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USING THRESHOLD OF SINGLE LINKAGE TO IMPROVE THE MATCH INDEX BETWEEN COMPUTER MODEL AND ARTIFACT
Chuan-Shu Kao� Jyh-Jeng Deng� Chia-Lin Liu� Chun-Ching Chen� Shih-Hung Wang� Yi-Ho Lai
Department of Industrial Engineering and Technology Management DaYeh University
ChangHua, Taiwan 515, R.O.C.
ABSTRACT
This paper investigates the relationship between geometric profile and measurement precision in repeated measurements of a wooden sculpture, christened as loving each other. Statistically, if the covariance matrix formed by the repeated measurement is dependent on the profile of the artifact, then given a large difference in the profile of two domains on
����� ���� ���� ����� 245
Journal of Technology, Vol. 23, No. 4, pp. 245-262 (2008)
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Key words : principal component, covariance matrix, repeated measure- ments, cluster analysis.
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the artifact, the corresponding covariance matrices would be significantly different. This study finds a rule of single linkage to discriminate outliers in repeated measurements based on similarities among them.
The measurement tool is MicroScribe G2; the display software is Rhino; and the analysis tool is XploRe. We convert a covariance matrix into a 1x6 vector and by using principal components analysis the vector is projected into a 2D point. Thirty points are chosen among the domains to explore different profiles of the artifact. Next cluster analysis is applied to the 30 points in the 2D graph to find points which share the common covariance matrix. This further renders a pooled covariance matrix for points within a 0.2 mm square which inscribes the most crowded points in the projected 2D principal components. Then 2000 pairs of simulated points from the pooled covariance matrix are generated, and the distance between the pair points is calculated. The sample mean and standard deviation of the distance are obtained and the upper limit, mean plus the three standard deviations, is used as an empirical single linkage threshold.
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2 7.0832 7.0832 7.0832
3 11.5295 11.4424 11.0438
4 11.2838 11.4301 11.1010
5 12.9642 12.7486 12.8594
6 13.3151 13.0277 12.9498
7 14.7723 14.6225 13.9873
8 14.3846 14.3892 14.0305
9 13.8669 12.2116 12.0309
10 17.8782 17.8782 17.8782
11 14.2130 14.2130 14.2130
12 12.1373 12.2009 12.1967
13 9.4993 9.4993 9.4993
14 8.0961 8.0961 8.0961
15 19.0013 19.0013 18.8232
16 9.1542 9.4530 9.6745
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0.00411560.000389470.0013748
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0.001374806-2.3839e-0.005589
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1. ���������� ����������
Statistical Analysis,” Springer, Berlin, Germany, (2003).
7. http://www.xplore-stat.de/index_js.html
8. ()*��+,-./01��23456789:
�L� �M�6N�OP#$%�QR (2008)
2008� 08� 11��
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0.00065103 0.00055013 0.0043399
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0.0053156 0.0018243 0.0011492
0.0018243 0.0057668 0.0015084
0.0011492 0.0015084 0.0045955
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=
2. V., Raja and Fernandes Kiran J., “Reverse Engineering -
An Industrial Perspective,” Springer, Berlin, Germany,
(2008).
3
“Least-Squares Fitting of Two 3-D Points Sets,” IEEE
Transactions on Pattern Analysis and Machine
Intelligence, Vol. PAMI-9, pp. 698-700 (1987).
Orientation using Unit Quaternions,” Journal of the Optical
Society of America A,” Vol. 4, pp.629-642 (1987).
Control,” 3rd ed. Pearson, London, UK, (2005).
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���Ç 3 à�/�yo���¸r����S 1 �T
����������� !�"#$�%&(2006)'
3. Arun, K. S., Huang, T. S., and Blostein, S. D.,
4. Horn, B. K. P., “Closed-form Solution of Absolute
5. Craig, John J., “Introduction to Robotics: Mechanics and
6. Hardle, W. and Simar, L., “Applied Multivariate
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0.00400970.000385830.0008278
0.000385830.003844505-5.0602e-
0.000827805-5.0602e-0.0045135
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0.000495680.0060460.00019167
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0.0048047 0.00063231 0.001278
0.00063231 0.0058554 0.00018118
0.001278 0.00018118 0.0050197
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0.00068983 0.0057611 8.1088e-05
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0.00055969 5.4207e-05 0.0044616
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0.0010597 -0.00021175 0.0044249
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0.3589
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0.0097483 -0.00028952 -0.001362
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-0.001362 0.0029365 0.0054059
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1 16 SVD6 Join_rep2 ��� check_rep2
2 7 SVD5 Join_rep1 ��� check_rep1
3 9 SVD8 Join_rep5 ��� check_rep5
4 14 SVD6 Join_rep3 ��� check_rep5
5 5 SVD5 Join_rep5 ��� check_rep3
6 6 SVD5 Join_rep3 �� check_rep2
7 12 SVD8 Join_rep2 �� check_rep3
8 10 SVD8 Join_rep3 �� check_rep1
9 2 SVD4 Join_rep3 ��� check_rep3
10 1 SVD4 Join_rep5 �� check_rep2
11 8 SVD5 Join_rep2 �� check_rep5
12 13 SVD6 Join_rep5 �� check_rep1
13 11 SVD8 Join_rep1 ��� check_rep2
14 4 SVD4 Join_rep2 ��� check_rep1
15 15 SVD6 Join_rep1 �� check_rep3
16 3 SVD4 Join_rep1 �� check_rep5
3,3,1
0.1949
0.0855
0.4514
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0.1500
0.0674
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; -----------------------------------------------------------------------------------------------------------------
; Description MVAclus8p performs cluster analysis for the 8 points example
;------------------------------------------------------------------------------------------------------------------
Iibrary(“xplore”)
Iibrary(“stats”)
X=read(“D:\position01.txt”)
;creates data
n=rows(x) ;rows of data
xs=string(“%1.0f”, 1:n) ;adds labels
�
; the second part
d=distance(x, “euclid”) ;Euclidean distance
;squared distance matrix
t=agglom(d, “ward”, 2) ;hier. Cluster anal., Single linkage
g=tree(t.g, 0, “CENTER”)
g=g.points
tg2=paf (g[,2], g[,2] ! = 0)
zg2=sort(tg2)
zg
1 = 5. *(1:rows(g)/5) = (0:4)1 – 4
setmask1 (g, 1, 0, 1, 1)
setmaskp (g, 0, 0, 0)
; show the dendrogram
tg=paf(t.g[,2], t.g[,2]!=0)
numbers=(0:(rows(x)-1))
numbers=numbers~((0)*matrix(rows(x)))
setmaskp(numbers, 1, 2, 3)
setmaskt(numbers, string(“%.of”, tg), 0, 0, 16)
dd2=createdisplay(1, 1)
show (dd2, 1, 1, g, numbers)
setgopt(dd2, 1, 1, “xlabel”, “”, “ylabel”, “Squared Euclidian Distance”)
setgopt(dd2, 1, 1, “title”, “Ward Linkage Dendrogram – 6 points”, “xoffset”, 10 10, “yoffset”, 10(3)
���� ���� �� �� � ���� ��������������� !"#$%&'()*+,- 261
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1 ��-�-check 1 ok ok ok
2 ��-�-check 2 ok ok ok
3 ��-�-check 3 ok ok ok
4 ��-�-check 4 ok ok ok
5 ��-�-check 5 ok ok ok
6 ��-�-check 6 ok ok ok
7 ��-�-check 7 ok ok ok
8 ��-�-check 8 ok ok ok
9 ��-�-SVD 1 ok ok ok
10 ��-�-SVD 2 ok ok ok
11 ��-�-SVD 3 ok 2,3 2,3
12 ��-�-SVD 4 ok 1 1
13 ��-�-SVD 5 ok ok ok
14 ��-�-SVD 6 ok ok 4
15 ��-�-SVD 7 ok 1 1
16 ��-�-SVD 8 ok 1,3 1,3,4
17 ��-�-check 1 ok 2 2
18 ��-�-check 2 ok ok ok
19 ��-�-check 3 ok ok ok
20 ��-�-check 4 ok ok ok
21 ��-�-check 5 ok ok ok
22 ��-�-check 6 ok ok 1,4
23 ��-�-check 7 ok 1,3 1,3
24 ��-�-SVD 1 ok ok ok
25 ��-�-SVD 2 ok ok ok
26 ��-�-SVD 3 ok ok ok
27 ��-�-SVD 4 ok ok ok
28 ��-�-SVD 5 ok ok 1,4
29 ��-�-SVD 6 ok 2,4 2,4
30 ��-�-SVD 7 4,5 1,4,5 1,4,5
31 ��-�-SVD 8 ok ok ok
32 �-check 1 ok ok ok
33 �-check 2 ok ok ok
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34 �-check 3 ok ok ok
35 �-check 4 ok ok ok
36 �-check 5 ok ok ok
37 �-check 6 ok ok ok
38 �-check 7 ok ok ok
39 �-check 8 ok ok ok
40 �-SVD 1 ok ok ok
41 �-SVD 2 ok ok ok
42 �-SVD 3 ok ok ok
43 �-SVD 4 ok ok 1
44 �-SVD 5 ok ok ok
45 �-SVD 6 ok ok ok
46 �-SVD 7 ok ok ok
47 �-SVD 8 ok ok 1,2
48 �-check 1 ok ok ok
49 �-check 2 ok ok ok
50 �-check 3 ok ok 1
51 �-check 4 ok ok ok
52 �-check 5 ok ok 1
53 �-check 6 ok ok ok
54 �-check 7 ok ok 2,5
55 �-SVD 1 ok ok ok
56 �-SVD 2 ok ok ok
57 �-SVD 3 ok ok ok
58 �-SVD 4 ok ok 5
59 �-SVD 5 3,4,5 3,4,5 3,4,5
60 �-SVD 6 ok ok 5
61 �-SVD 7 ok ok 1
62 �-SVD 8 ok ok ok
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