CN117173188B - Glass scar identification method - Google Patents
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- CN117173188B CN117173188B CN202311453560.8A CN202311453560A CN117173188B CN 117173188 B CN117173188 B CN 117173188B CN 202311453560 A CN202311453560 A CN 202311453560A CN 117173188 B CN117173188 B CN 117173188B
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- 231100000241 scar Toxicity 0.000 title claims abstract description 112
- 239000011521 glass Substances 0.000 title claims abstract description 48
- 238000000034 method Methods 0.000 title claims abstract description 22
- 230000002159 abnormal effect Effects 0.000 claims abstract description 36
- 230000002093 peripheral effect Effects 0.000 claims description 20
- 239000006185 dispersion Substances 0.000 claims description 5
- 230000037390 scarring Effects 0.000 claims description 4
- 230000014509 gene expression Effects 0.000 claims description 3
- 230000001105 regulatory effect Effects 0.000 claims description 3
- 239000000843 powder Substances 0.000 claims 1
- 238000012545 processing Methods 0.000 abstract description 5
- 230000002708 enhancing effect Effects 0.000 abstract description 3
- 230000009286 beneficial effect Effects 0.000 description 9
- 229910010293 ceramic material Inorganic materials 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 208000032544 Cicatrix Diseases 0.000 description 1
- 230000005856 abnormality Effects 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 230000037387 scars Effects 0.000 description 1
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/30—Computing systems specially adapted for manufacturing
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Abstract
The invention provides a glass scar identification method, which belongs to the technical field of image processing, wherein a color enhancement image is obtained by enhancing each color channel of a glass image, so that pixel points of a local abnormal region are different from a normal region, the abnormal region is better distinguished on the color enhancement image, the color enhancement image is subjected to gray level processing, abnormal points are removed, the influence of individual noise points is avoided, an image to be identified is obtained, the abnormal region is found according to the gray level distribution condition on the image to be identified, the abnormal region is used as a suspected scar region, the suspected scar region is compared with the normal region, and the abnormal region is further determined to be the scar region, so that the automatic glass scar identification method without manual work is realized.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a glass scar identification method.
Background
When the glass leaves the factory, the appearance of the glass needs to be checked, the smoothness of the glass is checked, and whether scar exists or not is observed. Although the scar exists on the glass, the scar is easy to judge by naked eyes of a person, the scar is observed manually, the scar is easy to miss when the working time is long and the glass reflects light, and particularly when the glass area is large, the whole condition of the glass is harder to comprehensively check.
Disclosure of Invention
The invention aims to provide a glass scar identification method which solves the problem that an existing automatic glass scar identification method is lacking.
The embodiment of the invention is realized by the following technical scheme: a method for identifying glass scars, comprising the following steps:
s1, carrying out channel color enhancement on a glass image to obtain a color enhancement chart;
s2, carrying out gray scale treatment on the color enhancement map to obtain a gray scale map;
s3, abnormal points are removed from the gray level image, and an image to be identified is obtained;
s4, according to the gray value distribution condition on the image to be identified, a suspected scar region is found;
and S5, calculating the scar degree of the suspected scar region and the normal region on the image to be identified, and when the scar degree is larger than an abnormal threshold value, the suspected scar region is provided with a scar.
Further, the step S1 includes: color enhancement is carried out on the R channel value of the glass image, color enhancement is carried out on the G channel value of the glass image, color enhancement is carried out on the B channel value of the glass image, and the expressions of the color enhancement are as follows:
wherein,to strengthen the post->Class channel->Individual channel values->Is->Channel-like mostThe value of the large channel is set,is->Minimum channel value of class channel,/>For the channel distance>Regulating parameters for the channel->For the->Class channel->Individual channel values->Is->Individual channel value->First->Class channel->And channel values.
The beneficial effects of the above further scheme are: the invention finds the maximum channel value and the minimum channel value of each type of channel, determines the enhancement proportion of each type of channel value, and adopts the channel value to be enhancedThe surrounding 8 channel values realize the balance of the channel values at the current positionThe amount avoids individual outliers.
Further, the channel distanceThe calculation formula of (2) is as follows:
wherein,is->Individual channel value->Upper side->Channel value of class channel,/>Is->Individual channel value->Lower side->Channel value of class channel,/>Is->Individual channel value->Right side->Channel-like communicationLane value, ->Is->Individual channel value->Left side->Channel value of class channel,/>R channel value->And is the value of the G channel,and is a B-channel value.
The beneficial effects of the above further scheme are: the channel distance adopts the channel value to be enhanced in the inventionThe four channel values of the same type are calculated, and when the distance between the four channel values of the same type is larger, the color change is severe, and the boundary point between the scar and the glass is possible, so that the emphasis is placed on reserving the channel value to be enhanced>When the distances between the four channel values of the same type are smaller, the color change is gentle, and the average value of the 8 channel values is taken with emphasis, so that the purpose of removing the abnormal channel values is achieved.
Further, the step S3 includes the following sub-steps:
s31, setting 3*3 gray blocks, moving the gray blocks on a gray map, and traversing pixel points on the gray map;
s32, calculating the distance from any pixel point at the periphery to other pixel points under the gray scale block according to the gray scale value of each pixel point under the gray scale block to obtain the peripheral gray scale distance, wherein any pixel point at the periphery is other pixel points under the gray scale block except the central pixel point;
s33, calculating the distance between the central pixel point and other pixel points under the gray scale block according to the gray scale value of each pixel point under the gray scale block to obtain the central gray scale distance;
s34, when the central gray scale distance and the peripheral gray scale distance meet the distance condition, the central pixel point is an abnormal point;
and S35, replacing the gray value of the abnormal point by the gray average value of other pixel points except the central pixel point under the gray block to obtain the image to be identified.
The beneficial effects of the above further scheme are: according to the method, the peripheral gray scale distance is obtained through the distance between any peripheral pixel point and other pixel points under the gray scale block, so that the gray scale value condition of the peripheral pixel point is estimated, and then the gray scale value condition of the central pixel point is estimated according to the distance between the central pixel point and the other pixel points.
Further, the calculation formula of the peripheral gray scale distance in S32 is as follows:
wherein,is->Peripheral gray scale distance->Gray value of any pixel point around +.>Is a natural constant which is used for the production of the high-temperature-resistant ceramic material,dividing gray value for gray block>External->Gray values of the individual pixels;
the calculation formula of the center gray scale distance is as follows:
wherein,is->Center gray distance, ">Is the gray value of the center pixel, +.>Dividing gray value for gray block>External->Gray values of individual pixels.
The beneficial effects of the above further scheme are: when the gray distance is calculated, the gray value of the pixel points is enhanced through the exponential function, so that the gray value difference between the pixel points is more obvious, and the fine difference is more convenient to find.
Further, the distance condition in S34 is:
wherein,is a distance threshold.
The beneficial effects of the above further scheme are: in the present invention when the peripheral gray scale distance is similar to the center gray scale distance,the closer to 1, the smaller the probability that the center pixel point is an outlier, and therefore, a distance threshold value of less than 1 is set in the present invention>And selecting pixel points with different gray distance distribution.
Further, the step S4 includes the following sub-steps:
s41, calculating the integral gray scale distribution coefficient of the image to be identified;
s42, calculating the gray scale distribution coefficient of each local area on the image to be identified;
s43, when the gray level distribution coefficient of the local area is larger than that of the whole gray level distribution coefficient, the area is a suspected scar area.
Further, the formulas for calculating the gray distribution coefficient in S41 and S42 are:
wherein,is a gray scale distribution coefficient>As an exponential function based on natural constants, < +.>The +.f. for the region of the gray-scale distribution coefficient to be calculated>Gray value of each pixel, +.>For the number of pixel points in the gray scale distribution coefficient region to be calculated,for the maximum gray value in the region of the gray distribution coefficient to be calculated,/>The minimum gray value in the gray distribution coefficient region to be calculated.
The beneficial effects of the above further scheme are: according to the method, the whole gray level distribution coefficient of the image to be identified is calculated, so that the whole gray level distribution condition is represented, then the local area is taken, the gray level distribution coefficient of the local area is calculated, the whole area is compared with the local area, and therefore the abnormal area is found to be the suspected scar area. The glass itself is a smooth plane, where there are few gray scale fluctuations, or there are gray scale value variations in some areas due to the different light intensities on the glass. The invention utilizes the point common knowledge to find the maximum gray value and the minimum gray value on the region of the gray distribution coefficient to be calculated so as to represent the gray fluctuation range of the region, and when the integral gray distribution coefficient is calculated, the difference between the maximum gray value and the minimum gray value is the largest, but the difference is equally divided into the integralThe gray level difference of each pixel point is small, so that the gray level value fluctuation existing in the scar area is definitely larger than that of the whole.
Further, the step S5 includes the following sub-steps:
s51, taking a normal area with the same area on the image to be identified according to the area of the suspected scar area;
s52, calculating scar degree values of the normal area and the suspected scar area;
and S53, when the scar degree is larger than an abnormal threshold value, the suspected scar area is provided with a scar.
The beneficial effects of the above further scheme are: in the invention, a suspected scar region on a glass image is found out, a non-suspected scar region is a normal region, the normal region is compared with the suspected scar region, a scar degree value is calculated, and when the scar degree is larger than an abnormal threshold value, a scar exists on the suspected scar region.
Further, the formula for calculating the scar extent value in S52 is:
wherein,for scar extent value, add->Is gray average value on suspected scar area, +.>Is the gray average value on the normal area,/-, and>for gray level spread on suspected scar area, +.>For gray level spread on normal area, +.>Gray level dispersion common to the suspected scar region and the normal region;
wherein,is the suspicious scar area->Gray value of each pixel, +.>Is the normal zone->Gray value of each pixel, +.>The absolute value of the pixel points is the number of the pixel points on the suspected scar area or the normal area.
The beneficial effects of the above further scheme are: the gray average value is used for comparing the similarity degree of the overall brightness between the two areas, the gray dispersion degree is used for comparing the similarity degree of gray value distribution between the two areas, and when the difference between the two areas is larger, the scar degree value is larger.
The technical scheme of the embodiment of the invention has at least the following advantages and beneficial effects: according to the invention, the color enhancement map is obtained by enhancing each color channel of the glass image, so that the difference between the pixel points of the local abnormal region and the normal region is highlighted, the abnormal region is better distinguished on the color enhancement map, the gray level processing is carried out on the color enhancement map, the abnormal points are removed, the influence of individual noise points is avoided, the image to be identified is obtained, the abnormal region is found according to the gray level value distribution condition on the image to be identified and is used as a suspected scar region, and the suspected scar region is compared with the normal region, so that the suspected scar region is further determined to be the scar region, and the automatic glass scar identification method without manpower is realized.
Drawings
Fig. 1 is a flow chart of a method of identifying glass scarring.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
As shown in fig. 1, a glass scar recognition method includes the following steps:
s1, carrying out channel color enhancement on a glass image to obtain a color enhancement chart;
the S1 comprises the following steps: color enhancement is carried out on the R channel value of the glass image, color enhancement is carried out on the G channel value of the glass image, color enhancement is carried out on the B channel value of the glass image, and the expressions of the color enhancement are as follows:
wherein,to strengthen the post->Class channel->Individual channel values->Is->The maximum channel value of the class channel,is->Minimum channel value of class channel,/>For the channel distance>Regulating parameters for the channel->For the->Class channel->Individual channel values->Is->Individual channel value->First->Class channel->And channel values.
The invention finds the maximum channel value and the minimum channel value of each type of channel, determines the enhancement proportion of each type of channel value, and adopts the channel value to be enhancedThe surrounding 8 channel values realize the measurement of the channel value at the current position, and avoid individual abnormal points.
The channel distanceThe calculation formula of (2) is as follows:
wherein,is->Individual channel value->Upper side->Channel value of class channel,/>Is->Individual channel value->Lower side->Channel value of class channel,/>Is->Individual channel value->Right side->Channel value of class channel,/>Is->Individual channel value->Left side->Channel value of class channel,/>R channel value->And is the value of the G channel,and is a B-channel value.
The channel distance adopts the channel value to be enhanced in the inventionThe four channel values of the same type are calculated, and when the distance between the four channel values of the same type is larger, the color change is severe, and the boundary point between the scar and the glass is possible, so that the emphasis is placed on reserving the channel value to be enhanced>When the distances between the four channel values of the same type are smaller, the color change is gentle, and the average value of the 8 channel values is taken with emphasis, so that the purpose of removing the abnormal channel values is achieved.
S2, carrying out gray scale treatment on the color enhancement map to obtain a gray scale map;
s3, abnormal points are removed from the gray level image, and an image to be identified is obtained;
the step S3 comprises the following substeps:
s31, setting 3*3 gray blocks, moving the gray blocks on a gray map, and traversing pixel points on the gray map;
in step S31, the pixel on each gray scale is set as the over-center pixel as much as possible.
S32, calculating the distance from any pixel point at the periphery to other pixel points under the gray scale block according to the gray scale value of each pixel point under the gray scale block to obtain the peripheral gray scale distance, wherein any pixel point at the periphery is other pixel points under the gray scale block except the central pixel point;
s33, calculating the distance between the central pixel point and other pixel points under the gray scale block according to the gray scale value of each pixel point under the gray scale block to obtain the central gray scale distance;
s34, when the central gray scale distance and the peripheral gray scale distance meet the distance condition, the central pixel point is an abnormal point;
and S35, replacing the gray value of the abnormal point by the gray average value of other pixel points except the central pixel point under the gray block to obtain the image to be identified.
According to the method, the peripheral gray scale distance is obtained through the distance between any peripheral pixel point and other pixel points under the gray scale block, so that the gray scale value condition of the peripheral pixel point is estimated, and then the gray scale value condition of the central pixel point is estimated according to the distance between the central pixel point and the other pixel points.
The calculation formula of the peripheral gray scale distance in S32 is as follows:
wherein,is->Peripheral gray scale distance->Gray value of any pixel point around +.>Is a natural constant which is used for the production of the high-temperature-resistant ceramic material,dividing gray value for gray block>External->Gray values of the individual pixels;
the calculation formula of the center gray scale distance is as follows:
wherein,is->Center gray distance, ">Is the gray value of the center pixel, +.>Dividing gray value for gray block>External->Gray values of individual pixels.
When the gray distance is calculated, the gray value of the pixel points is enhanced through the exponential function, so that the gray value difference between the pixel points is more obvious, and the fine difference is more convenient to find.
The distance condition in S34 is:
wherein,is a distance threshold.
In the present invention when the peripheral gray scale distance is similar to the center gray scale distance,the closer to 1, the smaller the probability that the center pixel point is an outlier, becauseIn this case, a distance threshold value +.1 is set in the present invention>And selecting pixel points with different gray distance distribution.
S4, according to the gray value distribution condition on the image to be identified, a suspected scar region is found;
the step S4 comprises the following substeps:
s41, calculating the integral gray scale distribution coefficient of the image to be identified;
s42, calculating the gray scale distribution coefficient of each local area on the image to be identified;
s43, when the gray level distribution coefficient of the local area is larger than that of the whole gray level distribution coefficient, the area is a suspected scar area.
The formulas for calculating the gray distribution coefficient in S41 and S42 are as follows:
wherein,is a gray scale distribution coefficient>As an exponential function based on natural constants, < +.>The +.f. for the region of the gray-scale distribution coefficient to be calculated>Gray value of each pixel, +.>For the number of pixel points in the gray scale distribution coefficient region to be calculated,for the maximum gray value in the region of the gray distribution coefficient to be calculated,/>The minimum gray value in the gray distribution coefficient region to be calculated.
In the present invention, the gray-scale distribution coefficient region to be calculated is: a global area or a local area.
According to the method, the whole gray level distribution coefficient of the image to be identified is calculated, so that the whole gray level distribution condition is represented, then the local area is taken, the gray level distribution coefficient of the local area is calculated, the whole area is compared with the local area, and therefore the abnormal area is found to be the suspected scar area. The glass itself is a smooth plane, where there are few gray scale fluctuations, or there are gray scale value variations in some areas due to the different light intensities on the glass. The invention utilizes the point common knowledge to find the maximum gray value and the minimum gray value on the region of the gray distribution coefficient to be calculated so as to represent the gray fluctuation range of the region, and when the integral gray distribution coefficient is calculated, the difference between the maximum gray value and the minimum gray value is the largest, but the difference is equally divided into the integralThe gray level difference of each pixel point is small, so that the gray level value fluctuation existing in the scar area is definitely larger than that of the whole.
And S5, calculating the scar degree of the suspected scar region and the normal region on the image to be identified, and when the scar degree is larger than an abnormal threshold value, the suspected scar region is provided with a scar.
The step S5 comprises the following substeps:
s51, taking a normal area with the same area on the image to be identified according to the area of the suspected scar area;
s52, calculating scar degree values of the normal area and the suspected scar area;
and S53, when the scar degree is larger than an abnormal threshold value, the suspected scar area is provided with a scar.
In the invention, a suspected scar region on a glass image is found out, a non-suspected scar region is a normal region, the normal region is compared with the suspected scar region, a scar degree value is calculated, and when the scar degree is larger than an abnormal threshold value, a scar exists on the suspected scar region.
The formula for calculating the scar degree value in the step S52 is as follows:
wherein,for scar extent value, add->Is gray average value on suspected scar area, +.>Is the gray average value on the normal area,/-, and>for gray level spread on suspected scar area, +.>For gray level spread on normal area, +.>Gray level dispersion common to the suspected scar region and the normal region;
wherein,is the suspicious scar area->Gray value of each pixel, +.>Is the normal zone->Gray value of each pixel, +.>The absolute value of the pixel points is the number of the pixel points on the suspected scar area or the normal area.
The gray average value is used for comparing the similarity degree of the overall brightness between the two areas, the gray dispersion degree is used for comparing the similarity degree of gray value distribution between the two areas, and when the difference between the two areas is larger, the scar degree value is larger.
In this embodiment, the abnormality threshold may be specifically set according to experience or experimental procedures.
According to the invention, the color enhancement map is obtained by enhancing each color channel of the glass image, so that the difference between the pixel points of the local abnormal region and the normal region is highlighted, the abnormal region is better distinguished on the color enhancement map, the gray level processing is carried out on the color enhancement map, the abnormal points are removed, the influence of individual noise points is avoided, the image to be identified is obtained, the abnormal region is found according to the gray level value distribution condition on the image to be identified and is used as a suspected scar region, and the suspected scar region is compared with the normal region, so that the suspected scar region is further determined to be the scar region, and the automatic glass scar identification method without manpower is realized.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. The glass scar identification method is characterized by comprising the following steps of:
s1, carrying out channel color enhancement on a glass image to obtain a color enhancement chart;
s2, carrying out gray scale treatment on the color enhancement map to obtain a gray scale map;
s3, abnormal points are removed from the gray level image, and an image to be identified is obtained;
s4, finding out a suspected scar region according to the gray level distribution coefficient on the image to be identified;
s5, calculating the scar degree of the suspected scar region and the normal region on the image to be identified, and when the scar degree is greater than an abnormal threshold value, the suspected scar region is provided with a scar;
the step S4 comprises the following substeps:
s41, calculating the integral gray scale distribution coefficient of the image to be identified;
s42, calculating the gray scale distribution coefficient of each local area on the image to be identified;
s43, when the gray level distribution coefficient of the local area is larger than the whole gray level distribution coefficient, the area is a suspected scar area;
the formulas for calculating the gray distribution coefficient in S41 and S42 are as follows:
wherein,is a gray scale distribution coefficient>As an exponential function based on natural constants, < +.>The +.f. for the region of the gray-scale distribution coefficient to be calculated>Gray value of each pixel, +.>For the number of pixel points in the region of the gray-scale distribution coefficient to be calculated, is->For the maximum gray value in the region of the gray distribution coefficient to be calculated,/>The minimum gray value in the gray distribution coefficient region to be calculated is obtained;
the step S5 comprises the following substeps:
s51, taking a normal area with the same area on the image to be identified according to the area of the suspected scar area;
s52, calculating scar degree values of the normal area and the suspected scar area;
s53, when the scar degree is larger than an abnormal threshold, a scar exists in the suspected scar region;
the formula for calculating the scar degree value in the step S52 is as follows:
wherein,for scar extent value, add->Is gray average value on suspected scar area, +.>Is the gray average value on the normal area,/-, and>gray scale powder for suspected scar areaDistribution degree (I/O)>For gray level spread on normal area, +.>Gray level dispersion common to the suspected scar region and the normal region;
wherein,is the suspicious scar area->Gray value of each pixel, +.>Is the normal zone->Gray value of each pixel, +.>The absolute value of the pixel points is the number of the pixel points on the suspected scar area or the normal area.
2. A method of identifying glass scarring according to claim 1, wherein S1 comprises: color enhancement is carried out on the R channel value of the glass image, color enhancement is carried out on the G channel value of the glass image, color enhancement is carried out on the B channel value of the glass image, and the expressions of the color enhancement are as follows:
wherein,to strengthen the post->Class channel->Individual channel values->Is->The maximum channel value of the class channel,is->Minimum channel value of class channel,/>For the channel distance>Regulating parameters for the channel->For the->Class channel->Individual channel values->Is->Individual channel value->First->Class channel->And channel values.
3. A method of identifying glass scarring as claimed in claim 2, wherein the channel distance isThe calculation formula of (2) is as follows:
wherein,is->Individual channel value->Upper side->Channel value of class channel,/>Is->Individual channel valuesLower side->Channel value of class channel,/>Is->Individual channel value->Right side->Channel value of class channel,/>Is->Individual channel value->Left side->Channel value of class channel,/>R channel value->And is the value of the G channel,and is a B-channel value.
4. A method of identifying glass scarring according to claim 1, wherein S3 comprises the sub-steps of:
s31, setting 3*3 gray blocks, moving the gray blocks on a gray map, and traversing pixel points on the gray map;
s32, calculating the distance from any pixel point at the periphery to other pixel points under the gray scale block according to the gray scale value of each pixel point under the gray scale block to obtain the peripheral gray scale distance, wherein any pixel point at the periphery is other pixel points under the gray scale block except the central pixel point;
s33, calculating the distance between the central pixel point and other pixel points under the gray scale block according to the gray scale value of each pixel point under the gray scale block to obtain the central gray scale distance;
s34, when the central gray scale distance and the peripheral gray scale distance meet the distance condition, the central pixel point is an abnormal point;
and S35, replacing the gray value of the abnormal point by the gray average value of other pixel points except the central pixel point under the gray block to obtain the image to be identified.
5. The method for identifying glass scar according to claim 4, wherein the calculation formula of the peripheral gray scale distance in S32 is:
wherein,is->Peripheral gray scale distance->Gray value of any pixel point around +.>Is natural constant (18)>Dividing gray value for gray block>External->Gray values of the individual pixels;
the calculation formula of the center gray scale distance is as follows:
wherein,is->Center gray distance, ">Is the gray value of the center pixel, +.>Dividing gray value for gray block>External->Individual pixelsGray value of the dot.
6. The method for identifying glass scar according to claim 5, wherein the distance condition in S34 is:
wherein,is a distance threshold.
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