10
Journal or Scientitic & Industrial Research Vo l. 62. June 2003, pp 573-582 The Preprocessing and Recognition Methods of an Integrated Automated Production Lot Number Inspection System Chern-Sheng Lin*, Yun-Long La/, Chia-Chin Huan 1 Hsing-Cheng Chang 1 , Thong-Shing Hwang 1 'Department of Automatic Control Engineering, Feng Chia University. Taichung, Taiwan, ROC 2 Department of Electronics Engineering, National Chin-Yi Institute of Technology, Taichung, Taiwan, RO C Received: II October 2002; accepted: 10 April 2003 In this stud y, an integrated OCR system was designed to identify numbers in an image. A new preprocess in g, image segmentation, and number recognition methods to search the threshold value automatically and divide the image into several use ful regions has been developed. A state transferring algorithm to evaluate the gray level variations of the information in the ava il a bl e data buffer. The processing based on segmentation algorithm deletes all unnecessary patterns and leaves only the character in order to increase the processing speed. The three-part comparisons algorithm is used in feature extraction. Many applications exist for this OCR system in industry, such as pattern recognition. The experimental results show that th e recognition rate can exceed 99.7 per cent even with hand written characters. Keywords : Production lot number, OCR , Image, Al gorithm, Segmentation 1 Introduction There have been many OCR systems developed for various applications. In conventional and some newly developed OCR systems, the document image is captured by a scanner, then subjected to skew correction, text graphics separation, line segmentation, zone detection, word and character segmentation 1. Many people have designated particular algorithms for each individual procedure. Gatos et al. 2 used curvature features, which were obtained according to the slopes of the character edge pixels in the multiclassifier for each character, and combined in a sequential manner. These authors further used a binary tree classification technique and classifier trained with the Zernike moments of the characters' . A new method for text identification in mixed-type documents has been presented 4 . Leung and Suen 5 used an energy minimization template match method while Hussain and Kabuka 6 developed character recognition usmg neural network technology. * Corresponding author In the manufacturing environment, optical sensor and computer visual inspections are utilized to check- automatic identification, surface defects, assembly correctness or adaptive production, etc. Automatic identification systems are helping manufactures to reduce labor costs and stock, shorten production times, improve customer service and increase production quality. The familiar automatic identification technology includes bar code, radio frequency identification, magnetic stripe, and machine vision with OCR and magnetic ink character recognition. Each of these has its advantages and disadvantages. Bar codes uses the term symbology to denote each particular bar code scheme and have spread from supermarkets to department stores. The low cost of the bar code printed label and readers combined with excellent accuracy, high speed and ease of use are important aspects in a wide range of industrial applications. The obvious disadvantages are the requirement for a close distance for the symbol to be identified. The recognition rate often falls below 99 per cent. This system al so cannot accept hand-written information if the data mu st be changed immediately.

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Journal o r Scientitic & Industri al Research

Vol. 62. June 2003, pp 573-582

The Preprocessing and Recognition Methods of an Integrated Automated Production Lot Number Inspection System

Chern-Sheng Lin*, Yun-Long La/, Chia-Chin Huan 1

Hsing-Cheng Chang1, Thong-Shing Hwang 1

'Department of Automatic Control Engineering, Feng Chia University. Taichung, Taiwan, ROC

2 Department of Electronics Engineering, National Chin-Yi Institute of Technology, Taichung, Taiwan , RO C

Received: II October 2002; accepted : 10 April 2003

In thi s study, an integrated OCR system was designed to identify numbers in an image. A new preprocess ing, image segmentation , and number recognition methods to search the threshold value automatically and divide the image into several useful regions has been developed . A state transferring algorithm to evaluate the gray level variations o f the information in the avail able data buffer. The processing based on segmentation algorithm deletes all unnecessary patterns and leaves onl y the character in order to increase the processing speed . The three-part comparisons algorithm is used in feature extraction. Man y applications exist for thi s OCR system in industry, such as pattern recognition. The experimental results show that the recognition rate can exceed 99.7 per cent even with hand written characters.

Keywords: Production lot number, OCR, Image, Algorithm, Segmentation

1 Introduction

There have been many OCR systems developed for various applications. In conventional and some newly developed OCR systems, the document image is captured by a scanner, then subjected to skew correction, text graphics separation, line segmentation, zone detection , word and character segmentation 1. Many people have designated particular algorithms for each individual procedure. Gatos et al.2 used curvature features, which were obtained according to the slopes of the character edge pixels in the multiclassifier for each character, and combined in a sequential manner. These authors further used a binary tree classification technique and classifier trained with the Zernike moments of the characters' . A new method for text identification in mixed-type documents has been presented4

. Leung and Suen5 used an energy minimization template match method while Hussain and Kabuka6 developed character recognition usmg neural network technology.

* Corresponding author

In the manufacturing environment, optical sensor and computer visual inspections are utilized to check­automatic identification, surface defects , assembly correctness or adaptive production, etc . Automatic identification systems are helping manufactures to reduce labor costs and stock, shorten production times, improve customer service and increase production quality. The familiar automatic identification technology includes bar code, radio frequency identification, magnetic stripe, and machine vision with OCR and magnetic ink character recognition . Each of these has its advantages and disadvantages. Bar codes uses the term symbology to denote each particular bar code scheme and have spread from supermarkets to department stores. The low cost of the bar code printed label and readers combined with excellent accuracy, high speed and ease of use are important aspects in a wide range of industrial applications. The obvious disadvantages are the requirement for a close distance for the symbol to be identified. The recognition rate often falls below 99 per cent. This system also cannot accept hand-written information if the data must be changed immediately.

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574 J SCI INO RES VOL 62 JU E 2003

T he data on a bar code labe l are encoded in the relative widths of the a lternating li ght-absorb ing bars and li ght-refl ecting spaces7

. The results of a bar code scans are influenced by the type of noise and distortions encountered8

. The finite s ize of projected li ght spot introduces a corresponding blur in the bar code image. The printed bars are someti mes unclear and have an upper limit on the avai lable s ignal intens it y. Identificat ion errors are unavoidable if a bar code dev ice ope rates without human interventi on9

.

He re we integrated computer vision tec hnology wi th a bar code reader. Coding is unnecessary and the coded data can also be read in a computer vision system. The application of a computer vision sys tem in conjuncti on with a bar code reader in lot number identifica tion has many advantages:

• Non-contac t sens ing

• Adaptability to see in sma ll , low light restricted areas or at a long range

• High-speed operation

• Acc uracy, exper imental results even with hand written c harac ters show that the recognition rate can exceed 99 .7 per cent.

The application of thi s OCR system is not limited to document process ing. As shown in Figure 1, it can also be modified to record the measuring data of an in strument without any communica ti on ports (Figure I a), inves tigate the series number of a bicycle frame (Figure I b), and check the appearance of a screen to veri fy th at there are no defects on the number disp lay (Figure Ie).

2 Preprocessing

This sys tem can obtain the gray level, difference, and 2nd order difference of pixe l data from a s ing le scan I ine of characters. For exampl e,

Gray leve l: 30 144 144 136 176 1360 160 136 168 144 176 152 184 168 152 168 160 168 136 160 128 168 160 16 2456 128 168 160 184 176 176 112 24 0 168 136 40 16 16 96 168 160 200 176 144 0 0 0 1760016.

Difference: -14408 -40 40 136 -16 16 -1 36 -32 24 -32 24 -32 16 16 -16 8 -8 32 -24 32 -40 8 144 -8-32 -72 -408-248064 88 24 -1683296240 -80-72 8-402432 14400-1761760 - 16.

2nd order difference: 144 -144 -8 48 -80 -96 152 -32 152 - 104 -56 56 -56 56 -48 0 32 -24 16 -40 56 -56

(b)

(c)

Figure I-The different appli ca ti on of a OCR system

72 -48-136 1522440 -32 -48 32 -32 8 -64 -24 64 192 -200 -64 72 24 80 -8 -8048 -64 -8 -I 12.

It is paradoxical to seek a reasonabl e boundary and character box that will match a member of the system's recognition alphabet without incorporating deta iled knowledge of the symbo l properties into the process. Instead of the ordinary OCR zoning and

. d IO- !? d b fe segmentation proce ure -, a temporary ata u ler

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LI N el al.: PROCES SI NG & RECOGNITION METHODS 575

was used to store temporary data and transfer it to the ava il able data buffer unde r appropri ate conditions. The info rmation in ava ilable data bu ffe r is the pre­segmentati on fo r the characte r image area. Here, we des igned a state transferring a lgorithm to eva luate the gray level vari ations with three states to transfer and record data (Figure 2).

State 0: idle

State 1: detect the left side of a word

State 2: detect the right side of a word

T hese states a re exchanged when the conditions of ">", "<", and "= " ° ho ld , e g, assume that the word is black and the background is white. Le t XI be the gray level of the current pixe l and Xo the gray level of the prev ious pixe l. Then State 0: X () - X I > 0: change to State I and ·record X I to

temporary data buffer

Xu - X I < 0 : no transfer and no record

X u - X I = 0 : no transfer and no record

State 1: Xu - X I > 0 : no transfer, but record X I to

temporary data buffe r

X u - X I < 0: change to State 2 and record X 0 to

temporary data buffe r

Xu - X I = 0 : count I = count I + I ;

When count > n, change to State ° and de le te temporary data bu ffe r, otherwise no transfer and no record where n is a constant for threshold .

State I >

=

Figure 2- Three states to transfer and record data

State 2: X 0 - X I > 0 : no transfer, but record X () to

temporary data buffe r

X 0 - X I < 0 : change to State 0,

1 if IIIX, 1-IIXo Ik-IIX , I

m merge temporary data buffer to ava il able data buffer otherwi se dele te the temporary data bu ffe r

X 0 - X I = 0 : count2 = count2+ I ;

When count > r, change to S tate 0,

1 if IIIXI I - II X o Ik -II X,I merge tempo-

m ra ry data buffe r to data buffe r otherwise de le te the te mporary data buffe r. count ~ r, no transfer and no record , where r is a constant.

Assume that the average gray leve l

o 1 24 ° - OJ -OJ - OJ - OJ '4 ' 4 '4 '4

width of an image is co, the at the regIons between

are X ° ' X I' X 2 ' X .\ , and the

summation of the di ffe rence are Sumo, Sum l, Sum" brightness reference va lue is G, and the di stance

from X 0 to X I is t.X, then

Gi2

= G + [LU / (Xi+l - XJj Sum i

So we can obtain a dynamic th resho ld va lue t from the brightness reference va lue and a weighting fac tor a:

t =ax(:EGi)

3 Character Segmentation

An image frame is composed of charac te rs, business logo, barcode, and background , e tc. To recogni ze a character, the segmentati on procedure

·11 b I,- IS I I W I e a necessary step · . . n our syste m, t le segmentation process de letes a ll unnecessary patterns and leaves onl y the characte r in orde r to increase the processing speed. A useful segmentati on method, which uses high process ing speed but is suitable for c lear image patterns, is introduced in thi s sec ti on.

Since a characte r string is written para ll e l on the same hori zontal line and two di ffe rent charac te rs are separated by a line space, we onl y need to check each hori zontal pi xe l and merge the character response pi xe ls as the characte r block. Thi s method cannot work well in s ituati ons where the image has some vertical noise pattern . T he merging segmentation

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576 J SCI INO RES VOL 62 JU NE 2003

algorithm was des igned to eliminate thi s kind of noise as foll ows:

The merge segmentation algorithm steps are shown in Figure 3. We defined a parameter named Char-Width , whi ch is a constant di stance between two bl ack pi xels. If the di stance between two black pi xels < Char-Width , then these two pixels are in the same area. Figure 3 shows fi ve different merge types based on thi s merging algorithm.

Merg ing Algorithm

The merging algorithm can be described in fo ll owing steps:

The first step is to determine pi xels on the same line and merge those pi xels together. The second step is to merge lines of the sa me character, such as merging of a line and another line o( a line and a character area. As shown in Figure 4, the di stance h between the merged line B and the bl oc k area A shoul d be less th an a constant height. If a line cannot be merged with any relat ive block then that line is the starter for a new block area.

Let Pi,y be a pixe l of a character in the horizontal line with a height of y. D(Pi,y, Pj .y) represents the distance between Pi.y and Pi.y. There are two import po ints in a segment, Ii' one is the start ing point Ps,j., and the other is the end point Pe.j

Psj = Pi.j I D(Pi- l,y , Pi,y) > C Pe.i = Pi.i I D(Pi.y, Pi+I.Y) > C,

where C is a constant, and depends on the space of two charac ters.

Then the method of the first step can be ex pressed as

jf Pi-I.y E Ij and D(Pi-l,y , Pi.y) < C then Pi,y E Ij

Simjlarl y, the four margins of a block can b( defined as:

left margin BLI! = min(Ps.i . . .. Ps.j ) I ii . . .. Ij E Z" right margin Br,1! = max(Pc.i .... Pe.j) Ii i .... Ij E Z" top margin Bt. 1! = min(yj) l)'j - )'j_1 > I bottom margin Bb.1l = max0'j)1 )'j - )'j+1 > I

where Z" is the nth block and Yi is the height 0

segment Ij .

Then the method of the second step can bE ex pressed as

if Ii-I E ZI! and YrYj- l= I , BL" < Pe.j , BLI! > Psj then Ij E

ZI! There is one exception:

if Ij E Z" and Ij E Zm then ZI! ' = Z" + Zm BLIl· = min(Ps.j , BL" , BLm) BLI! ' = max(Pe.j , BLI! , BLm) B",,· = min (Bt." , BI.111)

In thi s conditi on, it is suitab le to merge twe different block areas because each block area i ~

sati sfactory for an advanced merg . Figure 5 s how~ the scheme for the merging algorithm criteri a. The merit of thi s algorithm is more prec ise charactel block segmentati on but it i - also more time consumll1g.

4 Feature Extraction

When a block has been segmented, our concern is to determine if the bl ock is usefu l, i e, to find any character in thi s segmented block ' 6- ' 9. The three rul es employed for checking are as fo llows :

(a) combination for ( c) combination for line (e) combination for pi xel and pixel and line block and block

• •

(b) combination for (d) combination for line D L~ pixel and line and block

D Figure 3 - The steps of merging segmentation algorithm

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LI el CII.: PROCESSING & RECOG ITION METHODS 577

The reasonable width and the height of a block. We define the poss ible width and height of a block. Any character shou ld have a reasonable width and height limits. If a block is over the Ii mi t for width or height then the block must not be a character.

hea d rea r

L..-____ ..."I plane A

gap h (

segment B

Figure 4 - The distance between the merged line and the block area should be less than a constant height

Yes

No

2 The ratio of block height and block width for a specific character font is constant.

3 The Black Change (BC) Frequency

We defined a parameter ca lled BC, which is the number of level changes in pixe ls from white ( 0 black in the horizontal line divided by the number of black pixels in the horizontal line. When we an alyze a horizontal line of pixels, we find that the more complicated the pixe l line (more strokes), the greater the black change frequency. This characteri stic cannot be found in a uniforml y black background. Using the prev iously discussed three rul es to filter each segmented bl ock, most of the non-character patterns, such as the background or noi se can be deleted which saves a lot of recogniti on time.

A single di git pattern can be prec ise ly taken from a small square image in which each di gital block

Figure 5 - The scheme for the criteria of the merging algorithm

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578 J SCI IND RES VOL 62 JUNE 2003

I S a patte rn to be recogni zed in thi s secti on. The proposed method uses the directi on code to acquire the feat ures of a di g ita l pattern . T o de monstrate fea ture ex tracti on us ing the direc tion code, a seven­segment dig it from a calcul ator was used as an example. T he seven-segment dig it is composed of th ree hori zontal and fo ur vertical bars in a VFD (Vacuum F lorescent Display), as shown in Figure 6 . T he Arabic numerals, 0 to 9, can be recognized using suitable bar li ght ( I ) or darkness (0). That is, if we can determine whic h bars have light or darkness, the Arabic numera l could then be recogni zed .

T he direction code consists of hori zontal and vert ica l code. A dig ita l patte rn is sampled from the center of the verti ca l patte rn to dete rmine the light s ituat ion o f a ll hori zonta l bars in a VFD, ca lled the ve rtica l code. O n the contra ry, sampling from the upper fourth and lower three fo urths of all the vertical bars in a VFD is ca lled the hori zonta l code, e g, a di o it "8" shoul d be IIII for the hori zonta l and III fo r the vertical code; "9" should be 0 I I I for the hori zonta l and I I I for the verti cal code. A directio n code has seven pi xe ls, which a re composed of three hori zonta l and four ve rtica l bars in a VFD. An Arabic nu mera l is recognized afte r sampling 'and matching the d irec ti on code. T he merits of the directi on code a re speed and small amount of sampling data. The major ity of the diffe rent types of numerical di gits fo r a computer can be recogni zed using th is method. However, the recogniti on rate is not good enough fo r some home made Arabic numera l fonts . In our

syste m, a s ingle di g it image patte rn has at leas t 24x24

p ixe ls. T he image patte rn is sampled us ing an 8x8 (64 pixels) mes h. Each sampling pi xel is the node of the mesh. The thresho ld of the sampling p ixels is determined using a suitable va lue and the dig ita l patte rn can be converted into a binary form as shown

in Fi gure 7, and sorted as 8x8 binary dig it. All of the

8x8 b in ary di g its were di vided into three parts ca lled

the upper ha lf 8x4, the lower half 8x4, and the

ori gina l 8x8 binary pattern . Each testing patte rn is

matched by the upper half 8x4, the lower half 8x4,

and the entire 8x8 of a binary patte rn to increase the recognit ion rate, e g, the d igi ts "3" and "5 " are simil ar to the lower half of the bina ry patte rn . If a testing

patte rn is matched with the uppe r ha lf 8x4 o f di git

"3", the lower half 8x4 of dig it "5", and the 8x8 fo rm of di git "5 " then the testing digit is determined to be "5" . Hence, we proposed the three-part

Figure 6-A seven-segmen t digit is compo cd of three hori zonta l and four vertica l bars in a VFD (Vacuum Florescelll Display)

uppe r r- all lower

Figure 7-Allthe binary digits have be n divided in to three parts call ed the Lipper hal f, the lower half. and the original

bi nary pall ern

comparisons a lgorithm, described as fo ll ows. For an advanced ex planation, we used an 8x8 block example with a samp le M i.j and a template Si.j, where 0 ~ i ~ 7 , O ~ j ~ 7

M .. = 10

I . }

I

w \jPx,y 1:- 1 x = i X_h

8

e lse

H H y = jx _l> ::; y::; (;' + I) X_h . . 8 .. 8

where Wb and Hh are the wid th and he ight of the block. Simila rl y, we can obta in Si.j

M . 1:-5 .(11) 1·1 1../

c . ={O 1 • ./

1 M .. =5 .(n) I . J 1 • ./

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LI N et al.: PROCESSING & RECOGNITION METHODS 579

7 7

() e(n)= IIC;.j (n ) ;=0 j =O

3 7

() /I (11)= IIC;,j(n) ;=0 j =O

7 7

() e(n) = IIC;,j (n) ;=4 j =O

Let a e, a u, al be the similar coeffici ent corresponding to entire, upper and lower half block. Let N be the recogniti on result of the entire block. ae(N)=max( a e(n)) The recognition output will depend upon the template corresponding to the maximu a(n). (J(n)=(Ji n)+kl ll )+ ki n) Where weighting value kl n) and ki n) are obtained from Table I .

5 Experiments and Results

The digital segmentati on was introduced in Section 4 . During our experiments, we found that when a single digit stroke was too thin and less than one e ighth of the width of the entire pattern , it was impossible to acquire the sampling data. Hence the sampling meth od was rev ised as fo llows . Each sampling pixe l was replaced with the pixels of a line segment between two original sampling points, The original 64 sampling points were repl aced by 64 segments. If any pixe l gray leve ls within the segment were less than the threshold value the segment was set to I , otherwise it was set to O. In most of the Arabic numeral fonts, the same digit has the same strokes and the onl y difference is the size. Using the direc tion code, two different sized patterns will have the same re lative sampling area. This is why the proposed method has a better recogniti on rate for di ffe rent s ized Arabic numerals.

For convenience and reality the digital database is obtained from actual merchandise stickers, The digits were selected and thinned into an 8x8 binary pattern after processing through the proposed feature extracting method. Thi s demonstrates that the extracted digits were sampled precisely and no pixe ls were generated by noise,

Many processes were tested to acquire these results. Figure 8 depicts the test results from the

Table I-Weighting value k l(n) and k2(n)

N n GlI(n) >GlI(N) k I (n) GI(n» GI(N) k2(n)

0 6 5 0 9 0 5 4 4 0 7 2 2

2 3 0 5 7 0 5 8 0 2

3 2 0 5 7 0 4

8 2 2 9 4 0

4 7 3 0 5 3 5 0

6 4 3

6 0 2 0 5 4 3

8 4 0 9 2 2

7 2 2 2 0 3 9 4 0

8 6 4 0 9 0 4

9 0 0 2 6 2 2 7 4 0 8 0 4

~ ..cognition odiuslmont looming

Figure 8 - The test resul ts of the noise tiltering and the digit segmentation

noise filtering and di git segmentati on. It is obvious that the mjddle black area was not selected for digital segmentation , Although the '95721' and '196' blocks have some overlaps in the hori zontal directi on, the

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580 J SC I IND RES VOL 62 JUNE 2003

segmentati on as shown works we ll not on ly for the single block but also for the blocks in different regions.

The nex t experiment involved CCD on-line testing. All images were grabbed by a CCD and consisted of 256 gray levels with level 255 as white and leve l 0 as a black pixel. The main problem was the illumination of the object to be so lved and can be summarized into two categories. One is the non­uniform distribut ion of the illumination, wh ich means that a part of the testing object was too close to the li ght. The useful pi xe ls were black. Hence the ill uminati on of the background must be always lighter than digit itsel f in our system. If some strokes of the digit are illuminated too much or in a non-u niform manner, then a prec ise segmentation and feature ex tracti on wi ll be difficu lt. Thi s was the most difficult problem in the tests that we encountered.

image recognition a.djusb11ent leaming

result

13:::11 22491

'GrANT EUR0eE ' - -' "

~ROntRDAM ;.'PQ;NO: 92·12

, -< .. ", ,,'

The other problem involved too much or not enough illumination. A good contrast image should have a gray level di stributi on th at ranges between 0 and 255. Image gray levels that are cone ntrated in certain va lues are caused by illumination th ~ t is too strong or too weak. A good image is not onl y free from noise and complex background but also has a uniform and sui table illumination .

Some ex perimental res ults from the image tests are discussed here. Figure 9 shows the image of a non-uniform illumination. The illumination in the upper half of thi s image is greater than the lower part. Hence, with a constant threshold va lue and a a va lue for the image, on ly half of the image frame can be recognized . We found that the dynamic threshold va lue of a dim image is suitable for recogniti on. The digital patterns '22491 ' and '381 I ' can be recogni zed easily where the a va lue is the defaul t (0.6) and the

adjustme-nt

thresbold I ~-.l~ 17

(t

~- =.J ~ 0.60

r. auto.searching

gr aylevel 192

ma:{lmUrrI spac

~J -.l ~ 35

rninimurnr Iflidthiheightj ~ ~ ~ 0.33

ma:<imurn Be ~~ -~ 15

I r close

Figure 9 - The image o/" non· uniform illumination

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LI N el al.: PROCESSING & RECOGNITION METHODS 58 1

thresho ld value is 12. The di gital pattern '22491 ' above thi s image has some tiny di gits and those digits were neglected due to the limited space between the di gits.

Fi gure lOis a very c lear pattern . The digital pattern s '526266470183', '81002329' and '712181 ' are recognized in three specially defined regions . Thi s shows that the system described in thi s paper works we ll and separates the di gital pattern and background successfully. The last example shows if a bad bar code or a bad lot numbe r cannot be read by a bar code reader, our vi sion system can recognize the hand written numbers by examiners, as shown in Figure I I .

6 Conclusion

The preprocess ing and recognition methods of an integrated machine vision and bar code reader system for automated production lot number inspection has been presented through the application

i

i noise ~//

Figure I 0 - The digit patterns are recogni zed in three special de li ned regions

ABO UPC 8a,- Cod e

• #:rf- ... r ' ~ :l';';~ : .. 'i:'-

==Q"EiO€SII

::.~ .. ~. US BB0 5 608 8

· mlll lm l~ II~I IlIlI III~ J~11 Figure I I- The vision system can recognize the hand written

nlllnbers

of se lect algorithms described spec ificall y in th is paper. Us ing these al gorithms the recogniti on rate becomes greater and the sys te m becomes more fl exibl e in compari son to a bar code reader. The proposed method provides hi ghl y accurate resul ts with a low error rate, even if hand written di gits are used . The experime ntal results show that the performance of thi s integrated system is hi gh, and the recognition rate can exceed 99 .8 pe r cent.

Acknowledgment

Thi s work was sponsored by the Nati onal Sc ience Counc il , Ta iwan , Republic of C hina under grant number NSC-88-25 16-S-035-00 I and NSC-86-22 I 2-E-035-003 .

References

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