence rate.
The adjacent columns of an infrared image have similar gray level distribution [9–11]. We assume that a single column contains enough imaging information, the fixed noises between the column elements are independent of each other, and the mutual influence can be ignored. Also, there is a normal distribution influence between the target column elements and the adjacent column elements on the scene imaging, and the imaging of the target column elements can be represented by the adjacent column elements. Suppose the image has
where
where
Finally, restore each column’s pixels according to the transformation sequence and the original index:
where
where the interpretation of the ° operation is to transform Seq
After nonlinear filtering, most of the fringe non-uniform noise is removed. However, the random non-uniform noise still needs to be sampled. The purpose of cross sampling is to filter the random noise in the condition of protecting the details of the original pixels so as to obtain the final prediction image of the current frame. The rule of cross sampling is:
where
The traditional neural network method uses the mean of four neighborhoods as the forecast image [4] for stripe noise, but the algorithm effect is not ideal; Moreover, the traditional neural network method severely loses image information and cannot protect the edge of the image [12–14]. The traditional residual calculation ignores the characteristics of non-uniformity, and the changes of scene details will be mistaken for non-uniformity and filtered out. In this paper, we use nonlinear filtering to obtain the forecast image and calculate the actual residual with the original image, then predict the residuals in the time domain and the temperature response, and then use the weights to calculate the current frame residuals. Finally, the adaptive correction calculates the gain and bias coefficients. The proposed method estimates the dynamic growth of non-uniformity, protects the image details, and effectively improves the convergence speed and the degree of non-uniformity correction. The experiments show that the algorithm proposed in this paper has obvious effects on stripe noise and random noise. The linear correction model output function is expressed as:
where
For the linear response correction model, in order to achieve dynamic correction, we need to dynamically correct and update the gain and bias coefficient, respectively. We assume that the pixel value of the
and the error function
In the Eq. (8), non-uniformity is approximated by residuals. The residual of the nth frame is spatially similar to the residual of the first frame, but its value is gradually influenced by the surrounding environment. Therefore, the residual of the
where
where the residual estimate
where
In order to minimize the error function, we use the stochastic gradient descent method to update the gain and bias coefficients of each pixel point [17]. According to the error function, the variation of the gain and bias coefficients can be obtained as:
According to stochastic gradient descent method:
where
In the practical application of the algorithm, to reduce the negative impact of rapid scene changes on the algorithm, this paper uses a scene change threshold
First, we calculate the difference image
where
where
where
where
where
Figure 3 is a general flowchart of the algorithm.
In this experiment, we acquired three sets of raw video streams using the IRay Photoelectric Xcore_LT series temperature measurement uncooled infrared detector (Fig. 4). The image size was 640 × 512, and the experimental scenes are two cups at room temperature, a black-body radiation source at 40 ℃ and a palm at room temperature.
In this experiment, the data storage and computation were carried out using data structures from the OpenCV4.4 open-source library. The infrared images were acquired using the RTSP protocol. The nonlinear filtering residual estimation algorithm employed a Gaussian filter with a standard deviation of
To evaluate the performance and effectiveness of the proposed algorithm, we use roughness (
where
In special cases, such as in a uniform radiation field, peak signal-to-noise ratio (PSNR) is used as an auxiliary evaluation metric in this paper. For an image
and the definition of PSNR (in dB) is:
In our experiment, we employed roughness (
Figures 6–8 show a comparison of the correction results of different algorithms in three different scenarios. The smoother the image, the better the correction effect. As indicated in the figure, non-uniformity severely affects the imaging effect. The proposed algorithm in this paper provides the most intuitive removal of non-uniformity and effectively reduces the non-uniformity of the stripes while suppressing white noise.
In terms of the correction effect of images in the same scenario, the CoFNN algorithm has a lower degree of convergence, and the correction effect of random non-uniformity is obvious, but the non-uniformity of stripes is still clearly visible. The CS algorithm did not achieve complete convergence, and there are still some artifacts in the results. The algorithm proposed in this paper performs the best in terms of degree of convergence.
These results demonstrate the effectiveness of the proposed algorithm in removing non-uniformity and reducing noise in stripe patterns. The findings suggest that it can be applied in various scenarios and has great potential for further development.
Figures 9–11 show error images (grayscale) between the correction results of each algorithm and the original image. Subjectively, the striped information in the images represents the filtered non-uniformity, and the clearer the stripes, the stronger the filtering effect; The darker the image, the less obvious the filtering effect of non-uniformity and noise removal. From the images, it can be seen that the proposed algorithm has the highest pixel values in the annotated region and appears brighter, indicating that the proposed algorithm effectively filters non-uniformity. As for stripe texture, the proposed algorithm has clear column stripes in the annotated region, while the other two algorithms do not fully reflect the striped information. Therefore, the algorithm effectively filters most of the striped non-uniformity, and the obtained error image has a significant filtering effect, with clearer stripes. This indicates that the striped non-uniformity has been effectively suppressed, and the proposed algorithm has a significant advantage over other scene-based non-uniformity correction algorithms.
In Fig. 12, the output of each algorithm for moving the cup after a period of time in the focused state is presented. In Fig. 12(a), the CoFNN method failed to update parameters in time for the rapid transformation of the scene, and used the correction parameters before moving between the cup and the bottle, resulting in an incorrect output,
As shown in Table 1, this experiment used PSNR and roughness
TABLE 1 Peak signal-to-noise ratio (PSNR) and roughness of images corrected by different algorithms under uniform radiation
Analytical Method | Original | CoFNN | CS | Our |
---|---|---|---|---|
PSNR | 35.9738 | 38.3276 | 36.5379 | 40.7353 |
Roughness | 0.02796 | 0.01935 | 0.02315 | 0.01569 |
As shown in Table 2, in terms of convergence frames, this paper achieved convergence from the 100th frame, while the other two algorithms still maintained a high level of roughness at 100 frames. The CoFNN algorithm reduced non-uniformity by 47.6% in 10 frames, the CS algorithm reduced it by 21.4%, and the proposed algorithm reduced it by 52.3%. At the end of the 200th frame, the CoFNN algorithm removed 55.5% of the non-uniformity, the CS algorithm removed 24.6%, and the proposed algorithm removed 61.3%. The non-uniformity removal effect of the proposed algorithm was significantly better than that of other algorithms, and the data demonstrated that it has obvious advantages in non-uniformity correction.
TABLE 2 Roughness of image corrected by different algorithms in general environment
Frame | Original | CoFNN | CS | Our |
---|---|---|---|---|
1 | 0.202478 | 0.202478 | 0.202478 | 0.202478 |
10 | 0.210027 | 0.110701 | 0.165516 | 0.100062 |
50 | 0.208834 | 0.100453 | 0.170952 | 0.088301 |
100 | 0.208776 | 0.094651 | 0.167137 | 0.083539 |
150 | 0.208607 | 0.092677 | 0.162539 | 0.082162 |
200 | 0.207228 | 0.092182 | 0.156324 | 0.080299 |
Figure 14 shows the roughness variation curve of 200 frames of images corrected by different algorithms. It can be seen in the figure that the roughness of the original image fluctuates around 0.2, while the corrected image tends to converge after several frames. The curve in the figure indicates that the proposed algorithm has a better convergence effect than CS and CoFNN. In summary, the proposed method balances noise reduction and protection of image details, and has good suppression effects on non-uniformity and random noise, as well as on ghosting artifacts. Both subjective and objective evaluations confirm that the proposed algorithm has an ideal correction effect in practical applications.
We propose a scene-based non-uniformity correction method for IRFPA to solve the issue of IR image non-uniformity. The proposed method employs nonlinear filtering to remove the non-uniformity and random noise in a single column and calculates the actual residue with the original image. Then, the current residue is obtained by using the predicted residue from the previous frame and the actual residue. Finally, we adaptively calculate the gain and bias coefficients based on the global motion parameters control algorithm to reduce artifacts. The results show that compared with other correction methods, our method can effectively suppress ghosting and has advantages in convergence, image quality, correction effect, and detail preservation. It also has a significant limiting effect on stripe non-uniformity and random noise.
The authors declare no conflicts of interest.
Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.
Science and Technology Development Program of Jilin Province under Grant (20200401066GX).
Curr. Opt. Photon. 2023; 7(4): 408-418
Published online August 25, 2023 https://doi.org/10.3807/COPP.2023.7.4.408
Copyright © Optical Society of Korea.
Hongfei Song, Kehang Zhang , Wen Tan, Fei Guo, Xinren Zhang, Wenxiao Cao
School of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun, Jilin 130022, China
Correspondence to:^{*}cust_zkh123@163.com, ORCID 0000-0002-6744-666X
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Due to the technological limitations of infrared thermography, infrared focal plane array (IFPA) imaging exhibits stripe non-uniformity, which is typically fixed pattern noise that changes over time and temperature on top of existing non-uniformities. This paper proposes a stripe non-uniformity correction algorithm based on scene-adaptive nonlinear filtering. The algorithm first uses a nonlinear filter to remove single-column non-uniformities and calculates the actual residual with respect to the original image. Then, the current residual is obtained by using the predicted residual from the previous frame and the actual residual. Finally, we adaptively calculate the gain and bias coefficients according to global motion parameters to reduce artifacts. Experimental results show that the proposed algorithm protects image edges to a certain extent, converges fast, has high quality, and effectively removes column stripes and non-uniform random noise compared to other adaptive correction algorithms.
Keywords: Adaptive correction, Nonlinear filter, Non-uniformity correction, Residual estimation
As a main development direction of infrared thermal imaging, the infrared focal plane array (IFPA) has been widely employed in military, aerospace, civil, and other fields due to its high sensitivity, strong detection capability, and strong adaptability to harsh climate conditions [1]. However, due to the limitations of non-uniformity correction technology, different pixels in the focal plane array (FPA) have different response rates, resulting in fixed-pattern noise that seriously affects the imaging quality of the infrared system. In particular, pixels in the same column of the (FPA share the same integral readout circuit, resulting in column stripe noise in the imaging. Moreover, because the fixed noise will shift with temperature and time, it cannot be accurately calibrated [2].
There are currently two directions for non-uniformity correction algorithms: calibration-based and scene-based. The former includes typical methods such as the two-point correction method, multi-point correction method, and baffle correction method, which rely on the periodic use of radiation sources or baffles to provide uniform scenes for calibration [3]. The advantage of this method is its simplicity and obvious correction effect. However, in practical applications, periodic loss of targets may occur. The latter direction, scene-based correction, includes representative methods such as the generative adversarial network method proposed by Mou
Figure 1 is a comparison of infrared image before and after correction by non-uniform correction algorithm.
In this paper, a scene-based non-uniform correction (NUC) algorithm is proposed for removing column stripes and random noise caused by non-uniformity in infrared (IR) imaging systems. IR non-uniformity is often considered fixed pattern noise, which varies with time and temperature, and has a significant impact on image quality. Traditional methods ignore the characteristics of non-uniformity, and changes in scene details may be incorrectly identified as non-uniformity and filtered out. Based on the characteristics of visible light imaging, where adjacent pixels of a target pixel have a Gaussian distribution of mutual influence, it is assumed that the mutual influence between the target column pixel and adjacent column pixels in an IR image also follows a Gaussian distribution. Additionally, pixels in the same column of a FPA share the same integration readout circuit, and the impact of fixed noise between different columns can be ignored. Therefore, it is assumed that a single column contains sufficient imaging information, and the impact of fixed noise between column elements can be ignored. The proposed method uses a nonlinear filtering approach to remove non-uniformity and random noise from a single column, obtaining a single frame NUC image, and calculates the actual residual between the NUC image and the original image. Then, the current residual is obtained using the predicted residual from the previous frame and the actual residual. Finally, the algorithm adaptively calculates the gain and offset coefficients based on global motion parameters to reduce artifacts. Compared with other adaptive correction methods, this method can protect image edges to some extent and has a faster convergence rate.
The adjacent columns of an infrared image have similar gray level distribution [9–11]. We assume that a single column contains enough imaging information, the fixed noises between the column elements are independent of each other, and the mutual influence can be ignored. Also, there is a normal distribution influence between the target column elements and the adjacent column elements on the scene imaging, and the imaging of the target column elements can be represented by the adjacent column elements. Suppose the image has
where
where
Finally, restore each column’s pixels according to the transformation sequence and the original index:
where
where the interpretation of the ° operation is to transform Seq
After nonlinear filtering, most of the fringe non-uniform noise is removed. However, the random non-uniform noise still needs to be sampled. The purpose of cross sampling is to filter the random noise in the condition of protecting the details of the original pixels so as to obtain the final prediction image of the current frame. The rule of cross sampling is:
where
The traditional neural network method uses the mean of four neighborhoods as the forecast image [4] for stripe noise, but the algorithm effect is not ideal; Moreover, the traditional neural network method severely loses image information and cannot protect the edge of the image [12–14]. The traditional residual calculation ignores the characteristics of non-uniformity, and the changes of scene details will be mistaken for non-uniformity and filtered out. In this paper, we use nonlinear filtering to obtain the forecast image and calculate the actual residual with the original image, then predict the residuals in the time domain and the temperature response, and then use the weights to calculate the current frame residuals. Finally, the adaptive correction calculates the gain and bias coefficients. The proposed method estimates the dynamic growth of non-uniformity, protects the image details, and effectively improves the convergence speed and the degree of non-uniformity correction. The experiments show that the algorithm proposed in this paper has obvious effects on stripe noise and random noise. The linear correction model output function is expressed as:
where
For the linear response correction model, in order to achieve dynamic correction, we need to dynamically correct and update the gain and bias coefficient, respectively. We assume that the pixel value of the
and the error function
In the Eq. (8), non-uniformity is approximated by residuals. The residual of the nth frame is spatially similar to the residual of the first frame, but its value is gradually influenced by the surrounding environment. Therefore, the residual of the
where
where the residual estimate
where
In order to minimize the error function, we use the stochastic gradient descent method to update the gain and bias coefficients of each pixel point [17]. According to the error function, the variation of the gain and bias coefficients can be obtained as:
According to stochastic gradient descent method:
where
In the practical application of the algorithm, to reduce the negative impact of rapid scene changes on the algorithm, this paper uses a scene change threshold
First, we calculate the difference image
where
where
where
where
where
Figure 3 is a general flowchart of the algorithm.
In this experiment, we acquired three sets of raw video streams using the IRay Photoelectric Xcore_LT series temperature measurement uncooled infrared detector (Fig. 4). The image size was 640 × 512, and the experimental scenes are two cups at room temperature, a black-body radiation source at 40 ℃ and a palm at room temperature.
In this experiment, the data storage and computation were carried out using data structures from the OpenCV4.4 open-source library. The infrared images were acquired using the RTSP protocol. The nonlinear filtering residual estimation algorithm employed a Gaussian filter with a standard deviation of
To evaluate the performance and effectiveness of the proposed algorithm, we use roughness (
where
In special cases, such as in a uniform radiation field, peak signal-to-noise ratio (PSNR) is used as an auxiliary evaluation metric in this paper. For an image
and the definition of PSNR (in dB) is:
In our experiment, we employed roughness (
Figures 6–8 show a comparison of the correction results of different algorithms in three different scenarios. The smoother the image, the better the correction effect. As indicated in the figure, non-uniformity severely affects the imaging effect. The proposed algorithm in this paper provides the most intuitive removal of non-uniformity and effectively reduces the non-uniformity of the stripes while suppressing white noise.
In terms of the correction effect of images in the same scenario, the CoFNN algorithm has a lower degree of convergence, and the correction effect of random non-uniformity is obvious, but the non-uniformity of stripes is still clearly visible. The CS algorithm did not achieve complete convergence, and there are still some artifacts in the results. The algorithm proposed in this paper performs the best in terms of degree of convergence.
These results demonstrate the effectiveness of the proposed algorithm in removing non-uniformity and reducing noise in stripe patterns. The findings suggest that it can be applied in various scenarios and has great potential for further development.
Figures 9–11 show error images (grayscale) between the correction results of each algorithm and the original image. Subjectively, the striped information in the images represents the filtered non-uniformity, and the clearer the stripes, the stronger the filtering effect; The darker the image, the less obvious the filtering effect of non-uniformity and noise removal. From the images, it can be seen that the proposed algorithm has the highest pixel values in the annotated region and appears brighter, indicating that the proposed algorithm effectively filters non-uniformity. As for stripe texture, the proposed algorithm has clear column stripes in the annotated region, while the other two algorithms do not fully reflect the striped information. Therefore, the algorithm effectively filters most of the striped non-uniformity, and the obtained error image has a significant filtering effect, with clearer stripes. This indicates that the striped non-uniformity has been effectively suppressed, and the proposed algorithm has a significant advantage over other scene-based non-uniformity correction algorithms.
In Fig. 12, the output of each algorithm for moving the cup after a period of time in the focused state is presented. In Fig. 12(a), the CoFNN method failed to update parameters in time for the rapid transformation of the scene, and used the correction parameters before moving between the cup and the bottle, resulting in an incorrect output,
As shown in Table 1, this experiment used PSNR and roughness
TABLE 1. Peak signal-to-noise ratio (PSNR) and roughness of images corrected by different algorithms under uniform radiation.
Analytical Method | Original | CoFNN | CS | Our |
---|---|---|---|---|
PSNR | 35.9738 | 38.3276 | 36.5379 | 40.7353 |
Roughness | 0.02796 | 0.01935 | 0.02315 | 0.01569 |
As shown in Table 2, in terms of convergence frames, this paper achieved convergence from the 100th frame, while the other two algorithms still maintained a high level of roughness at 100 frames. The CoFNN algorithm reduced non-uniformity by 47.6% in 10 frames, the CS algorithm reduced it by 21.4%, and the proposed algorithm reduced it by 52.3%. At the end of the 200th frame, the CoFNN algorithm removed 55.5% of the non-uniformity, the CS algorithm removed 24.6%, and the proposed algorithm removed 61.3%. The non-uniformity removal effect of the proposed algorithm was significantly better than that of other algorithms, and the data demonstrated that it has obvious advantages in non-uniformity correction.
TABLE 2. Roughness of image corrected by different algorithms in general environment.
Frame | Original | CoFNN | CS | Our |
---|---|---|---|---|
1 | 0.202478 | 0.202478 | 0.202478 | 0.202478 |
10 | 0.210027 | 0.110701 | 0.165516 | 0.100062 |
50 | 0.208834 | 0.100453 | 0.170952 | 0.088301 |
100 | 0.208776 | 0.094651 | 0.167137 | 0.083539 |
150 | 0.208607 | 0.092677 | 0.162539 | 0.082162 |
200 | 0.207228 | 0.092182 | 0.156324 | 0.080299 |
Figure 14 shows the roughness variation curve of 200 frames of images corrected by different algorithms. It can be seen in the figure that the roughness of the original image fluctuates around 0.2, while the corrected image tends to converge after several frames. The curve in the figure indicates that the proposed algorithm has a better convergence effect than CS and CoFNN. In summary, the proposed method balances noise reduction and protection of image details, and has good suppression effects on non-uniformity and random noise, as well as on ghosting artifacts. Both subjective and objective evaluations confirm that the proposed algorithm has an ideal correction effect in practical applications.
We propose a scene-based non-uniformity correction method for IRFPA to solve the issue of IR image non-uniformity. The proposed method employs nonlinear filtering to remove the non-uniformity and random noise in a single column and calculates the actual residue with the original image. Then, the current residue is obtained by using the predicted residue from the previous frame and the actual residue. Finally, we adaptively calculate the gain and bias coefficients based on the global motion parameters control algorithm to reduce artifacts. The results show that compared with other correction methods, our method can effectively suppress ghosting and has advantages in convergence, image quality, correction effect, and detail preservation. It also has a significant limiting effect on stripe non-uniformity and random noise.
The authors declare no conflicts of interest.
Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.
Science and Technology Development Program of Jilin Province under Grant (20200401066GX).
TABLE 1 Peak signal-to-noise ratio (PSNR) and roughness of images corrected by different algorithms under uniform radiation
Analytical Method | Original | CoFNN | CS | Our |
---|---|---|---|---|
PSNR | 35.9738 | 38.3276 | 36.5379 | 40.7353 |
Roughness | 0.02796 | 0.01935 | 0.02315 | 0.01569 |
TABLE 2 Roughness of image corrected by different algorithms in general environment
Frame | Original | CoFNN | CS | Our |
---|---|---|---|---|
1 | 0.202478 | 0.202478 | 0.202478 | 0.202478 |
10 | 0.210027 | 0.110701 | 0.165516 | 0.100062 |
50 | 0.208834 | 0.100453 | 0.170952 | 0.088301 |
100 | 0.208776 | 0.094651 | 0.167137 | 0.083539 |
150 | 0.208607 | 0.092677 | 0.162539 | 0.082162 |
200 | 0.207228 | 0.092182 | 0.156324 | 0.080299 |