Pattern Recognition System on the Basis of Similarity

PATTERN RECOGNITION SYSTEM ON THE BASIS OF SIMILARITY H. Kono Mechu.nical Engineering Laboratory, 4-12-1 Igusa , Suginamiku, Tokyo , Japan

This paper deals with a newly developed methodology and related system for the automatic pattern recognition of machine parts etc., on the basis of the similarity. In the methodology, two parameters of feature extraction are adopted and these are obtained by the projection of the shape on the reference line. Similarity is defined by the distance between a shape pattern and the matching pattern in the S- 6S-N coordinates system qenerated by using pattern-classification value S and group-classification value N. The developed pattern recognition system is featured by the capability of )' ecognizing in less than 4 seconds per one pattern and classifying into 22 kinds of matchinq patterns which are memorized in the minicomputer. Abstra~.

Keywords. Pattern recognition; identification; qroup theory; digital computer applications. I NTRODUCTI ON For the purpose of sorting and classifying machine parts, packages and containers etc., these articles upon rough and general observation may be regarded as possessing quite simple shapes. When these articles are closely observed, however, their shapes are in many cases too complicated to be recognized by a pattern recognition apparatus. In spite of the fact that exact recognition of complicated shapes may not be practicable, desired sorting and classification of such articles can be obtained through the recognition of the approximate shapes. These articles generally do not have simple geometric shapes such as triangle, equilateral hexagon and circle. Therefore, it is advantageous to effect the sorting and classification of articles through the recognition of the approximate shape of the articles. Heretofore, the pattern recognition (Ref. 1,2, 3) of an article has been accomplished by obtaining an outline into very short line segments, calculating the contour function from these line segments by the minimum square method and determining the shape of the object from the contour function. For pattern recognition of articles which have simple geometric shapes or shapes similar thereto, there has been suggested a method (Ref. 4) whereby the recognition of the shape of an article is accomplished on the basis of the number of maximum and minimum projection values determinable by measuring side-to-side distances in a figure obtained by projecting the article as it is rotated by 180° and subsequently calculating a projection characteristic of the shape. According to this method, however, the rotation by 180 ° must be about the center of

the article. As an improvement of the method for pattern recognition described above, there has been proposed a method (Ref. 5) which accomplishes pattern recognition on the basis of a decision reached from the comparision of the characteristic of projection values of an article subjected to the pattern recognition with that of projection values of reference patterns memorized in advance. This paper deals with a newly developed methodology (Ref. 6,7,8,9,10) and related system for the automatic pattern recognition of machine parts etc., on the basis of the degree of similarity found between the article and the matching pattern memorized in the minicomputer. To recognize the object described above according to the degree of similarity, there is provided a method for the recognition of the approximate shape of an article, which comprises finding from the projection of the article the largest width, the largest height and the area of the article relative to the reference line, finding a pattern-classification value S obtainable from the ratio of the area found to the product of the largest width multiplied by the largest height. This procedure is continued by rotating the postural angle of the article by 180°. The average value S and the range of variance 6S are calculated from the pattern-classification value measured in consequence of the 180° rotation. Simultaneously, the group-classification value N is obtained by differentiating the projection of the shape. By plotting the measured data in the S-6S-N coordinates system, three dimensional coordinates system is decided. The degree of similarity is defined by the distance between a shape pattern and the matching pattern in the S- 6S-N coordinates system. Therefore, the r~cognition of the approximate shape of an article is performed by comparing the results 909

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H. Ko no

of the average pattern-classification value, the range and the group-classification value with the values of a desired number of matching patterns and consequently determining the degree of similarity of the shape with the relevant matching pattern.

times without reference to the pos ture of the article . The average pattern-cla ss ification value for any article having the shape of a circle is invariably n/ 4 or about 0.786. Other shapes such as regular pentaqon, regular he xagon, regular heptagon and regular octagon, each ha s its own pattern-classification value. TABLE 1 shows the average pattern-classification value s METHODOLOGY OF PATTERN RECOGNITION of such geometric shape s and the corre s ponding ranges of the pattern-classification values. As Pattern-classification Value it i s evident, each shape has a pattern-classification value of it s own. By plotting the data With reference to Fig. 1, two dimensional of various kinds of shape patterns in the 5- 6S shape pattern of an article is settled at an coordinates system in which the vertical axi s arbitrary angle of 8 relative to the reference is graduated for the range of variation 6S and line t . Therefore, there is obtained a shape the horizontal axis for the average patternclassification value 5 , the coordinates system pattern shown in Fig. l(a). When this pattern representing the sectional shape of the artishown in Fig. 2 i s obtained. cle is projected perpendicularly onto the In the case of a trapezoid having two equal reference line t, the perpendicular projection sides, with the ratio of the parallel side s pattern shown in Fig. l(b) is obtained. In the being 1:2, the maximum of the pattern-clas s ifiprojection pattern of the article, let Ax cation value is 0.75 and the minimum of that is stand for the largest width on the reference 0.5. Therefore, the locus is located at 0.1 25 line, Ay stand for the largest height from the on the ordinate and 0.625 on the ab scissa. It is defined that the corner with an angle of reference line and Aa stand for the area of the perpendicular projection. By considering 180 ° or more is categorized as a concave corner. the ratio of the Aa to the product of the Ax On the contrary, the corner with an angle less multiplied by the Ay, the pattern-classificathan 180 ° is categorized as a convex corner. tion value is calculated. The values assumed Therefore, it i s defined that the shape of all by this pattern-classification value as the convex corners is the convex shape pattern. The postural angle 8 of the article relative to shape pattern having at least one concave corner the reference line which is changed in the i s defined as the concave shape pattern. The range of 0° to 180 ° have been found to have a general characteristic of the pattern-classifispecific relationship with the shape of the cation value is that it is constant with regular article. Specifically, the pattern-classifica- convex polygons except for multiple-of-four tion value S is defined by the following polygons. However, in the multiple-of-four polyequation. gons, common conve x and concave shapes, the pattern-cla ssification value changes by changing S= Aa (1) the postural angle and maintains a 180 ° period Ax • Ay of cycle. The pattern-classification value S is variable Fig. 3 i s the coordinates system wherein the with the postural angle of the article in loci of various kinds of concave shape pattern s general . Therefore, the avera ge pattern-clasare plotted. As it becomes obvious from Fig . 2 sification value and the range are defined by and Fig. 3, the convex pattern and the concave the following equations by us ing the maximum pattern are overlaped in the 5- 6S coordinates and minimum of the pattern-classification system. To eliminate this defect, that is, to value. discriminate convex from concave pattern and to allow mutual classification between convex and + Smin Smax (2 ) 5= concave pattern, a new parameter of feature 2 extra ction for group-classification value N wa s ado pted. t S= Smax -2 Smin (3) In the case of an article whose shape is a triangle, the projection pattern on the reference line is a triangle for all value s of 8. Therefore, if the postural angle of the article is changed from 0° to 180 ° , the area of the projection pattern is always one half the product of the largest width Ax multiplied by the largest height Ay. This means that the pattern-classification value S for any arti cle of triangular shape is 0.5 invariably. The pattern-classification value is variable in the range of from 0.5 to 1.0 in the case of a square. Therefore, the average pattern-classification value 5 for squares is 0.75 and the range of this value 6S is 0.25. In the case of an article whose shape is circle, the largest width Ax, the larges t height Ay and the area Aa of the shape are the same at all

Group-classification Value The group-classifi cation value N i s also obtai ned by the projection of the shape produced on the reference line as shown in Fig. 4(b). And, Fig. 4(c) shows the result of first differentiating the projection of the shape. Fig. 4(d) shows the second differential of the projection. In the figure, the first pulse and the last pulse are inverted in siqn. Therefore, by operating second differential to the projection of the shape, the pulse row shown in Fig. 4(e) is obtained. The positive pulse and the negative pulse corresponding to the concave and convex corner respectively. The Np and the Nn are the number of positive and negative pulse. This detecting procedure is continued by rotating the postural angle of the article by 180 ° and

911

Patte rn Recognit i o n System

TABLE 1 Characteristic of Regular Polygon ~iCS Pattern

~ la)

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-

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-

0.5 -O.S - 1.0

~

0.75

~

0 .738 1

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0.706-0.826

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,

0

.0.75

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-

0.691

0 .786

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S

0.691

0

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0

0.738

0

0.766

0.06

0.786

0

0.3 4

8_ 02 ~s

Fig . 2. Projection to (5, 65) coordinates for the convex pattern. 05

Fig . 3. Projection to (5, 65) coordinates for the concave pattern.

H. Kono

912

simultaneously the pattern-classification value is obtained. I~ the maximum value of Np and Nn which is detected by changing postural angle of the article are Np,max and Nn,max respectively, the group-classification value is defined by the following equation. N=

Np,max (4) Nn ,max + Np,max In the figure (Ref. Fig. 4(e)), the Np,max and the Nn,max are equal to 2 and 6 respectively. Therefore, the group-classification value is calculated as 0.250. The group-classification value of U-shaped pattern categorized to the concave group is 0.250, and H-shaped pattern is 0.333. However, all patterns categorized to the convex group are 0.000. Therefore, the group-classification value is an effective parameter of feature extraction in discriminating convexity from concavity, in extracting patterns categorized to the same group and in manifesting the complexity of the shape patterns . Considering the group-classification value to the Hshaped patterns (Ref. Fig. 3), the result of projection on the S- 6S-N coordinates system is shown in Fig. 5. In this case, a trigonal pyramid with the group-classification value of the matching pattern as a vertex is formed. And various kinds of transformed patterns are projected on the pyramid surface. The groupclassification values of these transformed patterns are given as the values which are projected on the pyramid surface. Degree of Similarity When the loci of the various kinds of shapes are plotted on the S- 6S-N coordinates system, the degree of similarity between two shapes can be expressed in terms of the distance between the corresponding loci, a shorter distance indicating a higher degree of similarity. According to the representation of the various shapes of articles in the coordinates system shown in Fig. 2, a triangle is recognized to be a pattern having more similarity to a circle than to a square and a regular pentagon to be a pattern having more similarity to a circle than to a triangle. The recognition of similarity at times differs to some extent from the recognition by the human faculty. An analysis conducted on this matter involving a number of ordinary adults has revealed that the similarity between a triangle and a square is about 12 %, the similarity between a triangle and a circle is about 3% and similarity between a circle and a square is about 27%. Therefore, in order to be matched to the recognition of similarity by the human faculty, the S- 6S-N coordinates system is transformed to the St- 6St-Nt coordinates system. This transformation of coordinates is namely the transformation of sensefilter. The transformation of coordinates is performed by the following equations.

Sf= Cl 6St= S

S £. 6Sm

Nt=

N ;)

y •

(7)

The degree of similarity Pi j of the shape of an article subjected to the pattern recognition to the various matching patterns is expressed by the following equation. Pij = L - Lij xlOO L

(8)

Wherein, the subscript i is the shape subjected to the pattern recognition and j is the matching pattern . Therefore, Lij is the distance between the shape pattern and the matching pattern. And, distance L is the criterion for the decision of similarity. Furthermore, distance Lij is expressed by the following equations.

i

li j = Sti } +6Sti } +Nti } +2.Sti J ' 6St ij ·cosu+ ~ 2· 6Stij ·Ntij ·cos v+2·Nt ij ·Stij ·cosW (9)

Wherein, Stij =St i -St,i , 6Sti ,i =6Sti - 6St j , Nt i,i = Nt i -Nt j . The parameter u, v and w represent the angle between the St axis and the 6St axis, the angle between the ASt axis and the Nt ~is and the angle between the Nt axis and the St axis respectively. By the analysis of human being, the favourable values in the equations from (5) to (7) were decided as £,=4.0, m=0.9, ;)=0.01. Fig. 6 shows the sense-filter of the convex shape pattern. The sense-filter of the H-shaped pattern is shown in Fig. 7. In these figures, pattern symbol is identified to the pattern shown in Fig. 2 and Fig. 3. The transformation of coordinates is intended to establish the degree of similarity to the various matching patterns and the attitude to be involved during the similarity recognition. HARDWARE Visual Input System

The developed system utilizes one television camera as a visual input device. The television camera is fixed above the worktable in vertical direction and is used to control the position of the article. Furthermore, the camera mounts the zooming-up mechanism which is automatically zooming up the pattern shape of the articles. The video output signal is quantified into two levels 1 and 0 by a comparator whose threshold level is manually adjustable into 1,000 steps. The 1 level corresponds to a durk image and 0 to a bright image. The quantified video signal is fed to a buffer register. The buffer register is a 256 (16 x16) bits serial-in parallel-out shift register. Parallel outputs of the buffer register are transferred to the computer memory through the direct memory acce~s channel. The time required to read in a complete image consisting of 64 x48 meshes is 1/60 second. The read-in time is equal to the one flame scanning time of the television camera. As the lighting method of the article, the shadow lighting method is adopted. Because, this method is superior to the reflective one when it is (5) applied to the pattern recognition system for (6) machine parts, packages and containers etc ..

Pattern Recognitio n System

913

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Fig. 4. Group-classification value.

Fig. 5. Projection of the H-shaped pattern.

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Fig. 7. Sense-filter of the H-shaped pattern.

Similarity

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Fig. 8. Overview of the system.

Fig. 9. General block diagram of the recognition system.

914

H. Ko no

Worktable Control System The worktab1e has three degree of freedom of motion, that is, two linear X and Y axes and rotational 8 axis. These X, Y and 8 axes are operated by the electrical pulse motors. The worktab1e is available for controlling the position of the articles and is numerically controlled through the program controlled channel connected to the minicomputer PDP11/34. The working range of X and Y axes are ±200 mm respectively and for 8 axis is ±180°. The rotational speed of 8 is 60 0 /sec in the maximum state . The overview of the system is shown in Fig. 8.

result is matching to and similar to the matching pattern respectively. The recognition time is less than 4 seconds per one pattern. The results are favourably satisfied. The programs are written in ASSEMBLER and FORTRAN LANGUAGE, and occupied about 8K words including data areas of 192 words for image storage area. CONCLUSION

The newly developed methodology and the system for the automatic pattern recognition of machine parts etc . have been obtained extremely desirable results, by adopting the concept on the basis of the similarity between a shape pattern to be recognized and the matching pattern . In this OPERATION OF THE SYSTEM system, the stored matching pattern data need only be a small capacity of memory and the device The schematic block diagram of the developed employed for processing these data is required to s imilarity recognition algorithms are shown have only a very simple structure. Furthermore, in Fig. 9 and Fig . 10 . The shape pattern of even if an article subjected to pattern recognithe article detected by the television camera tion fails to conform to any of the matching is converted into a perpendicular projection, patterns, there still can be obtained the degree on the basis of which the area Aa, the largest of similarity of the article to each of the width Ax and the largest height Ay of the matching patterns. This system can extensively article at the initial postura1 angle 81 are be utilized for the purpose of sorting and c1asdetermined and consequently the pattern-c1as- sifying machine parts, packages and containers. sification value S is measured. Simultaneously , by operating second differential to the projection data of the article, the pulse row REFERENCES is obtained and the number of the positive and negative pulse are counted. The detection (1) Roberts, L.G. (1963). Machine perception of the shape pattern and the measurement of of three-dimensional solid. MIT Technical the pattern-classification value and the Report NO. 315. (2) Gozman, A. (1968). Decompos it i on of a group-classification value will be likewise carried out at the second postura1 angle 82 visual scene into three-dimensional bodies. Fall Joint Computer Conf., 291 . (=81+68) to which the article has been rotated by a given incremental angle 68=5 ° from the (3) Shirai, Y., and S. Tsuji (1971). Extraction initial postura1 angle 81. The procedure of the line drawing of 3-dimensiona1 objects is repeated while the postura1 angle of the by sequential illumination from several directions. 2nd. Artificial Intell igence shape pattern is increased from 0° to 180° by rotating the article. Consequently, there will Conf., 71. (4) Tsuboi, Y., E. Tsuda, T. Shiraishi, and N. be obtained the range of variation 6S, the average of the pattern-classification value Kosaka (1973). A mini-computer controlled S and the group-classification value N. By industrial robot with optical sensor in using the S, 6S and N, the transformation of gripper . Proc . of 3rd. Int. Symp. on sense-filter is executed. In this processing, Industrial Robots, 343. (5 ) Yoda, H., and M. Ejiri (1973). A Hand-eyethe selection of the sense-filter is dec i ded system for Selection Process. Proc. of 2nd. by using following information that is maximum of the positive pulse, minimum of the negative Symp. on Industrial Robots, Chubu Automation pulse and the pulse arrangement. Society. Fig. 11 shows the comparision of the experi(6) Kono, H. (1975). Pattern Recognition by the mental and theoretical results between the Pattern-classification Value of the Shape . postural angle and the pattern-classification Proc. of 14th. SICE, Japan, 267. value for some kinds of convex shape patterns. (7) Kono, H. (1975) . Pattern Recognition on the The similarity recognition process is shown in basis of Similarity. Proc. of 14th. SICE, Fig. 12. In this case, a square shape pattern Japan, 265 . is caught by the shadow lighting. In the (8) Kono, H. (1976). Pattern-classification figure, (a) is a monitor image, (b) i s a digiValue and Shape. Proc. of 15th. SICE, Japan, tized image, (c) is a input data, (d) is d 451. perpendicular projection data, (e) is a second (9) Kono, H. (1976). Similarity Recognition using Pattern-classification Value. Proc. differential result of the perpendicular projection data and (f) is the display of the of 15th. SICE, Japan, 453. recognition result. The result of the similar- (10) Kono, H. (1977). Similarity Recognition of ity recognition is displayed as matching to, the Shape with Hole using Pattern-classifisimilar to and no matching to the matching cation Value . Proc. of 16th. SICE, Japan , pattern which is memorized in the minicomputer 625. memory. Twenty-two kinds of matching patterns shown in TABLE 2 are memorized. In the table, symbol. and, mean s that the recognition

Pattern Recognition System

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Fig. 10. Block diagram of similarity recognition.

Fig. 11. Comparision of experimental and theoretical results.

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(f) Display of the recognition result Fig. 12. Similarity recognition process.

H. Kono

916

TABLE 2 Similarity Recognition Results of the Developed System

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