CN104239903A - QPSO (quantum-behaved particle swarm optimization) algorithm based image edge detection method - Google Patents
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Abstract
The invention relates to a QPSO (quantum-behaved particle swarm optimization) algorithm based image edge detection method. The method includes: forming an image edge detector by four ANFIS (adaptive neuro-fuzzy inference systems) sub-detectors and a postprocessing module; before using the method to perform edge detection on an image, constructing a training image artificially, independently training the four sub-detectors by means of QPSO and a LSE (linear least square method), and determining parameters in a system; when the four sub-detectors are all train, forming the image edge detector by the sub-detectors with the postprocessing module, and detecting the edge of the test image. The image edge detection method has the advantages that even if the test image is polluted by noise, edge information in the image can be extracted effectively without image filter preprocessing.
Description
Technical field
The present invention relates to a kind of method for detecting image edge based on quantum behavior particle group optimizing (QPSO) algorithm, belong to technical field of image processing.
Background technology
Rim detection is the basis of many image processing operations as Iamge Segmentation, Object identifying, image registration, Images Classification etc., and its Detection job determines the effect of these subsequent operations to a great extent.
Edge detection algorithm solves image segmentation problem by detecting the edge comprising zones of different.Edge is made up of edge pixel, and edge pixel is those pixels of gray scale sudden change in image.The maximum value of edge detection algorithm general image first order derivative or the zero crossing information of second derivative provide the basic foundation judging marginal point.Robert operator, Prewitt operator and Sobel operator are all the operators based on gradient, and they use different templates to ask the approximate value of each pixel place first-order partial derivative in image.These edge detection algorithms based on gradient are easy to realize, but their not only edge information sensings, equally also very sensitive to noise.J.Canny adopts the first order derivative of Gaussian function, and proposes edge detection operator and should meet following 3 judgment criterion: signal-to-noise ratio (SNR) Criterion, positioning precision criterion and single edges response criteria, derives edge detection operator-Canny operator thus.And the founder D.Marr of computer vision proposes to adopt Laplacian operator to ask the second derivative of Gaussian function to obtain LOG (Laplacian of Gaussian) filter operator.The algorithm of these classics can extract the edge in image to a certain extent effectively, but needs the value determining some parameters in the algorithm, and the determination of the optimal value of these parameters, is a more difficult problem.
Digital picture may cause because of various reasons being mixed into noise signal in normal view data in its acquisition, transmitting procedure.In noise image, details or the difference between edge and noise are also not obvious.Uncertainty and the imperfection of this information bring difficulty to Digital Image Processing, and fuzzy theory just in time can adapt to these uncertainties.Artificial Neural Network can find out inner link between constrained input data according to learning sample, is particularly suitable for many nonlinear problems in image procossing.In recent years, the probabilistic ability in fuzzy neuron synthesis in theory fuzzy theory analog image processing procedure and the powerful learning ability of artificial neural network, be applied in image processing process gradually.
Summary of the invention
The technical matters solved
Problem to be solved by this invention is, proposes a kind of method for detecting image edge based on QPSO algorithm, even if test pattern is by noise pollution, without the need under carrying out filter preprocessing process condition, also can carry out the method for rim detection.
Technical scheme
Technical characteristic of the present invention is, comprises the following steps:
Step one: four sub-detecting devices of Adaptive Neuro-fuzzy Inference (ANFIS) and an aftertreatment block are formed an Image Edge Detector, before this detecting device of use carries out rim detection to image, manual construction training image, QPSO and linear least square (LSE) is used to train separately four sub-detecting devices, the parameter in certainty annuity;
Step 2: when four sub-detecting devices are all trained complete, just can form an Image Edge Detector, carry out rim detection to test pattern together with an aftertreatment block.
Described step one is further comprising the steps:
Steps A: the sub-detecting device of each ANFIS has four inputs, an output, manual construction original image, the spiced salt impulsive noise of adding 30% on this image obtains noise image, as the training image of the input of every sub-detecting device, edge flag image can be obtained by original image, as the training image of the desired output of every sub-detecting device, obtain all groups of training datas by the training image of the training image inputted and desired output;
Step B: establish iterations n=0.Initialization population, comprises the number of particle, search volume, each particle initial position of random initializtion;
Step C: when first time iteration, the initial position of each particle is individual desired positions.The position of each particle is the premise parameter in ANFIS system, and employing LSE algorithm obtains the consequent parameter corresponding to this particle.Calculate the actual output of the ANFIS system of all input group data, the target function value corresponding to this particle is obtained according to reality output and desired output, the target function value of all particles is compared and just can be found a particle with minimum target functional value, the position of this particle is overall desired positions, preserves the consequent parameter matrix corresponding to this particle (premise parameter) simultaneously;
Step D: calculate individual average desired positions by the individual desired positions of all particles, upgrade the position of each particle, adopts LSE algorithm to obtain corresponding consequent parameter, calculates the target function value of each particle, and upgrade individual desired positions.Finally, the individual desired positions of more all particles, obtains overall desired positions, preserves the consequent parameter matrix had corresponding to overall desired positions particle simultaneously;
Step e: when reaching iteration termination condition, training terminates, and overall desired positions is premise parameter to be determined, and the consequent parameter matrix of preservation is the consequent parameter that will determine.When iteration termination condition does not reach, if n=n+1, forward step D to.
Described step 2 is further comprising the steps:
Steps A: the input picture of test pattern as detecting device that need carry out rim detection, start with the pixel in the upper left corner in input picture (this pixel is current operation pixel), with from top to bottom on image, mode is from left to right slided, all over getting all pixels in input picture;
Step B: for current operation pixel, extracts by four data four inputs that block obtains four sub-detecting devices of ANFIS;
Step C: every sub-detecting device all can obtain an output, these export the input being aftertreatment block, aftertreatment block is averaged to these four inputs, again by this mean value compared with a threshold value preset, obtain one finally to export, this output is the gray-scale value of the edge flag image pixel corresponding with input picture current operation pixel;
Step D: to choose in input picture next pixel as current operation pixel, repeat step (B) and (C), when pixels all in input picture all obtain after output through detecting device, just can obtain an output image, this output image is edge flag image.
Beneficial effect
Method for detecting image edge of the present invention can extract the marginal information in image effectively.Edge detection method proposed by the invention, probabilistic ability in fuzzy theory analog image processing procedure and the powerful learning ability of artificial neural network are fully utilized, even if test pattern is by noise pollution, also effectively can extract marginal information in image and without the need to carrying out image filtering preprocessing process, thus the tasks such as follow-up Iamge Segmentation, feature extraction and image recognition more can be carried out effectively.
Accompanying drawing explanation
Fig. 1 is edge detector network structure
Fig. 2 is ANFIS detecting device training optimizing process figure
Fig. 3 is expert along training image
Fig. 4 is the topological structure that four data extract corresponding to block
Fig. 5 is the selection that intermediate value extracts action pane size
Fig. 6 is test pattern and reference edge image
Fig. 7 is the result figure obtained after making differently to carry out rim detection to the test pattern polluted by 10% spiced salt impulsive noise
Fig. 8 is the Score value making differently to obtain
Fig. 9 is the PSNR value making differently to obtain
Embodiment
Below in conjunction with Fig. 1 to Fig. 9, the present invention is described in further detail.
Step one: four sub-detecting devices of Adaptive Neuro-fuzzy Inference (ANFIS) and an aftertreatment block are formed an Image Edge Detector, before this detecting device of use carries out rim detection to image, manual construction training image, QPSO and linear least square (LSE) is used to train separately four sub-detecting devices, the parameter in certainty annuity;
Concrete steps are as follows:
Steps A: the sub-detecting device of each ANFIS has four inputs, an output, manual construction original image, the spiced salt impulsive noise of adding 30% on this image obtains noise image, as the training image of the input of every sub-detecting device, edge flag image can be obtained by original image, as the training image of the desired output of every sub-detecting device, obtain all groups of training datas by the training image of the training image inputted and desired output;
Fig. 1 is Image Edge Detector structural drawing, comprises four sub-detecting devices of ANFIS and an aftertreatment block, and before this detecting device of use carries out rim detection to image, every sub-detecting device all needs to train separately.Fig. 2 is ANFIS detecting device training optimizing process figure.Training image obtains by Artificial structure, Fig. 3 (a) is original image, this image size is 128 × 128, be made up of 1024 4 × 4 color lumps, 16 pixels in each color lump have identical gray-scale value, the gray-scale value of different color blocks is different, all over all values got in 0 to 255, the position of color lump in picture of different gray-scale value is random, Fig. 3 (b) is the training image of the input of sub-detecting device, it is the noise image obtained in the spiced salt impulsive noise of the upper interpolation 30% of Fig. 3 (a), Fig. 3 (c) is the edge flag image obtained according to Fig. 3 (a) original image, the namely training image of sub-detecting device desired output, in figure, grey scale pixel value is 0 expression current pixel is edge pixel, be shown as black, grey scale pixel value is 1 expression current pixel is not edge pixel, be shown as white.
Obtain all training datas by the training image of the training image inputted and desired output, be set to N group.In FIG, the corresponding data of the sub-detecting device of each ANFIS extract block, and each data extract block for the sub-detecting device of corresponding ANFIS provides four inputs.Concrete steps are as follows:
(1) as shown in Figure 4, with current operation pixel p
2centered by, obtain 3 × 3 action panes, the topological structure different according to level, vertical, left diagonal line and right diagonal line these four kinds obtains grey scale pixel value p
1, p
2and p
3;
(2) still with current operation pixel p
2centered by, obtain a predefined intermediate value in addition and extract action pane, by the gray-scale value of pixels all in this window, obtain intermediate value m;
(3) each Adaptive Neuro-fuzzy Inference four is made to input x
1, x
2, x
3and x
4be respectively:
Data extract block when choosing intermediate value m, need determine that intermediate value extracts action pane size.By simulation results show, according to varying in size of impulsive noise image noise intensity, adopt method determination intermediate value in Fig. 5 to extract action pane size, experimental result is best.
Step B: establish iterations n=0.Initialization population, comprises the number of particle, search volume, each particle initial position of random initializtion;
Every sub-detecting device all needs to train separately, the parameter in certainty annuity, namely uses the premise parameter in QPSO algorithm optimization renewal system, obtains consequent parameter with LSE algorithm.In QPSO algorithm, the solution of each optimization problem can regard a particle in vector subspace as, and each particle determines its adaptive value by objective function.Particle dynamically adjusts the positional information of oneself by the overall desired positions of the individual desired positions and colony of following self.
Initialization population, the number of particle is M, and the dimension of search volume and each particle is D, and for i-th particle, its position can be expressed as x
i=(x
i1, x
i2..., x
id..., x
iD), wherein i=1,2 ..., M, d=1,2 ..., D.The each particle initial position of random initializtion
the position vector of each particle is one group of premise parameter in ANFIS system, is optimized renewal by the position of QPSO algorithm to each particle, and finally determine an optimum particle, its position vector is premise parameter to be determined.The position with best target function value of i-th particle is called individual desired positions (p
best), be expressed as: P
i=(p
i1, p
i2..., P
iD).The position with best target function value of whole population is called overall desired positions (g
best), be expressed as: G=(G
1, G
2..., G
d).
Step C: when first time iteration, the initial position of each particle is individual desired positions.The position of each particle is the premise parameter in ANFIS system, and employing LSE algorithm obtains the consequent parameter corresponding to this particle.Calculate the actual output of the ANFIS system of all input group data, the target function value corresponding to this particle is obtained according to reality output and desired output, the target function value of all particles is compared and just can be found a particle with minimum target functional value, the position of this particle is overall desired positions, preserves the consequent parameter matrix corresponding to this particle (premise parameter) simultaneously;
Each data extract block for the sub-detecting device of corresponding ANFIS provides four inputs, and for each input, definition three broad sense bell subordinate functions respectively, then each ANFIS comprises 81 (3 altogether
4) rule, its Fuzzy Rule Sets is as follows:
Rule 1:if (x
1is M
11) and (x
2is M
21) and (x
3is M
31) and (x
4is M
41), then y
1=d
11x
1+ d
12x
2+ d
13x
3+ d
14x
4+ d
15
Rule 2:if (x
1is M
11) and (x
2is M
21) and (x
3is M
31) and (x
4is M
42), then y
2=d
21x
1+ d
22x
2+ d
23x
3+ d
24x
4+ d
25
Rule 3:if (x
1is M
11) and (x
2is M
21) and (x
3is M
31) and (x
4is M
43), then y
3=d
31x
1+ d
32x
2+ d
33x
3+ d
34x
4+ d
35
Rule 81:if (x
1is M
13) and (x
2is M
23) and (x
3is M
33) and (x
4is M
43), then y
81=d
81,1x
1+ d
81,2x
2+ d
81,3x
3+ d
81,4x
4+ d
81,5
Wherein M
ijrepresent i-th jth subordinate function inputted, d
klfor consequent parameter, y
kfor the output that system obtains according to a kth rule, i=1,2,3,4, j=1,2,3, k=1 ..., 81, l=1 ..., 5.For input x
i, the broad sense bell subordinate function of definition is:
Wherein a
ij, b
ijand c
ijpremised on parameter.
The output Y of ANFIS equals each rule and exports y
kweighted mean:
Weighting coefficient w in formula
krepresent the excitation density of kth rule.W
kcomputing formula as follows:
w
1=M
11(x
1)·M
21(x
2)·M
31(x
3)·M
41(x
4)
w
2=M
11(x
1)·M
21(x
2)·M
31(x
3)·M
42(x
4)
w
3=M
11(x
1)·M
21(x
2)·M
31(x
3)·M
43(x
4)
.
.
.
w
81=M
13(x
1)·M
23(x
2)·M
33(x
3)·M
43(x
4) (4)
When first time iteration, the initial position of each particle is individual desired positions, namely
the position of each particle is the premise parameter in ANFIS system, and employing LSE algorithm obtains the consequent parameter corresponding to this particle.Then, the actual output Y of the ANFIS system of all input group data is obtained by formula (3)
t(t=1,2 ..., N).For each group input
t=1,2 ..., actual output and the desired output of the sub-detecting device of N, ANFIS are respectively Y
tand Yd
t, objective function can be represented by average root-mean-square error (RMSE):
The target function value corresponding to this particle can be obtained by formula (5)
the target function value that all M particle obtains is compared and just can be found a particle with minimum target functional value, and the position of this particle is overall desired positions G
n, preserve the consequent parameter matrix corresponding to this particle (premise parameter) simultaneously.
Step D: calculate individual average desired positions by the individual desired positions of all particles, upgrade the position of each particle, adopts LSE algorithm to obtain corresponding consequent parameter, calculates the target function value of each particle, and upgrade individual desired positions.Finally, the individual desired positions of more all particles, obtains overall desired positions, preserves the consequent parameter matrix had corresponding to overall desired positions particle simultaneously;
The research of M.Clerc shows, the convergence process of particle i is with point
for attractor, its coordinate is:
Wherein
it is the upper equally distributed random number in an interval (0,1).
By adopting the mode of Monte-Carlo Simulation, the location updating equation of particle can be written as:
Wherein
for the uniform random number on interval (0,1).
being the characteristic length of δ potential well, is most important parameter in evolutionary process,
may be defined as
Wherein β is called converging diverging coefficient.Generally, parameter beta can adopt the mode linearly reduced with iterations to control.
be called average desired positions (m
best), be defined as the average of the individual desired positions of all particles, namely
Like this, the particle position of formula (7) more new formula can be changed into
The probability got "+" in formula or get "-" is all 0.5.Finally, formula (6) and (10) just constitute the location updating formula of each particle in QPSO algorithm.
According to formula (9), individual average desired positions is obtained by the individual desired positions of all particles, the position of each particle is upgraded by formula (6) and (10), then LSE algorithm is adopted to obtain corresponding consequent parameter, calculated the target function value of each particle by formula (5), upgrade individual desired positions by following formula:
Wherein, f is objective function.Finally, the individual desired positions of more all particles, obtains the overall desired positions of whole population
wherein
Preserve the consequent parameter matrix had corresponding to overall desired positions particle simultaneously.
Step e: when reaching iteration termination condition, training terminates, and overall desired positions is premise parameter to be determined, and the consequent parameter matrix of preservation is the consequent parameter that will determine.When iteration termination condition does not reach, if n=n+1, forward step D to.
Step 2: when four sub-detecting devices are all trained complete, just can form an Image Edge Detector, carry out rim detection to test pattern together with an aftertreatment block.
Concrete steps are as follows:
Steps A: the input picture of test pattern as detecting device that need carry out rim detection, start with the pixel in the upper left corner in input picture (this pixel is current operation pixel), with from top to bottom on image, mode is from left to right slided, all over getting all pixels in input picture;
Step B: for current operation pixel, extracts by four data four inputs that block obtains four sub-detecting devices of ANFIS;
Step C: every sub-detecting device all can obtain an output, these export the input being aftertreatment block, aftertreatment block is averaged to these four inputs, again by this mean value compared with a threshold value preset, obtain one finally to export, this output is the gray-scale value of the edge flag image pixel corresponding with input picture current operation pixel;
In Fig. 1, four outputs can be obtained respectively by four sub-detecting devices of ANFIS, be designated as Y
k(K=1,2,3,4).These four outputs are the input of aftertreatment block.Aftertreatment block is averaged to these four inputs by formula (13), is designated as Y
av.Again by formula (14), by Y
avcompared with a threshold value Th, try to achieve the final output Y of detecting device
f.It should be noted that, in the present invention, the grey scale pixel value of all images is all defined between interval [0,1].Final output Y
fvalue be 0 expression current operation pixel be edge pixel, be shown as black; Y
fvalue be 1 expression current operation pixel be not edge pixel, be shown as white.
Whether a pixel is detected as edge is determined by the threshold value Th in formula (14).When Th value close to 0 time, the pixel being detected as edge can tail off, and that is some edge pixels may flase drop be non-edge pixels.On the contrary, when Th value close to 1 time, the pixel being detected as edge can become many, but some non-edge pixels may flase drop be edge pixel.
Step D: to choose in input picture next pixel as current operation pixel, repeat step (B) and (C), when pixels all in input picture all obtain after output through detecting device, just can obtain an output image, this output image is edge flag image.
For testing the performance of the Edge detected of the inventive method, the edge image that each method can be obtained and reference edge image (ground truth, GT) compare, the image that three width obtain from Malik database can be used to the rim detection ability of testing various method.Fig. 6 (a) and Fig. 6 (b) respectively illustrates the reference edge image of three width original images and its correspondence, and image size is 481 × 321.For the detectability of test edge detector under noise exists situation, in three width original images, add 3% ~ 30% spiced salt impulsive noise respectively.Original image and noise image all as test pattern, for testing the rim detection performance of each method.
In emulation experiment, will compare respectively the inventive method and Sobel operator, LOG operator and Canny operator, provide quantitative and qualitative analysis evaluation.For the inventive method, every sub-detecting device has 4 inputs, and corresponding 3 the broad sense bell subordinate functions of each input, each subordinate function has 3 parameter (a
ij, b
ijand c
ij), therefore every sub-detecting device has 4 × 3 × 3=36 premise parameter.In QPSO algorithm, the dimension D of each particle is equal with the number of premise parameter, and namely 36.In emulation experiment, consider effect and the operational efficiency of optimization, the size M of population is set to 30.Converging diverging system β linearly reduces with iterations, and its span is [1,0.5].Threshold value Th in formula (14) is set to 0.38.
Fig. 7 display be to noisy 10% test pattern carry out the result of rim detection.The spiced salt impulsive noise test pattern of Fig. 7 (a) for containing 10%.Fig. 7 (b)-(e) is respectively the edge image detecting gained by Sobel operator, LOG operator, Canny operator and the inventive method.As can be seen from the figure, Sobel operator, LOG operator and Canny operator are deposited in case at noise, and the ability of rim detection sharply declines, and many noises are edge by flase drop, and a lot of edge cannot detect because of affected by noise.And noise is less on the inventive method impact, still more correctly can detects edge, and to noise, there is robustness.
For quantitative evaluation various method rim detection ability, use TP, TN, Score and PSNR (Y-PSNR) as evaluation criterion.Score may be defined as:
Score=TP+TN (15)
Wherein TP (True Positive) represents the number simultaneously being regarded as edge pixel by the edge image that reference edge image (GT) and detecting device obtain; TN (True Negative) represents the number simultaneously being regarded as non-edge pixels by the edge image that reference edge image (GT) and detecting device obtain.From the definition of evaluation criterion Score, its size reflects the ability of the correct Edge detected of detecting device.Score value is larger, shows that the ability of correct Edge detected is stronger.
What Fig. 8 showed is use different detection methods to obtain Score value, and detected image comprises original image and contains 3% ~ 30% impulsive noise image.The Score value corresponding to each noise density in Fig. 8 is the mean value of three width image Score values.Can obviously find out from figure, compared to other method, the Score value of the inventive method is maximum, and this shows that the ability of the correct Edge detected of the inventive method is the strongest.
For evaluating detecting device to the robustness of noise, can this index of PSNR be used, namely for certain detecting device, the edge image obtained by noise image be compared with the edge image obtained by original image (non-noise image).PSNR may be defined as:
PSNR=10log
10(1/MSE) (16)
Wherein O (i, j) and N (i, j) represents the edge image pixel obtained by original image and the edge image pixel obtained by noise image respectively, and image size is M × N.The larger expression detecting device of PSNR value is better to the robustness of noise.
What show in Fig. 9 is the PSNR value making differently to obtain.As can be seen from Figure, the PSNR value that the inventive method obtains will be far longer than the PSNR value that three kinds of classic methods (Sobel operator, LOG operator and Canny operator) obtain, this further demonstrates the conclusion that qualitative evaluation obtains, namely deposit in case at noise, the rim detection ability of these three kinds of classic methods is poor, and noise is relatively little on the impact of the inventive method.
As can be seen from the simulation experiment result, compared to three kinds of classic methods, the inventive method has stronger rim detection ability, especially under noise exists situation.QPSO algorithm is used for, in the parameter optimization of ANFIS, improve rim detection performance significantly.
Claims (3)
1., based on a method for detecting image edge for quantum behavior particle group optimizing (QPSO) algorithm, it is characterized in that, comprise the following steps:
Step one: four sub-detecting devices of Adaptive Neuro-fuzzy Inference (ANFIS) and an aftertreatment block are formed an Image Edge Detector, before this detecting device of use carries out rim detection to image, manual construction training image, QPSO and linear least square (LSE) is used to train separately four sub-detecting devices, the parameter in certainty annuity;
Step 2: when four sub-detecting devices are all trained complete, just can form an Image Edge Detector, carry out rim detection to test pattern together with an aftertreatment block.
2. the method for detecting image edge based on QPSO algorithm according to claim 1, it is characterized in that, step one is further comprising the steps:
Steps A: the sub-detecting device of each ANFIS has four inputs, an output, manual construction original image, the spiced salt impulsive noise of adding 30% on this image obtains noise image, as the training image of the input of every sub-detecting device, edge flag image can be obtained by original image, as the training image of the desired output of every sub-detecting device, obtain all groups of training datas by the training image of the training image inputted and desired output;
Step B: establish iterations n=0.Initialization population, comprises the number of particle, search volume, each particle initial position of random initializtion;
Step C: when first time iteration, the initial position of each particle is individual desired positions.The position of each particle is the premise parameter in ANFIS system, and employing LSE algorithm obtains the consequent parameter corresponding to this particle.Calculate the actual output of the ANFIS system of all input group data, the target function value corresponding to this particle is obtained according to reality output and desired output, the target function value of all particles is compared and just can be found a particle with minimum target functional value, the position of this particle is overall desired positions, preserves the consequent parameter matrix corresponding to this particle (premise parameter) simultaneously;
Step D: calculate individual average desired positions by the individual desired positions of all particles, upgrade the position of each particle, adopts LSE algorithm to obtain corresponding consequent parameter, calculates the target function value of each particle, and upgrade individual desired positions.Finally, the individual desired positions of more all particles, obtains overall desired positions, preserves the consequent parameter matrix had corresponding to overall desired positions particle simultaneously;
Step e: when reaching iteration termination condition, training terminates, and overall desired positions is premise parameter to be determined, and the consequent parameter matrix of preservation is the consequent parameter that will determine.When iteration termination condition does not reach, if n=n+1, forward step D to.
3. the method for detecting image edge based on QPSO algorithm according to claim 1, it is characterized in that, step 2 is further comprising the steps:
Steps A: the input picture of test pattern as detecting device that need carry out rim detection, start with the pixel in the upper left corner in input picture (this pixel is current operation pixel), with from top to bottom on image, mode is from left to right slided, all over getting all pixels in input picture;
Step B: for current operation pixel, extracts by four data four inputs that block obtains four sub-detecting devices of ANFIS;
Step C: every sub-detecting device all can obtain an output, these export the input being aftertreatment block, aftertreatment block is averaged to these four inputs, again by this mean value compared with a threshold value preset, obtain one finally to export, this output is the gray-scale value of the edge flag image pixel corresponding with input picture current operation pixel;
Step D: to choose in input picture next pixel as current operation pixel, repeat step (B) and (C), when pixels all in input picture all obtain after output through detecting device, just can obtain an output image, this output image is edge flag image.
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