CN110532825A - A kind of bar code identifying device and method based on artificial intelligence target detection - Google Patents
A kind of bar code identifying device and method based on artificial intelligence target detection Download PDFInfo
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Abstract
The present invention relates to a kind of bar code identifying device and method based on artificial intelligence target detection, coarse positioning is carried out to the bar code image in complex environment by convolutional neural networks algorithm of target detection, obtain bar code roughing information, then fine positioning is carried out to roughing information, obtain decoding figure and corresponding decoding additional information, finally decoding is schemed according to decoding additional information to carry out decoded operation, obtains bar code electronic information.The present invention can identify the bar code under complex situations, and have the characteristics that efficient, high speed, high robust.
Description
Technical field
The present invention relates to bar codes to identify field, and in particular to a kind of bar code identifying device based on artificial intelligence target detection
And method.
Background technique
Bar code identification mission is mainly made of detection, positioning, decoding three parts.The effect of Detection task is in entire image
In range, the object identification for having bar code feature is come out;The effect of location tasks is providing bar code on the basis of detection
Specific coordinate (x1, y1, x2, y2 define a rectangle frame);The effect of decoding task is the electronic data the bar code navigated to
Information parses.
The front end physical message acquisition of bar code identification has based on laser and based on two clock method of imaging sensor.Based on laser
Bar code identification it is effective only for single bar code, when there are multiple bar codes, knowledge while which is difficult to realize multiple bar codes
Not, above there is significant drawback in application.
Bar code identification based on imaging sensor then completes detection, positioning, decoding task using traditional images identification technology.
For example, being iterated multiple calculating using different zones of the sliding window technique to whole picture figure, and item is designed by traditional-handwork
The method of code characteristic matching completes detection, then bar code coordinate is come out to positioning by traditional images identification technology, and final complete
At decoding effort.
It is existing that image preprocessing or image enhancement technique are relied on to realize interference based on the identification of the bar code of imaging sensor
The filtering of noise relies on the correctness of hand-designed bar code feature templates.Therefore, when complex environment, complex background
It is ineffective, especially when remote, strong noise.Particularly, when occur multi-code with figure (a width figure include 2 very
To more bar codes) the case where, due to traversal search characteristic of the traditional technology in detection and positioning, the change of number of codes mostly can be into
The difficulty that one step causes detection to position becomes larger, is slack-off.
In short, existing bar code recognition identifies the bar code when a plurality of code, complex background, complex environment
It is all showed in speed and precision not good enough.
Summary of the invention
In order to solve the problems existing in the prior art, the present invention provides a kind of bar code identification based on artificial intelligence target detection
Apparatus and method can effectively identify bar code under complex environment.
To achieve the above object, the technical solution adopted by the present invention is that:
A kind of bar code identifying device based on artificial intelligence target detection comprising sequentially connected image acquisition unit, image
Pretreatment unit, bar code coordinate coarse positioning unit, bar code coordinate fine positioning unit and decoding unit,
Described image acquiring unit, for obtaining the image comprising bar code from imaging sensor;Described image pretreatment unit is used
In to the image progress image procossing comprising bar code;
The bar code coordinate coarse positioning unit counts pretreated image using convolutional neural networks algorithm of target detection
It calculates, obtains bar code roughing information, which includes multiple entries, and the particular content that each entry includes is bar code kind
Class, bar code code system, bar code coordinate, bar code angle, confidence level;The bar code coordinate coarse positioning unit is also used to believe bar code roughing
Breath is filtered, and to obtain roughing reliable information, which includes multiple entries;
The bar code coordinate fine positioning unit, for carrying out fine positioning to each entry in roughing reliable information, to obtain solution
Additional information is schemed and decoded accordingly to code;
The decoding unit selects phase for receiving decoding figure and decoding additional information accordingly, and according to decoding additional information
The algorithm answered carries out decoded operation to decoding figure, obtains bar code electronic information.
The filtering screening rule that the bar code coordinate coarse positioning obtains roughing reliable information is as follows:
(1) entry that confidence level is less than N is deleted, wherein value range < 1 of N;
(2) entry that bar code coordinate the ratio of width to height is greater than M is deleted, M is preset value;
(3) entry that bar code angle is greater than X is deleted, X is preset value;
(4) illegal code system entry is deleted;
(5) illegal type entry is deleted.
The bar code coordinate fine positioning unit operates each purpose fine positioning specifically:
(1) bar code coordinate extension extends: adding respectively on the basis of former coordinate (x1, x2, y1, y2), subtracts some numerical value T, obtains new
Extension bar code coordinate (x1_k, x2_k, y1_k, y2_k);
(2) with new extension coordinate, the corresponding region in original image is intercepted out, obtains bar code figure;
(3) according to bar code angle, inverse rotation operation is carried out to bar code figure;
(4) bar code is obtained on the boundary (x1_b, x2_b) of X-direction;
(5) bar code border extends: bar code border (x1_b, x2_b) will add and subtract respectively some numerical value B in original basis, obtain new
Bar code border (x1_bk, x2_bk);
(6) binarization operation is carried out to bar code figure;
(7) on the basis of bar code figure, interception coordinate is the figure of (x1_bk, x2_bk, y1_k, y2_k) as decoding figure, bar code kind
Class, bar code code system and original coordinates are then used as the decoding additional information of the figure.
When the bar code coordinate extension extends, T is determined according to confidence level, when confidence level is between 0.6-0.7, T=
(x2-x1);When confidence level is between 0.7-0.8, T=(x2-x1)/2.
A kind of bar code recognition based on artificial intelligence target detection comprising following steps:
Step 1 obtains image and carries out image preprocessing;
Step 2 calculates pretreated image using convolutional neural networks algorithm of target detection, obtains bar code roughing letter
Breath, the bar code roughing information include multiple entries, and the particular content that each entry includes is bar code type, bar code code system, bar code
Coordinate, bar code angle, confidence level;
Step 3 is filtered screening to roughing information, obtains roughing reliable information, which includes multiple entries;
Step 4 carries out fine positioning calculating to each entry of roughing reliable information respectively, obtains the decoding figure and phase of each entry
The decoding additional information answered;
Step 5 selects corresponding algorithm to scheme to carry out decoded operation to decoding according to decoding additional information, exports N number of bar code electronics
Information and corresponding bar code coordinate, complete the identification of bar code.
In the step 3, the rule for being filtered screening to roughing information is as follows:
(1) entry that confidence level is less than N is deleted, wherein value range < 1 of N;
(2) entry that bar code coordinate the ratio of width to height is greater than M is deleted, M is preset value;
(3) entry that bar code angle is greater than X is deleted, X is preset value;
(4) illegal code system entry is deleted;
(5) illegal type entry is deleted.
In the step 4, each purpose fine positioning is operated specifically:
(1) bar code coordinate extension extends: adding respectively on the basis of former coordinate (x1, x2, y1, y2), subtracts some numerical value T, obtains new
Extension bar code coordinate (x1_k, x2_k, y1_k, y2_k);
(2) with new extension coordinate, the corresponding region in original image is intercepted out, obtains bar code figure;
(3) according to bar code angle, inverse rotation operation is carried out to bar code figure;
(4) bar code is obtained on the boundary (x1_b, x2_b) of X-direction;
(5) bar code border extends: bar code border (x1_b, x2_b) will add and subtract respectively some numerical value B in original basis, obtain new
Bar code border (x1_bk, x2_bk);
(6) binarization operation is carried out to bar code figure;
(7) on the basis of bar code figure, interception coordinate is the figure of (x1_bk, x2_bk, y1_k, y2_k) as decoding figure, bar code kind
Class, bar code code system and original coordinates are then used as the decoding additional information of the figure.
When the bar code coordinate extension extends, T is determined according to confidence level, when confidence level is between 0.6-0.7, T=
(x2-x1);When confidence level is between 0.7-0.8, T=(x2-x1)/2.
In the new coordinate (x1_k, x2_k, y1_k, y2_k) that the bar code coordinate extension extends, x1_k=x1-
T, y1_k=y1-T, x2_k=x2+T, y2_k=y2+T.
The bar code border extends to obtain in new bar code border (x1_bk, x2_bk), x1_bk=x1_b-B, x2_bk
= x2_b+B。
After adopting the above scheme, the present invention passes through convolutional neural networks algorithm of target detection to the item in complex environment first
Code image carries out coarse positioning, obtains bar code roughing information, then carries out fine positioning to roughing information, obtains decoding figure and corresponding
Additional information is decoded, finally decoding is schemed according to decoding additional information to carry out decoded operation, obtains bar code electronic information.Wherein,
Algorithm of target detection based on artificial intelligence can more accurately identify bar code feature compared to the prior art, thus in complicated feelings
The approximate location of bar code is oriented under condition, and there is high efficiency;And positioning is further screened according to the approximate location of bar code, it obtains quasi-
True barcode position information has high robust and high accuracy.In short, the present invention can identify the bar code under complex situations,
And have the characteristics that efficient, high speed, high robust.
Detailed description of the invention
Fig. 1 is the functional block diagram of bar code identifying device of the present invention;
Fig. 2 is bar code recognition flow chart of the present invention;
Fig. 3 is the roughing information image that coarse positioning of the present invention obtains;
Fig. 4 is the decoding figure that fine positioning of the present invention obtains.
Specific embodiment
As shown in Figure 1, present invention discloses a kind of bar code identifying devices based on artificial intelligence target detection comprising figure
As acquiring unit, image pre-processing unit, bar code coordinate coarse positioning unit, bar code coordinate fine positioning unit and decoding unit, figure
As the input terminal of the output end connection image pre-processing unit of acquiring unit, the output end connecting bar code of image pre-processing unit is sat
Mark the input terminal of coarse positioning unit, the input of the output end connecting bar code coordinate fine positioning unit of bar code coordinate coarse positioning unit
End, the input terminal of the output end connection decoding unit of bar code coordinate fine positioning unit, the output end of decoding unit then export bar code
Electronic information.
Wherein, image acquisition unit, for obtaining the image comprising bar code from imaging sensor;Image pre-processing unit,
For carrying out necessary image procossing to the image comprising bar code, to improve recognition accuracy or facilitate subsequent calculating.At image
Reason includes but are not limited to: denoising, fuzzy, sharpening, colour turn black and white, scale, subtract mean value, normalization etc..
Bar code coordinate coarse positioning unit counts pretreated image using convolutional neural networks algorithm of target detection
It calculates, obtains bar code roughing information, which includes multiple entries, and the particular content that each entry includes is bar code kind
Class (1 dimension, 2 dimension, 3 dimension etc.), bar code code system (such as EAN13, QR, CODE 128), bar code coordinate (such as x1, x2, y1, y2),
Bar code angle (between 0 ~ 90 degree), confidence level.
Bar code coordinate coarse positioning unit is also used to be filtered bar code roughing information, should to obtain roughing reliable information
Roughing reliable information equally includes multiple entries, and each entry equally includes bar code type, bar code code system, bar code coordinate, item
Code angle, confidence level.The filtering screening rule for obtaining roughing reliable information is as follows:
(1) entry that confidence level is less than N is deleted, wherein value range < 1 of N, occurrence needs are arranged according to scene, typical
Value is 0.6.
(2) entry that bar code coordinate the ratio of width to height is greater than M is deleted, occurrence needs are arranged according to scene, representative value 10.
(3) entry that bar code angle is greater than X is deleted, occurrence needs are arranged according to scene, and representative value is 45 degree.
(4) illegal code system entry is deleted, the set of specific illegal code system is determined by application, usually can not under current scene
The code system that can occur.
(4) illegal type entry is deleted, the set of specific illegal type is determined by application, usually can not under current scene
The type that can occur.
Bar code coordinate fine positioning unit, for carrying out fine positioning to each entry in roughing reliable information, to obtain solution
Additional information is schemed and decoded accordingly to code.The fine positioning specifically:
(1) bar code coordinate extension extends: add respectively on the basis of former coordinate (x1, x2, y1, y2), subtract some numerical value T, specifically,
X1_k=x1-T, y1_k=y1-T, x2_k=x2+T, y2_k=y2+T.Wherein, T is according to confidence level come really
It is fixed, for example, when confidence level is between 0.6-0.7, T=(x2-x1);When confidence level is between 0.7-0.8, T=(x2-x1)/
2.Finally obtain new extension bar code coordinate (x1_k, x2_k, y1_k, y2_k).
(2) with new extension coordinate, the corresponding region in original image is intercepted out, obtains bar code figure.
(3) according to bar code angle, inverse rotation operation is carried out to bar code figure.For example, when bar code angle is 30 degree, to bar code
Figure executes the rotation process of -30 degree.
(4) bar code is obtained on the boundary of X-direction.Here it can be realized using a variety of image processing techniques, for example pass through X
Projection on axis calculates, and cooperates suitable threshold parameter, to identify bar code border, bar code border is (x1_b, x2_b).
(5) bar code border extends.According to the requirement of different code systems, bar code border will be in original basis (x1_b, x2_b) point
Some numerical value B is not added and subtracted, specifically, x1_bk=x1_b-B, x2_bk=x2_b+B.To obtain new bar code border (x1_
Bk, x2_bk).
(6) binaryzation carries out binarization operation to bar code figure according to suitable threshold information.
(7) on the basis of bar code figure, interception coordinate is the figure of (x1_bk, x2_bk, y1_k, y2_k) as decoding figure, item
Code type (1 dimension, 2 dimensions, 3 dimensions etc.), bar code code system (such as EAN13, QR, CODE 128) and original coordinates (x1, x2, y1, y2)
Then as the decoding additional information of the figure.
Decoding unit selects phase for receiving decoding figure and decoding additional information accordingly, and according to decoding additional information
The algorithm answered carries out decoded operation to decoding figure, obtains bar code electronic information.
Based on the same inventive concept, present invention further teaches a kind of bar code identification sides based on artificial intelligence target detection
Method, as shown in Fig. 2, itself the following steps are included:
Step 1 obtains image and carries out image preprocessing.
When obtaining image, the image comprising bar code is obtained from imaging sensor by certain medium (such as USB or Ethernet).
And image preprocessing includes the necessary image processing tasks in order to improve recognition accuracy or facilitate subsequent calculating and carry out, including
But be not limited only to following content: denoising, fuzzy, sharpening, colour turn black and white, scale, subtract mean value, normalization etc..
Step 2 calculates pretreated image using convolutional neural networks algorithm of target detection, and it is thick to obtain bar code
Information is selected, which includes multiple entries, and the particular content that each entry includes is bar code type (1 dimension, 2 dimensions, 3
Dimension etc.), bar code code system (such as EAN13, QR, CODE 128), bar code coordinate (such as x1, x2, y1, y2), bar code angle (0 ~ 90
Between degree), confidence level.
Convolutional neural networks algorithm of target detection can be software form and be calculated by CPU, be also possible to example, in hardware by
Asic chip calculates.Convolutional neural networks algorithm of target detection can use any neural network model, such as SSD or YOLO.
Step 3 is filtered screening to roughing information, obtains roughing reliable information (including multiple entries), roughing is credible
Each entry of information includes bar code type (1 dimension, 2 dimensions, 3 dimensions etc.), bar code code system (such as EAN13, QR, CODE 128), item
Code coordinate (such as x1, x2, y1, y2), bar code angle (between 0 ~ 90 degree), confidence level.The choosing rule of filter screen is as follows:
(1) entry that confidence level is less than N is deleted, wherein value range < 1 of N, occurrence needs are arranged according to scene, typical
Value is 0.6.
(2) entry that bar code coordinate the ratio of width to height is greater than M is deleted, occurrence needs are arranged according to scene, representative value 10.
(3) entry that bar code angle is greater than X is deleted, occurrence needs are arranged according to scene, and representative value is 45 degree.
(4) illegal code system entry is deleted, the set of specific illegal code system is determined by application, usually can not under current scene
The code system that can occur.
(5) illegal type entry is deleted, the set of specific illegal type is determined by application, usually can not under current scene
The type that can occur.
Step 4 carries out fine positioning calculating to each entry of roughing reliable information respectively, and the fine positioning of each entry is such as
Under:
(1) bar code coordinate extension extends.Namely add respectively on the basis of former coordinate (x1, x2, y1, y2), subtract some numerical value T, have
Body, x1_k=x1-T, y1_k=y1-T, x2_k=x2+T, y2_k=y2+T.Wherein, T is according to confidence level
It determines, for example, when confidence level is between 0.6 ~ 0.7, T=(x2-x1);When confidence level is between 0.7 ~ 0.8, T=(x2-
X1)/2.Finally obtain new extension bar code coordinate (x1_k, x2_k, y1_k, y2_k).
(2) with new extension coordinate, the corresponding region in original image is intercepted out, obtains bar code figure.
(3) according to bar code angle, inverse rotation operation is carried out to bar code figure.For example, when bar code angle is 30 degree, to bar code
Figure executes the rotation process of -30 degree.
(4) bar code is obtained on the boundary of X-direction.Here it can be realized using a variety of image processing techniques, for example pass through X
Projection on axis calculates, and cooperates suitable threshold parameter, to identify bar code border, bar code border is (x1_b, x2_b).
(5) bar code border extends.According to the requirement of different code systems, bar code border will be in original basis (x1_b, x2_b) point
Some numerical value B is not added and subtracted, specifically, x1_bk=x1_b-B, x2_bk=x2_b+B.To obtain new bar code border (x1_
Bk, x2_bk).
(6) binaryzation carries out binarization operation to bar code figure according to suitable threshold information.
(7) on the basis of bar code figure, interception coordinate is the figure of (x1_bk, x2_bk, y1_k, y2_k) as decoding figure, item
Code type (1 dimension, 2 dimensions, 3 dimensions etc.), bar code code system (such as EAN13, QR, CODE 128) and original coordinates (x1, x2, y1, y2)
Then as the decoding additional information of the figure.
Step 5, multiple decoding figures that step 4 is obtained and corresponding decoding additional information, are input to bar code decoding module;
Bar code decoding module selects corresponding algorithm to scheme to carry out decoded operation to decoding according to decoding additional information, exports N number of bar code electricity
Sub-information and corresponding bar code coordinate (x1, x2, y1, y2), complete the identification of bar code.
It is of the invention it is critical that the present invention passes through convolutional neural networks algorithm of target detection in complex environment first
Bar code image carries out coarse positioning, obtains bar code roughing information, then carries out fine positioning to roughing information, obtains decoding figure and corresponding
Decoding additional information, finally according to decoding additional information to decoding scheme carry out decoded operation, obtain bar code electronic information.
The above is only the embodiment of the present invention, is not intended to limit the scope of the present invention, therefore all
Any subtle modifications, equivalent variations and modifications to the above embodiments according to the technical essence of the invention still fall within this
In the range of inventive technique scheme.
Claims (10)
1. a kind of bar code identifying device based on artificial intelligence target detection, it is characterised in that: obtained including sequentially connected image
Unit, image pre-processing unit, bar code coordinate coarse positioning unit, bar code coordinate fine positioning unit and decoding unit are taken,
Described image acquiring unit, for obtaining the image comprising bar code from imaging sensor;Described image pretreatment unit is used
In to the image progress image procossing comprising bar code;
The bar code coordinate coarse positioning unit counts pretreated image using convolutional neural networks algorithm of target detection
It calculates, obtains bar code roughing information, which includes multiple entries, and the particular content that each entry includes is bar code kind
Class, bar code code system, bar code coordinate, bar code angle, confidence level;The bar code coordinate coarse positioning unit is also used to believe bar code roughing
Breath is filtered, and to obtain roughing reliable information, which includes multiple entries;
The bar code coordinate fine positioning unit, for carrying out fine positioning to each entry in roughing reliable information, to obtain solution
Additional information is schemed and decoded accordingly to code;
The decoding unit selects phase for receiving decoding figure and decoding additional information accordingly, and according to decoding additional information
The algorithm answered carries out decoded operation to decoding figure, obtains bar code electronic information.
2. a kind of bar code identifying device based on artificial intelligence target detection according to claim 1, it is characterised in that: institute
The filtering screening rule for stating bar code coordinate coarse positioning acquisition roughing reliable information is as follows:
(1) entry that confidence level is less than N is deleted, wherein value range < 1 of N;
(2) entry that bar code coordinate the ratio of width to height is greater than M is deleted, M is preset value;
(3) entry that bar code angle is greater than X is deleted, X is preset value;
(4) illegal code system entry is deleted;
(5) illegal type entry is deleted.
3. a kind of bar code identifying device based on artificial intelligence target detection according to claim 1, it is characterised in that: institute
Bar code coordinate fine positioning unit is stated to operate each purpose fine positioning specifically:
(1) bar code coordinate extension extends: adding respectively on the basis of former coordinate (x1, x2, y1, y2), subtracts some numerical value T, obtains new
Extension bar code coordinate (x1_k, x2_k, y1_k, y2_k);
(2) with new extension coordinate, the corresponding region in original image is intercepted out, obtains bar code figure;
(3) according to bar code angle, inverse rotation operation is carried out to bar code figure;
(4) bar code is obtained on the boundary (x1_b, x2_b) of X-direction;
(5) bar code border extends: bar code border (x1_b, x2_b) will add and subtract respectively some numerical value B in original basis, obtain new
Bar code border (x1_bk, x2_bk);
(6) binarization operation is carried out to bar code figure;
(7) on the basis of bar code figure, interception coordinate is the figure of (x1_bk, x2_bk, y1_k, y2_k) as decoding figure, bar code kind
Class, bar code code system and original coordinates are then used as the decoding additional information of the figure.
4. a kind of bar code identifying device based on artificial intelligence target detection according to claim 1, it is characterised in that: institute
When stating the extension of bar code coordinate extension, T is determined according to confidence level, when confidence level is between 0.6-0.7, T=(x2-x1);When setting
When reliability is between 0.7-0.8, T=(x2-x1)/2.
5. a kind of bar code recognition based on artificial intelligence target detection, it is characterised in that: the following steps are included:
Step 1 obtains image and carries out image preprocessing;
Step 2 calculates pretreated image using convolutional neural networks algorithm of target detection, obtains bar code roughing letter
Breath, the bar code roughing information include multiple entries, and the particular content that each entry includes is bar code type, bar code code system, bar code
Coordinate, bar code angle, confidence level;
Step 3 is filtered screening to roughing information, obtains roughing reliable information, which includes multiple entries;
Step 4 carries out fine positioning calculating to each entry of roughing reliable information respectively, obtains the decoding figure and phase of each entry
The decoding additional information answered;
Step 5 selects corresponding algorithm to scheme to carry out decoded operation to decoding according to decoding additional information, exports N number of bar code electronics
Information and corresponding bar code coordinate, complete the identification of bar code.
6. a kind of bar code recognition based on artificial intelligence target detection according to claim 5, it is characterised in that: institute
It states in step 3, the rule for being filtered screening to roughing information is as follows:
(1) entry that confidence level is less than N is deleted, wherein value range < 1 of N;
(2) entry that bar code coordinate the ratio of width to height is greater than M is deleted, M is preset value;
(3) entry that bar code angle is greater than X is deleted, X is preset value;
(4) illegal code system entry is deleted;
(5) illegal type entry is deleted.
7. a kind of bar code recognition based on artificial intelligence target detection according to claim 5, it is characterised in that: institute
It states in step 4, each purpose fine positioning is operated specifically:
(1) bar code coordinate extension extends: adding respectively on the basis of former coordinate (x1, x2, y1, y2), subtracts some numerical value T, obtains new
Extension bar code coordinate (x1_k, x2_k, y1_k, y2_k);
(2) with new extension coordinate, the corresponding region in original image is intercepted out, obtains bar code figure;
(3) according to bar code angle, inverse rotation operation is carried out to bar code figure;
(4) bar code is obtained on the boundary (x1_b, x2_b) of X-direction;
(5) bar code border extends: bar code border (x1_b, x2_b) will add and subtract respectively some numerical value B in original basis, obtain new
Bar code border (x1_bk, x2_bk);
(6) binarization operation is carried out to bar code figure;
(7) on the basis of bar code figure, interception coordinate is the figure of (x1_bk, x2_bk, y1_k, y2_k) as decoding figure, bar code kind
Class, bar code code system and original coordinates are then used as the decoding additional information of the figure.
8. a kind of bar code recognition based on artificial intelligence target detection according to claim 7, it is characterised in that: institute
When stating the extension of bar code coordinate extension, T is determined according to confidence level, when confidence level is between 0.6-0.7, T=(x2-x1);When setting
When reliability is between 0.7-0.8, T=(x2-x1)/2.
9. a kind of bar code recognition based on artificial intelligence target detection according to claim 7, it is characterised in that: institute
It states in the new coordinate (x1_k, x2_k, y1_k, y2_k) that bar code coordinate extension extends, x1_k=x1-T, y1_k=y1
- T, x2_k=x2+T, y2_k=y2+T.
10. a kind of bar code recognition based on artificial intelligence target detection according to claim 7, it is characterised in that:
The bar code border extends to obtain in new bar code border (x1_bk, x2_bk), x1_bk=x1_b-B, x2_bk=x2_b+
B。
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