Chapter 4 Experimental Results
4.2 Results of Bad Pixel Correction
For the evaluation of noise suppression algorithms, we will use two noise model to simulate different models
of the “walking to bed person” (a) Original image of frame 3. (b) Corrected image with the proposed NUC method using adaptive learning rate plus momentum and regularization.
Results of Bad Pixel Correction
For the evaluation of noise suppression algorithms, we will use two noise model models of distortions.
{ , , } denote the original pixel and let xi' denote the pixel corrupted by the noise process. Then the image pixels are distorted according to the (a) Original image of frame 3. (b)
method using adaptive
For the evaluation of noise suppression algorithms, we will use two noise models
denote the pixel corrupted by the noise process. Then the image pixels are distorted according to the
1 2 3
probability and p1, p2, p3 are corruption probabilities of each color channel, so that
4
In this noise model, we use fig. 3.3. (a) as sample to calculate the proportion of each noise type which is detected by sensor, and we add realistic noise with the ratio of noise types. We can accordance with the proportional increase or decrease in noise until the sample corruption probability p is our settings. The image pixels are distorted like Eq. (4.3), and each neighboring noise have the same distortion.
In this experiment, we add the impulse noise with 5%, 10%, 15%, and 20%; and we add the realistic noise with 1%, 4%, 7%, 10%. Because noise density is less than 1% in Figure 3.3, we add noise proportion of the realistic noise is smaller than the noise proportion of the realistic noise.
For the measurement of the restoration quality, we employ the Pseudo Signal to Noise Ratio (PSNR) performance metric, which is based on the Root Mean Square Error (RMSE). The RMSE and PSNR are defined as:
( ( ) )
2the original image vector and the filtered image, at pixel position
( )
i j, ,respectively.For the evaluation of the detail preservation capabilities of the proposed filtering design the mean absolute error (MAE) has been used
1
( )
humans, the restoration errors are often analyzed using the perceptually uniform color spaces. In this paper, we will use the CIE LUV color space and the normalized color difference (NCD) defined as:of the original image color vector in the L a b color space. * * *
Figure 4.8 shows the results of each filter in 5% impulse noise density, and table 4.1 shows the performances with each sample corruption probability of impulse noise;
Figure 4.7 shows the results of each filter in 1% realistic noise density, and table 4.2 shows the performances with each sample corruption probability of realistic noise. In order to quickly see the advantages and disadvantages of each method, I will normalize parameters which are RMSE, MAE, and NCD. The parameters are normalized numbers which are between 0 and 1, and the larger value for the parameters indicates better performances. Equation is expressed as follows:
max( ) ( )
The fig. 4.9. show that the bad pixels which are blobs are corrected by our proposed method, and others filter cannot correct the bad pixels in blobs. In the zoomed images (see fig. 4.6 (c) – (k)), we can see that some bad pixels are similar to neighbor pixels, and the bad pixels cannot be detected by our proposed method. The reason is that we use the same threshold d value in the different working window. If we can automatically select the threshold, the problem may be solved. The image is blurred in
the detail part, because we detect dead pixels with 5 × 5 working window. We hope that if we can detect dead pixels with 3 × 3 working window, and we use the larger working window when the bad pixels are blobs.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
(k)
(l) (m)
(n) (o)
(p) (q)
(r) (s)
(t) (u)
filters. (a) Original image. (b) Corrupted image with 5% impulse noise. (c)−(k) are filtering results. Image filtering results filtered by (c) our proposed filter. (d) Vector median filter (VMF). (e) Basic vector directional filter (BVDF). (f) Directional distance Filter (DDF). (g) Fast Peer Group Filter (FPGF). (h) Fuzzy Modified Peer Group Filter (FMPGF). (i) Fast similarity-based impulsive noise removal vector filter (FSVF). (j) Fuzzy metric FSVF (FMFSVF). (k) Fuzzy Peer Group Averaging Filter (FPGA). (l) is zoomed parts of (b). (m)−(u) are zoomed “Lena” filtering results.
Zoomed results filtered by (l) our proposed filter. (m) VMF. (n) BVDF. (o) DDF. (p) FPGF. (q) FMPGF. (r) FSVF. (s) FMFSVF. (t) FPGA.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
(k) (l)
(m) (n)
(o) (p)
(q) (r)
(s) (t)
Fig. 4.9. Bad pixel correction results of Lena image filtered by different realistic noise filters. (a) Corrupted image with 1% realistic noise. (b)−(j) are filtering results. Image filtering results filtered by (b) our proposed filter. (c) Vector median filter (VMF). (d) Basic vector directional filter (BVDF). (e) Directional distance Filter (DDF). (f) Fast Peer Group Filter (FPGF). (g) Fuzzy Modified Peer Group Filter (FMPGF). (h) Fast similarity-based impulsive noise removal vector filter (FSVF). (i) Fuzzy metric FSVF (FMFSVF). (j) Fuzzy Peer Group Averaging Filter (FPGA). (k) is zoomed parts of (a).
(l)−(t) are zoomed “Lena” filtering results. Zoomed results filtered by (l) our proposed filter. (m) VMF. (n) BVDF. (o) DDF. (p) FPGF. (q) FMPGF. (r) FSVF. (s)
FMFSVF. (t) FPGA.
Table 4.1
The evaluation results of Lena image filtered by the following filter:
(a) Corrupted image with 5% impulse noise.
Filter RMSE MAE NCD RMSE- normalized
MAE- normalized
NCD-
normalized Sum
Our method 3.5957 0.4377 0.0048 0.8865 0.9701 0.9574 2.8140 FIVF 2.5723 0.3069 0.0033 0.9703 0.9939 0.9935 2.95763
FMPGF 6.0304 0.6896 0.0080 0.6872 0.9242 0.8834 2.4948 FPGA 3.1922 0.4384 0.0039 0.9195 0.9699 0.9782 2.8677 FSVF 2.3992 0.2756 0.0034 0.9845 0.9996 0.9908 2.97492 PGF 2.2093 0.2735 0.0030 1.0000 1.0000 1.0000 3.00001
BVDF 14.4265 5.7611 0.0456 0.0000 0.0000 0.0000 0.0000 DDF 14.0460 5.2382 0.0446 0.0311 0.0953 0.0249 0.1513 VMF 6.6024 3.8029 0.0356 0.6404 0.3568 0.2344 1.2317
(b) Corrupted image with 10% impulse noise.
(c) Corrupted image with 15% impulse noise.
Filter RMSE MAE NCD RMSE-
(d) Corrupted image with 20% impulse noise.
Filter RMSE MAE NCD RMSE- normalized
MAE- normalized
NCD-
normalized Sum
Our method 5.2512 1.2236 0.0127 0.9350 0.9659 0.9608 2.8618 FIVF 4.3763 1.0194 0.0110 1.0000 1.0000 1.0000 3.00001
FMPGF 9.8929 2.0342 0.0229 0.5902 0.8306 0.7281 2.1489 FPGA 5.1914 1.2713 0.0125 0.9394 0.9580 0.9659 2.86333 FSVF 7.4217 1.3642 0.0225 0.7738 0.9425 0.7370 2.4533 PGF 4.4594 1.0709 0.0113 0.9938 0.9914 0.9931 2.97832 BVDF 17.8379 7.0108 0.0549 0.0000 0.0000 0.0000 0.0000 DDF 17.4112 6.4963 0.0538 0.0317 0.0859 0.0243 0.1419 VMF 7.3442 4.2557 0.0390 0.7795 0.4598 0.3622 1.6016
Table 4.2
The evaluation results of Lena image filtered by the following filter:
(a) Corrupted image with 1% realistic noise.
Filter RMSE MAE NCD RMSE- normalized
MAE- normalized
NCD-
normalized Sum
Our method 2.4088 0.1387 0.0017 1.0000 1.0000 1.0000 3.00001
FIVF 4.0657 0.2834 0.0031 0.6786 0.9667 0.9595 2.60482
FMPGF 7.2351 0.4181 0.0053 0.0638 0.9356 0.8969 1.8964 FPGA 5.5436 1.6414 0.0137 0.3919 0.6540 0.6612 1.7070 FSVF 6.5536 0.3204 0.0048 0.1960 0.9581 0.9131 2.0672 PGF 6.3073 0.3044 0.0041 0.2437 0.9618 0.9312 2.13683
BVDF 7.5638 4.4813 0.0372 0.0000 0.0000 0.0000 0.0000 DDF 6.7914 3.9355 0.0360 0.1498 0.1257 0.0342 0.3098 VMF 6.4934 3.6915 0.0350 0.2076 0.1819 0.0638 0.4534
(b) Corrupted image with 4% realistic noise.
(c) Corrupted image with 7% realistic noise.
Filter RMSE MAE NCD RMSE-
(d) Corrupted image with 10% realistic noise.
Filter RMSE MAE NCD RMSE- normalized
MAE- normalized
NCD-
normalized Sum
Our method 4.7496 0.8634 0.0086 1.0000 1.0000 1.0000 3.00001
FIVF 10.2902 1.5584 0.0172 0.7343 0.8559 0.8452 2.43553
FMPGF 19.3414 3.2260 0.0403 0.3003 0.5101 0.4321 1.2425 FPGA 8.4397 1.5953 0.0147 0.8231 0.8482 0.8907 2.56202 FSVF 25.6040 4.5280 0.0644 0.0000 0.2402 0.0000 0.2402 PGF 17.9512 5.6863 0.0549 0.3670 0.0000 0.1715 0.5384 BVDF 10.4649 5.0824 0.0429 0.7259 0.1252 0.3863 1.2375 DDF 9.7540 4.5290 0.0417 0.7600 0.2400 0.4066 1.4066 VMF 9.5453 4.2751 0.0407 0.7700 0.2926 0.4256 1.4882
Chapter 5 Conclusion
In this thesis, we employ two-point correction method and LMS method to correct non-uniformity among pixels of NIR sensor. Two-point correction is a highly accurate method, unfortunately, he needs sophisticated instruments to measure the reference image, and correction parameters which were measured before cannot meet the correct situation when the system is in use of increased working hours. On the other hand, LMS method only need the readout infrared data captured by the imaging system and compensate the non-uniform response of pixels during its normal operation. We changed the parameters set so that LMS can be adapted to all the circumstances. Furthermore, we use peer group filter which can adjust the size of the working window automatically. We use 3×3 window as default working window for sharpness maintenance, if the small window does not correct a bad pixel, the window size will increase automatically to enhance the correction capability. Although the detail of the image may be blurred, most of the bad pixels can be corrected.
In the future, more advanced NUC method will be investigated to improve NIR sensor performance. We can the above two methods in the application, two-point correction do not need to re-measurement gain and offset, we use the LMS method to make it without sophisticated measurement. Furthermore, in order to apply in real time, If we can find out the location of the dead pixels in advance, we can save a lot of time in the detection, We only need regular dead pixel detection to find out dead pixels generated due to mechanical aging, we can achieve the purpose of quickly and effectively.
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