CN107067376A - A kind of RBF interpolation the images with salt and pepper noise restorative procedure - Google Patents
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Abstract
To improve the images with salt and pepper noise repairing quality, the present invention discloses a kind of RBF interpolation the images with salt and pepper noise restorative procedure.Basic skills is：Pixel in noise image is divided into pollution pixel and uncontaminated pixel, pollution pixel valuation problem look at the unorganized points problem based on uncontaminated pixel；Using RBF unorganized points methods, with uncontaminated pixel image coordinate, pixel value training RBF model parameters, to pollute pixel image coordinate as input, using RBF interpolation methods estimation pollution pixel value, the pixel value of pollution pixel is replaced, the images with salt and pepper noise reparation is realized.The method have the advantages that：High density salt-pepper noise pollution image signal to noise ratio can be significantly increased.
Description
Technical Field
The invention relates to the technical field of digital image processing, in particular to a method for repairing an RBF interpolation salt and pepper noise image.
Background
The digital imaging sensor CCD or CMOS and the like are widely applied to the fields of industry, entertainment, civil use and the like, and in the actual use process, the digital imaging sensor CCD or CMOS and the like are influenced by factors such as manufacturing defects, device aging, transmission errors and the like, and the obtained imaging image has pepper and salt noise pollution. Salt and pepper noise often appears as constant extremely bright or dark pixels, and the value of the salt and pepper noise pixels is usually 255 or 0, taking a grayscale image with the value range of 0-255 as an example. Such noise can significantly degrade image quality and severely degrade visual performance. As shown in fig. 1, 1 is an original image and 2 is a 30% salt and pepper noise contaminated image. The impulse noise has the largest influence on the image quality, and some nonlinear filtering methods are used for denoising the impulse noise image. Median filtering was used for image denoising of salt-and-pepper noise at the earliest, which replaces the current pixel with the median in the neighborhood of the pixel for image filtering, and fig. 3 is the median filtering result of fig. 2. The filtered image is distorted because the median filtering will erroneously replace the non-contaminated pixels with the median of the pixels in the neighborhood. For this purpose, Sun et al ([ Sun, T, Neuvo, Y., 1994. Detail-preserving media based filters in image processing. Pattern Recognition Lett.15 (4); 341) propose for the first time a Switched Median Filter (SMF). The basic idea of SMF is: firstly, marking polluted pixels (for example, pixels with the pixel value of 255 or 0 are polluted pixels) and non-polluted pixels (pixels with the pixel value between 0 and 255) in a polluted image; in the image restoration process, only the polluted pixels are processed, and the non-polluted pixels are kept unchanged. This ensures that the uncontaminated pixels are not replaced by the median of the pixels in the neighborhood, but with higher fidelity. And 4 is the switching median filtering result of 2, and it can be seen that the switching median filtering result is obviously superior to that of the traditional median filtering method. However, when the salt and pepper noise pollution density is large, for example, more than 80%, 5 in fig. 1, the median filtering and the on-off median filtering are difficult to obtain a perfect restored image. As shown in fig. 1, 6 is the median filtering result of 5, and 7 is the selected median filtering result of 5.
The problem of denoising images polluted by high-density (the pollution rate of the salt and pepper noise is more than 50%) salt and pepper noise is widely concerned by scholars at home and abroad. For example, Esakkirajan (2011), et al (Esakkirajan S, Veerakumar T, Subramanyam AN, PremChand CH. Removal of high diversity salt and pepper noise modified precision base unsystem contaminated media filter IEEESignal Process Lett 2011;18(5): 287-90.) propose asymmetric three-state filtering for repairing high density salt and pepper noise contaminated images. Lu (2012) et al (Lu C. -T, Chou T. -C. Denoising of salt and pepper corrected image using modified directional-weighted-median filter, Pattern Recognition Letters, vol. 33, No. 10, pp. 1287-1295,2012.) propose an improved directional weighted median filtering algorithm that can be used to repair 80% salt and pepper noise contaminated images. Mu (2013) and the like (Mu H, Fan C, et al, Fast and effective media filter for removing 1-99% levels of salt and pigment noise in images. Engineering Applications of organic Intelligent reference.26 (2013) 1333 and 1338) according to different noise density levels, the size and direction of a SMF algorithm search window are improved, a rapid and high-density salt-pepper noise elimination algorithm is provided, and 99% salt-pepper noise pollution image restoration can be realized. Vijaykumar (2014) et al (V.R. Vijaykumar, G.Santhana, et al. Fast switching based on a media filter for high sensitivity and spreader noise removal. International Journal of Electronics and communications. p: 1145-1155, 2014) propose a selected mean median filtering algorithm, which can realize 90% salt and pepper noise contaminated image restoration by increasing the size of a search window. Zhang (2014) and the like (Zhang C, Wang k. et al. Removal of high-sensitivity inpulse base on switching morphology-mean filter. international Journal of electronics and communications. 2014) fuse morphology and selective filtering, propose selective morphology filtering, and through 2-layer selective open and closed morphology filtering, can realize 90% impulse noise pollution image restoration. However, in such a selective filtering method based on the median, the mean, and the extremum (the maximum or the minimum) in the local window, when the high-density salt-pepper noise image is restored, the image is easily blurred by the larger filtering window, and the signal-to-noise ratio of the restored image is further reduced. In addition, the existing method generally adopts a mode of detecting the brightest or darkest pixel in the image to detect salt and pepper noise. This detection method is easy to misjudge the non-contaminated pixels located in the lighter or darker area as noise contaminated pixels.
Disclosure of Invention
In order to further improve the restoration quality of the salt and pepper noise image, the invention provides a RBF interpolation salt and pepper noise image restoration method. The technical scheme provided by the invention is as follows: dividing a pixel p in a salt-pepper noise image I into a polluted pixel e and an uncontaminated pixel t, and looking at the estimation problem of the polluted pixel e at the scattered point interpolation problem based on the uncontaminated pixel t; adopting RBF scattered point interpolation method to obtain t image coordinate x of non-polluted pixeltAnd a pixel value qtTraining RBF model to pollute pixel e image coordinate xeAs input, a RBF interpolation method is adopted to estimate the pixel value q of the polluted pixel ee'Replacing the pixel value q of the dirty pixel eeThe restoration of the salt and pepper noise image is realized;
the specific operation steps are as follows:
the first step is as follows: detecting salt and pepper noise of image
Giving a salt and pepper noise image I with the size of w x h pixels and the bit width of b bits, wherein the value range of the image width w is 1-100000000, the value range of the image height h is 1-100000000, the value range of the image bit width b is 1-100, the image coordinate of a pixel p is x, x = (u, v), (u, v) are horizontal and vertical coordinates of the pixel, and the pixel value is q;
the specific method for detecting the polluted pixels in the salt-pepper noise image I is as follows:
at step 1.1, a matrix of marks F, F (u, v) of size w x h is set) All elements in A are set to be 1, and (u, v) are horizontal and vertical coordinates of an image, a salt and pepper noise detection threshold value A = { a1, a2, a3, a4, a5 and a6} is set, and the value range of the elements in A is 0-100; setting a pixel brightness detection threshold value m with a value range of 0-2b-1; setting a neighborhood similarity detection thresholdThe value range is 0-2b-1; setting an initial value d of the neighborhood size L, wherein the value range of d is 0-100;
step 1.2, a pixel p (u, v) in the pepper salt noise image I is taken, and the pixel value is q (u, v) whenTurning to the step 1.8;
step 1.3, setting the neighborhood size L = d, and calculating the salt and pepper noise detection metric value N1(u,v)、N2(u,v)：
Formula (1)
Formula (2)
Wherein S is1Is the number of over-bright pixels in the neighborhood of pixel q (u, v), P1The number of non-over-bright pixels in the neighborhood of the current pixel, which have smaller difference with the current pixel; s2Is the number of over-dark pixels, P, in the current pixel neighborhood2The number of non-too-dark pixels in the neighborhood of the current pixel, which have smaller difference with the current pixel;
formula (3)
Formula (4)
e1Equal to 1 indicates that the pixel is an over-bright pixel;
formula (5)
Formula (6)
g1A value equal to 1 indicates that the pixel is a non-overly bright pixel and has a small difference from the pixel at the (u, v) position;
formula (7)
Formula (8)
e2 equal to 1 indicates that the pixel is too dark;
formula (9)
Formula (10)
g2A value equal to 1 indicates that the pixel is a non-overly dark pixel and has a small difference from the pixel at the (u, v) position;
in the formula (1-10), RL(u, v) is a local neighborhood of size (2L + 1) × (2L + 1) centered on pixel p (u, v),the pixel coordinates in the local neighborhood range are 1-2L + 1;
step 1.4, when N is1(u,v)>=a1And N is2(u,v)>=a2Or N1(u,v)+N2(u,v)>=a3Turning to the step 1.8;
step 1.5, setting a neighborhood size parameter L = d +1, and calculating N again according to the formula (1-10)1(u,v)、N2(u,v);
Step 1.6, when N is1(u,v)>=a4And N is2(u,v)>=a5Or N1(u,v)+N2(u,v)>=a6Turning to the step 1.8;
step 1.7, setting F (u, v) = 0;
step 1.8, returning to the step 1.2 until all pixels in the salt-pepper noise image I are processed;
traversing all pixels p (u, v) in the salt-pepper noise image I according to the marking matrix F, and marking the pixel as a polluted pixel e when F (u, v) =1, wherein the pixel coordinate of the polluted pixel e is xePixel value of qe(ii) a When F (u, v) =0, the pixel is marked as an uncontaminated pixel t, and the pixel coordinate of the uncontaminated pixel t is xtPixel value of qt(ii) a All the polluted pixels e form a polluted pixel setAll the uncontaminated pixels t form a set of uncontaminated pixelsAnd m and n have the value range of [ 0-w x h]，n=w*h-m；
The second step is that: constructing RBF interpolation model by using uncontaminated pixel setTraining RBF interpolation model parameters;
step 2.1: building RBF interpolation model：
Formula (11)
Wherein,is the k-th contaminated pixel ekK is in the range of [ 1-m%]，Is the ith non-contaminated pixel tiThe value range of i is [ 1-n ]]，Is the parameter of the model and is,is an interpolation function, an interpolation functionThe method comprises the following steps:
gaussian function:
formula (12)
A quadratic function:
formula (13)
Linear function:
formula (14)
Cubic function:
formula (15)
Trigonometric function:
formula (16)
Wherein,is a Gaussian and quadratic function parameter with the value range of 0 to 100]，Is the ith non-contaminated pixel tiAnd the kth contaminated pixel ekThe Euclidean distance of the image pixel coordinates;
step 2.2: using uncontaminated pixel setsCalculating parameters of the RBF interpolation model:
using uncontaminated pixel setsImage coordinates ofPixel value ofN linear equations are constructed:
formula (17)
Estimating the optimum parameters of equation (17)；
The third step: substituting the pixel coordinates of the polluted pixel set E into the RBF interpolation model to estimate the pixel value of the polluted pixel;
collecting polluted pixelsPixel coordinates ofRBF interpolation model of successive substitution formula (18)Calculating the pixel value of the contaminated pixel
Formula (18)
The fourth step: will be provided withAnd replacing pixels at corresponding positions in the salt-pepper noise image I to finish the restoration of the polluted image.
The invention has the beneficial effects that:
1) the noise detection method can effectively overcome the error detection caused by the fact that the brightest or darkest pixel is used as the detector in the existing method. In the invention, the noise detection is more reasonable and effective by taking the statistical information of the over-bright pixels, the over-dark pixels, the non-over-dark pixels and the non-over-bright pixels in the neighborhood as the comprehensive criterion compared with the method of simply utilizing the brightness value of one pixel.
2) The signal to noise ratio of the restored image can be obviously improved, and the visual information of the restored image is enhanced. As shown in fig. 2, a Lena gray image with 1024 × 1024 pixels and a pixel depth of b =8bits is used for test evaluation, the image noise density is 90%, and compared with the existing impulse noise restoration algorithm, the linear function is selected as the interpolation kernel function in the method of the present invention. The existing method for repairing the salt-pepper noise image participating in comparison comprises the following steps: median filtering, Weighted median filtering (WMF, Yin L, Ruikang Yang, Moncefgabbouj, Yrjo Neuvo, Weighted median filters: tubular. IEEETrans Circuits Syst II 1996;43(3): 157-92.), central Weighted median filtering (CWMF, KoS-J, LeeYH. Center Weighted median filters and the third Weighted median filters to images transmission. IEEE Trans Circuits Syst 1991.38(9): 984-93.), Adaptive central Weighted median filtering (ACWMF, Chen T, Wu HR. Adaptive median detecting median-Weighted median filtering-Weighted median filters IEEE Signal Lett, I80, Adaptive median filtering for IEEE transaction, I1-3, W HR. median filtering for IEEE 1-3, and E1-80, hwang H, Haddad RA. additive media filters, new algorithms and results IEEE Transmission Image Process 1995;4(4) 499, 502.), boundary discriminant noise detection (BDND, Ng P-E, Ma K-K. A switching media filter with boundary discriminant noise detection for absolute corrected Image, IEEE Transmission Image Process 2006;15(6) 1506-16 ], median filtering for noise filter of high-level noise Signal, IEEE Transmission Image Process 2007; EbenezerD. A new cost and effect detection for absolute corrected Image, simply filtered by three-state filter, SDM 3, 14, Simple filtering for noise filter of high-level noise, IEEE Transmission noise Process, SDM, eskkarajan S, Veerkumar T, Subramanyam AN, PremChand CH. Removal of high diversity and spreader noise modified localized median filter, IEEE Signal Process letter 2011;18(5): 287-90.), mean median Filter Algorithm (SMMF, V.R.Vijaykumar, G.Santana, et al.fast switching basis median filter for high diversity and spreader noise Removal, International journal of Electronics and Communications [ J ] (1145.), and the results of example 1 of the present invention. From fig. 2, it can be seen that the repair result of embodiment 1 of the present invention retains more image details, and the repair effect is significantly better than algorithms such as AMF, BDND, DBA, SAMF, MMF, SMMF, and the like. FIG. 3 also shows the repairing result of the method of the present invention under the condition of 99% noise density, which shows that the method of the present invention has good repairing capability to the high density noise pollution image.
Drawings
FIG. 1 shows the image pollution of salt and pepper noise and the denoising result of the existing method.
When the noise density is 90%, the image restoration effect of the algorithm is compared with that of the existing algorithm.
Figure 399% noise density contaminated image the method of the invention repairs the results.
In the figure, 1 is an original image, 2 is a 30% salt and pepper noise contaminated image, 3 is a median filtering result of 2, 4 is a selected median filtering result of 2, 5 is an 80% salt and pepper noise contaminated image, 6 is a median filtering result of 5, 7 is a selected median filtering result of 5, 8 is a 90% salt and pepper noise contaminated image, 9 is a median filtering result of 8, 10 is a WMF processing result of 8, 11 is a CWMF processing result of 8, 12 is an ACWMF processing result of 8, 13 is a PSMF processing result of 8, 14 is an AMF processing result of 8, 15 is a BDND processing result of 8, 16 is a DBA processing result of 8, 17 is a SAMF processing result of 8, 18 is a DBUTMF processing result of 8, 19 is an SMMF processing result of 8, and 20 is a processing result of the method of the present invention.
Detailed Description
The invention is further illustrated by the following figures and examples.
Example 1
Selecting a Lena gray image with the size of 1024 × 1024 pixels and the pixel depth of b =8bits, carrying out an evaluation test on a Matlab2014a platform, and simulating to generate a salt-pepper noise pollution image I by adopting an immunity function in the Matlab, wherein the noise density is 90%.
The first step is as follows: detecting salt and pepper noise of image
At step 1.1, a flag matrix F, F (u, v) of 1024 × 1024 is set to 1 for all elements, a = {2,7,7,4,16,18} is set, m =5 is set, and a parameter is set=5, setting parameter d = 1;
step 1.2, whenTurning to the step 1.8;
step 1.3, setting a neighborhood size parameter L = d, and calculating：
Wherein,
formula (1)
Formula (2)
Formula (3)
Formula (4)
Formula (5)
Formula (6)
Formula (7)
Formula (8)
Formula (9)
Formula (10)
In the formula (1-10), the metal oxide,is the horizontal and vertical coordinates of the image pixels,is a local neighborhood with pixel q (u, v) as the center and size of (2L + 1) × (2L + 1),the pixel coordinates in the local neighborhood range are 1-2L + 1;
step 1.4, whenAnd isOr is orTurning to the step 1.8;
step 1.5, setting a neighborhood size parameter L = d +1, and calculating again according to the formula (1-9);
Step 1.6, whenAnd isOr is orTurning to the step 1.8;
step 1.7, setting F (u, v) = 0;
step 1.8, returning to the step 1.2 until all pixels in the image I are traversed;
traversing all pixels p in the image I according to the marking matrix F, and marking the pixel as a polluted pixel e when F (u, v) =1, wherein the pixel coordinate of the polluted pixel e is xePixel value of qe(ii) a When F (u, v) =0,marking the pixel as an uncontaminated pixel t, wherein the pixel coordinate of the uncontaminated pixel t is xtPixel value of qt(ii) a All the polluted pixels e form a polluted pixel setAll the uncontaminated pixels t constitute an uncontaminated pixelThe value ranges of m and n are as follows: [ 0-w x h [ ]]，n=w*h-m；
The second step is that: constructing RBF interpolation model using uncontaminated pixelsTraining RBF interpolation model parameters;
step 2.1: building RBF interpolation model：
Formula (11)
Wherein,is the k-th contaminated pixel ekK is in the range of [ 1-m%]，Is the ith non-contaminated pixel tiThe value range of i is [ 1-n ]]，Is the parameter of the model and is,is an interpolation function, an interpolation functionThe method comprises the following steps:
gaussian function:
formula (12)
A quadratic function:
formula (13)
Linear function:
formula (14)
Cubic function:
formula (15)
Trigonometric function:
formula (16)
Wherein,is a Gaussian and quadratic function parameter with the value range of 0 to 100]，Is the ith non-contaminated pixel tiAnd the kth contaminated pixel ekThe Euclidean distance of the image pixel coordinates;
step 2.2: using uncontaminated pixel setsCalculating parameters of the RBF interpolation model:
using uncontaminated pixel setsImage coordinates ofPixel value ofN linear equations are constructed:
formula (17)
Estimating the optimal parameter of equation (7)；
The third step: substituting the pixel coordinates of the polluted pixel set E into the RBF interpolation model to estimate the pixel value of the polluted pixel;
collecting polluted pixelsPixel coordinates ofRBF interpolation model of successive substitution formula (18)Calculating the pixel value of the contaminated pixel
Formula (18)
The fourth step: will be provided withAnd replacing the pixels at the corresponding positions in the image I to finish the restoration of the polluted image.
Example 2
Unlike embodiment 1, the image pixel depth b =12 bits.
Example 3
Unlike embodiment 1, the image pixel depth b =16 bits.
Example 4
Unlike embodiment 1, the image pixel depth b =20 bits.
Example 5
Unlike embodiment 1, the image pixel depth b =24 bits.
Example 6
Unlike in embodiment 1, the image pixel depth b =12bits, and the noise density is 99%.
Example 7
Unlike embodiment 1, the image pixel depth b =16bits, and the noise density is 99%.
Example 8
Unlike embodiment 1, the image pixel depth b =20bits, and the noise density is 99%.
Example 9
Unlike embodiment 1, the image pixel depth b =24bits, and the noise density is 99%.
Example 10
Unlike embodiment 1, the interpolation function selects a quadratic function，。
Example 11
Unlike embodiment 1, the interpolation function selects a linear function。
Example 12
Unlike embodiment 1, the interpolation function selects a cubic function。
Example 13
Different from embodiment 1, the interpolation function is a trigonometric function。
Example 14
Different from embodiment 1, the image pixel depth b =12bits, and the interpolation function selects a quadratic function，。
Example 15
Different from embodiment 1, the image pixel depth b =16bits, and the interpolation function selects a linear function。
Example 16
Unlike embodiment 1, the image pixel depth b =20bits, and the interpolation function selects a cubic function。
Example 17
Different from embodiment 1, the image pixel depth b =24bits, and the interpolation function selects a trigonometric function。
Claims (1)
1. A RBF interpolation salt and pepper noise image restoration method is characterized by comprising the following steps: dividing a pixel p in a salt-pepper noise image I into a polluted pixel e and an uncontaminated pixel t, and looking at the estimation problem of the polluted pixel e at the scattered point interpolation problem based on the uncontaminated pixel t; adopting RBF scattered point interpolation method to obtain t image coordinate x of non-polluted pixeltAnd a pixel value qtTraining RBF model to pollute pixel e image coordinate xeAs input, a RBF interpolation method is adopted to estimate the pixel value q of the polluted pixel ee'Replacing the pixel value q of the dirty pixel eeRealizing the noise of spiced saltRestoring the acoustic image;
the specific operation steps are as follows:
the first step is as follows: detecting salt and pepper noise of image
Giving a salt and pepper noise image I with the size of w x h pixels and the bit width of b bits, wherein the value range of the image width w is 1-100000000, the value range of the image height h is 1-100000000, the value range of the image bit width b is 1-100, the image coordinate of a pixel p is x, x = (u, v), (u, v) are horizontal and vertical coordinates of the pixel, and the pixel value is q;
the specific method for detecting the polluted pixels in the salt-pepper noise image I is as follows:
step 1.1, setting all elements in a mark matrix F with the size w x h, F (u, v) as 1, wherein (u, v) is the horizontal and vertical coordinates of an image, and setting a salt and pepper noise detection threshold value A = { a1, a2, a3, a4, a5, a6}, wherein the value range of the elements in A is 0-100; setting a pixel brightness detection threshold value m with a value range of 0-2b-1; setting a neighborhood similarity detection thresholdThe value range is 0-2b-1; setting an initial value d of the neighborhood size L, wherein the value range of d is 0-100;
step 1.2, a pixel p (u, v) in the pepper salt noise image I is taken, and the pixel value is q (u, v) whenTurning to the step 1.8;
step 1.3, setting the neighborhood size L = d, and calculating the salt and pepper noise detection metric value N1(u,v)、N2(u,v)：
Formula (1)
Formula (2)
Wherein S is1Is the number of over-bright pixels in the neighborhood of pixel q (u, v), P1The number of non-over-bright pixels in the neighborhood of the current pixel, which have smaller difference with the current pixel; s2Is the number of over-dark pixels, P, in the current pixel neighborhood2The number of non-too-dark pixels in the neighborhood of the current pixel, which have smaller difference with the current pixel;
formula (3)
Formula (4)
e1Equal to 1 indicates that the pixel is an over-bright pixel;
formula (5)
Formula (6)
g1A value equal to 1 indicates that the pixel is a non-overly bright pixel and has a small difference from the pixel at the (u, v) position;
formula (7)
Formula (8)
e2 equal to 1 indicates that the pixel is too dark;
formula (9)
Formula (10)
g2A value equal to 1 indicates that the pixel is a non-overly dark pixel and has a small difference from the pixel at the (u, v) position;
in the formula (1-10), RL(u, v) is a local neighborhood of size (2L + 1) × (2L + 1) centered on pixel p (u, v),the pixel coordinates in the local neighborhood range are 1-2L + 1;
step 1.4, when N is1(u,v)>=a1And N is2(u,v)>=a2Or N1(u,v)+N2(u,v)>=a3Turning to the step 1.8;
step 1.5, setting a neighborhood size parameter L = d +1, and calculating N again according to the formula (1-10)1(u,v)、N2(u,v);
Step 1.6, when N is1(u,v)>=a4And N is2(u,v)>=a5Or N1(u,v)+N2(u,v)>=a6Turning to the step 1.8;
step 1.7, setting F (u, v) = 0;
step 1.8, returning to the step 1.2 until all pixels in the salt-pepper noise image I are processed;
traversing all pixels p (u, v) in the salt-pepper noise image I according to the marking matrix F, and marking the pixel as a polluted pixel e when F (u, v) =1, wherein the pixel coordinate of the polluted pixel e is xePixel value of qe(ii) a When F (u, v) =0, the pixel is marked as an uncontaminated pixel t, and the pixel coordinate of the uncontaminated pixel t is xtPixel value of qt(ii) a All the polluted pixels e form a polluted pixel setAll the uncontaminated pixels t form a set of uncontaminated pixelsAnd m and n have the value range of [ 0-w x h]，n=w*h-m；
Second step of: constructing RBF interpolation model by using uncontaminated pixel setTraining RBF interpolation model parameters;
step 2.1: building RBF interpolation model：
Formula (11)
Wherein,is the k-th contaminated pixel ekK is in the range of [ 1-m%]，Is the ith non-contaminated pixel tiThe value range of i is [ 1-n ]]，Is the parameter of the model and is,is an interpolation function, an interpolation functionThe method comprises the following steps:
gaussian function:
formula (12)
A quadratic function:
formula (13)
Linear function:
formula (14)
Cubic function:
formula (15)
Trigonometric function:
formula (16)
Wherein,is a Gaussian and quadratic function parameter with the value range of 0 to 100]，Is the ith non-contaminated pixel tiAnd the kth contaminated pixel ekThe Euclidean distance of the image pixel coordinates;
step 2.2: using uncontaminated pixel setsCalculating parameters of the RBF interpolation model:
using uncontaminated pixel setsImage coordinates ofPixel value ofN linear equations are constructed:
formula (17)
Estimating the optimum parameters of equation (17)；
The third step: substituting the pixel coordinates of the polluted pixel set E into the RBF interpolation model to estimate the pixel value of the polluted pixel;
collecting polluted pixelsPixel coordinates ofRBF interpolation model of successive substitution formula (18)Calculating the pixel value of the contaminated pixel
Formula (18)
The fourth step: will be provided withAnd replacing pixels at corresponding positions in the salt-pepper noise image I to finish the restoration of the polluted image.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112419190A (en) * | 2020-11-24 | 2021-02-26 | 海南大学 | Pulse noise filtering method and system based on local statistical information and geometric distance |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103530856A (en) * | 2013-10-25 | 2014-01-22 | 上海交通大学 | Method and system for removing salt and pepper noise from Bayer image |
| CN104167005A (en) * | 2014-07-07 | 2014-11-26 | 浙江大学 | Salt and pepper noise filtering method based on similar function with better self-adaptation, denoising and detail protection capabilities |
| CN104809701A (en) * | 2015-04-16 | 2015-07-29 | 南京航空航天大学 | Image salt-and-pepper noise removal method based on mean value in iteration switch |
| CN104915938A (en) * | 2015-07-02 | 2015-09-16 | 中国人民解放军国防科学技术大学 | Restoration method for image with high density impulse noise pollution |
| CN105654442A (en) * | 2015-12-31 | 2016-06-08 | 大连理工大学 | Noise elimination method for impact noise image |
-
2017
- 2017-01-15 CN CN201710027145.4A patent/CN107067376A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103530856A (en) * | 2013-10-25 | 2014-01-22 | 上海交通大学 | Method and system for removing salt and pepper noise from Bayer image |
| CN104167005A (en) * | 2014-07-07 | 2014-11-26 | 浙江大学 | Salt and pepper noise filtering method based on similar function with better self-adaptation, denoising and detail protection capabilities |
| CN104809701A (en) * | 2015-04-16 | 2015-07-29 | 南京航空航天大学 | Image salt-and-pepper noise removal method based on mean value in iteration switch |
| CN104915938A (en) * | 2015-07-02 | 2015-09-16 | 中国人民解放军国防科学技术大学 | Restoration method for image with high density impulse noise pollution |
| CN105654442A (en) * | 2015-12-31 | 2016-06-08 | 大连理工大学 | Noise elimination method for impact noise image |
Non-Patent Citations (3)
| Title |
|---|
| CSDN: "《径向基函数插值（1）》", 《HTTPS://BLOG.CSDN.NET/QQ_18343569/ARTICLE/DETAILS/48227839》 * |
| 彭溯: "《径向基函数在数字图像处理中的应用》", 《中国优秀硕士学位论文全文数据库 信息科技辑》 * |
| 沈德海，等: "《一种基于纵横子窗口的去椒盐噪声算法》", 《计算机技术与发展》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112419190A (en) * | 2020-11-24 | 2021-02-26 | 海南大学 | Pulse noise filtering method and system based on local statistical information and geometric distance |
| CN112419190B (en) * | 2020-11-24 | 2023-06-20 | 海南大学 | Pulse noise filtering method and system based on local statistical information and geometric distance |
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