紀智超碩士論文.PDF

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2 Y ( )...32 X ( ) i

3 RGB ii

4 Fuzzy C-Means Clustering RGB iii

5 [~3] [4] [5] [6,7] [8~] [2,3] [4~20] RGB (fuzzy theory) [2~3] (fuzzy relation)

6 .. ( ) 2

7 3

8 4

9 5

10 . 2. ( )

11 4. [32~35] 7

12 [44] 8

13 45 ( ) [44] [32] 9

14 . [45] (733/00) (68/590) (P<0.0) 2. [46] 3. [47] (94%) 9 (6%) 58 2 (3%) 63% 2% 0% % [48] [49] ( 8 ) 5 0

15 2 00% 6. [50] %(34 ) 7. [5] [52] % 68.4% 72% 3/5 66% % 9. Friedberg C.K.[53] 20 ( ).2 RGB HSI

16 B (0,0,) (0,,0) G (,0,0) R.2 RGB RGB RGB RGB.2 RGB [0,] RGB RGB RGB RGB HSI RGB 2

17 HSI HSI (I) (H) (S).3 HSI B R H P G I.3 HSI H P I S P RGB HSI ( R + G B) I = + 3 (-) 3 S =, (-2) [ min ( R, G B) ] ( R + G + B) [( R G) + ( R B) ] 2 2 ( R G) + ( R B)( G B) H = cos (-3) 2 [ ] 3

18 (Histogram equalization) (gray- level transformation function) ( r) s = T (-4) r s r 4

19 [0,] (-4) (a) T(r)0r (b) 0r0r) n k P( r ) = 0 r k = 0,, L, L k n n L P(r k ) k n k r k n k n k k L -6) n j S = T ( rk ) = = P( rj ) k = 0,,, L j= 0 j=

20 .7 (thresholding).8 T T T.4 [2~3] 965 Zadeh (INFORMATION AND 6

21 CONTROL) FUZZY SET (Fuzziness) (Randomness) (crisp set) (characteristic function) 0 (universal set) A X x X 7

22 f A ( x) = 0 x A x A (fuzzy set) (membership function) 0 X A f A X [0,] X={5,0,20,30,40,50,60,70,80}.2 ( ) (fuzzy relation) (pattern classification) X (pattern set) (one-step fuzzy relation) f ( x, y ) n- f f ( x, x) = x X ( x y) = f ( y, x) x, y X, (n-step fuzzy relation) ( x y ) f n, 8

23 f n ( x, y ) = sup x, x 2, L, x n X L, f ( x min[ n, y )] f ( x, x ), f ( x, x 2 ), n = 2,3, L f n + ( x, y ) = = sup x, L, x n, x n X L, f x, L, sup L, f f n x n 2, ( x x ( x ( x, y ) n X min[ f, n n x n ), min[ f, y ), f ( x, x f ( x n ( x, x ),, y )] ), ( y, y )] 0 f ( x, y ) f 2 ( x, y ) L f n ( x, y ) f n + ( x, y ) L f ( x, y ) = lim fn ( x, y ) n λ [0,] (fuzzy binary relation) Rλ xr y f,. (reflexive)f ( x, x ) = λ ( x y) λ 2. (symmetric) f ( x, y ) = f ( y, x ) 3. (transitive) f ( x, z ) max min[ f ( x, y), f ( y, z )] Rλ (equivalence relation) y (threshold)λ R (class) R ( x, y ). R ' = R ( R o R ) (transitive closure) ( x y) λ R T, 2. R ' R R R ' = 9

24 3. R ' = R T R R o (composition) (membership matrix) M = P ], M = [ q ] R P o Q P [ i, k Q k, j = M = ] R [ r i, j [ r i j ] = [ p i, k ] o [ q k, r, j = max min( pi, k,, q k, k i, j j ] ) (product) min (sum) max o = Fuzzy c-means Clustering Method (clustering) (Pattern Recognition) (clustering) (cluster) (cluster) (cluster center) X = x, x,..., x } { 2 n X (fuzzy pseudo partition) c- (fuzzy c-partition)x (fuzzy subset) (family) P = A, A,..., A } k Ν n c 0 < i= n A i ( x k ) = k= A ( x ) < n i k { 2 c X (vector)x k X 20

25 x k = [ x x 2... x ] R k k kp P v, v 2,..., vc P = { A, A2,..., Ac} c (cluster centers) v v,...,, 2 v c v i = n k = n [ A ( x k = i [ A ( x i k )] k m )] x m k ( i N c, m > R) Fuzzy c-means. t=0 (fuzzy pseudo partition) (0) P A,...,, A2 A c 2. v n k = i = n [ A ( x k= i i k [ A ( x )] k m )] x m k m P (t) ( t) c ( t ) ( t v ), v 2,..., vc 3. X x k 2 ( ) (i)x t > 0 i k v i N c A ( t+ ) i ( x k c ) = j= k x v k v v ( t) i ( t) j 2 2 m 2 ( ) (ii) t ( t x = 0 i I N I i A + ) ( x ) k v i ( t+ A ) ( x ) = i N I ( t+ A ) ( x ) = 0 i I i k ( t 4. + ) ( t p p ) ε t 2. m (fuzzier) m Fuzzy c-means Classical c-meansm (cluster center) X ε (t) P P ( t+) c i i k k 2

26 k k 2 k 3 k 5 5 x y k k 2 k 3 k 4 K 5 k 6 k 7 k 8 k 9 k 0 k k 2 k 3 k 4 K 5 x y A A 2 A A 2 k K 2 K 3 k 4 k 5 K 6 k 7 K 8 k 9 k 0 k k 2 k 3 k 4 K 5 A A Fuzzy c-means k k 2 k 3 k 4 k 5 K 6 k 7 K 8 k 9 k 0 k k 2 k 3 k 4 K 5 A A A A 2 K 8 (3,2) A A 2 Fuzzy c-means 22

27 (pattern recognition) (decesion analysis) (fuzzy expert system) (fuzzy logic control FLC) (fuzzy associative memory) fuzzy model.9 (crisp) Fuzzy c-means (cluster relation) 23

28 24.5 () (2) (3).0 RGB Fuzzy c-means clustering Method.0

29 RGB 25

30 0 (uncertainty) (fuzzy theory) (fuzzy relation) (membership function) (fuzziness) 26

31 27 (Gray Card) RGB 2.2

32 ( 5300K 300Lux) (Hue ) [0] 28

33 2.3 Nikon E2 (.3 pixels280*000) RGB CCD (Gray card) (Luminance) (saturation) [0] 2.2 ( 280*000 6bits bitmap ) 29

34 Y X 2.4 X Y Y X Y X X Y 30

35 Y ( ) Y (RGB ) Y (i) RGB R28~20G24~90B00~50 (ii) RGB R-G25~60G-B2~60R-B6 (iii) RGB R32 G50 B50 (iv) RGB R30~20G30~90B00~50 (v) RGB R-G20~60G-B20~60R-B20 (vi) RGB R32 G50 B50 (RGB ) ( ) ( ) Y Y Y ( ) ( ) Y ( ) ( ) X ( ) (RGB ) (RGB 3

36 Y (RGB ) (RGB ) 2.5 Y ( ) Y Y ( ) (RGB ) ( i )( ii ) ( ) ( ) (RGB ) ( iii ) (X 460~820Y 0~432)

37 2.6 (RGB ) ( i )( ii ) (RGB ( iii ) X 460~820Y 0~432 (RGB ) (RGB ) ( i )( ii )( iii ) Y Y 2.7 Y Y (X 460~780Y 248~770)

38 X 460~780Y 248~770 (RGB ) (RGB ) ( iv )( v )( vi ) Y Y Y X 600~724 Y 0~432 Y X 600~724 (RGB )Y Y Y 0~432 Y 248~770 34

39 2.9 Y X ( ) (X 264~579 Y ~ ) X 264~579Y ~ (RGB )R35 G30 B30 ( ) (RGB ) R5 G5 B 35

40 5 X 2. X (X 742~085Y ~ ) X 742~085Y ~ (RGB )R35 G30 B30 ( ) (RGB ) R5 G5 B 5 X 36

41 ( ) RGB 37

42 G G G B G B R G, R B (2-) R B G RB G R G G B + if R G, R B R G R G G B + G B + 38

43 (2-2) (2-2) (2-2) 80 < R + G + B < 480 (2-3) RGB 80 0 RGB ( ) (2-3) (2-2) x M = (2-4) C ( x M ) V = C R G x = C (2-3) G B M-V M M+V 0 m

44 VLow=M-VVHigh=M+V (2-2) VLow VHigh (2-2) M (2-2) M VLow 0 VHigh 255 VLow VHigh (2-2) VLow VHigh X V x VLow = m 0 X 0 V = 255 m x M X m 40 if if x M x > M (2-5) (2-6) R G x = m (2-5) VLow M G B + 0 m (2-6) M VHigh m

45 (2-4) M (2-2) M M m 69 (2-2).5 (2-2).5 M m HC LC ratio = HC LC m 2. M m 4

46 ratio M ratio m 0~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ratio m m m

47 2.4. 0( ) ( ) 255( ) 0( ) 43

48 2.7 (flood fill) 2.8 0( ) 44

49 (flood fill) 255( ) 0( ) 2.9 X Y

50 ( ) 46

51 2.22 ( ) 2.23 ( ) 47

52 2.24 ( ) x, ) x, ) x, ) y y y 2 3 ( y = ax 2 = ax = ax bx + bx + bx 3 ( 2 y2 2 + c + c + c ( 3 y 3 abc 2 c y = ax + bx

53 2.26 RGB 49

54 3. (i)rgb R88~20G72~2B56~04 (ii)rgb R-G0~20G-B4~6R-B8~32 (i)(ii) 255( ) 0( ) ( ) 0( ) 50

55 3.2 (flood fill) 3.3 0( 5

56 52 ) (flood fill) 255( ) 0( ) 3.4

58 3.3.4 Fuzzy c-means Fuzzy c-means % % 0.99 % % 5.24 % 00 % % % % % 6.35 % 00 % % % 2.75 % 97.7 % 2.29 % 00 % 0/ % 3.90 % /5 7.0 % 20.9 % 2/ % 7.8 % 3/ % 98.6 % 4/5.39 % 00 % 3/5 (83.77, 54

59 72.75, 84.96, 7.8) 3/5 (94.76, 00, 97.7, 98.6) Fuzzy c-means

60 56

61 57

62 RGB 58

63 [] 995: [2] 993:2-5 [3] [4] [5] [6] 993():58 [7] :-2 [8] 989 2:47 [9] [2] APSC 993: [3] 993: [4] Rafael C. Gonzalez and Richard E. Woods, Digital Image 59

64 Processing, Addison-Wesley Publishing Company, USA, 992. [5] William K. Pratt, Digital Image Processing, Second Edition, A Wiley-Interscience Publication, USA, 99. [6] Anil K. Jain, Fundamentals of Digital Image Processing, Prentice-Hall International, Inc., USA, 989. [7] Kenneth R. Castleman, Digital Image Processing, Prentice-Hall International, Inc., USA, 996. [8] Czerwinski R., and Jones D., and O'Brien Jr W., Line and Boundary Detection in Speckle Images, IEEE Trans. Imag. Proc., vol. 7, No. 2, 998 [9] Djuric P., Fwu J., Line and Boundary Detection in Speckle Images, IEEE Trans. Imag. Proc., vol. 6, No., 997 [20] Sharma G., Trussell H., Digital Color Imaging, IEEE Trans. Imag. Proc., vol. 6, No. 7, 997 [2] George J. Klir and Tina A. Folger, Fuzzy Sets, Uncertainty, and Information, New Jersey, 988. [22] Shinichi Tamura, Seihaku Higuchi, and Kokichi Tanaka, Pattern Classification Based on Fuzzy Relations, IEEE Trans. Syst., Man, Cyber., Vol., No., pp. 6-66, Jan. 97. [23] L. A. Zadeh, Fuzzy algorithms, Inform. Contr., Vol. 2, pp , Feb [24] L. A. Zadeh, Fuzzy sets and systems, Proc. 965 Symp. On Syst. Theory, pp [25] Fuzzy 993:-66 [26] Bart Kosko 60

65 995:2-54 [27] 997:6-~8-32 [28] L. A. Zadeh, Fuzzy sets, Inform. Contr., vol. 8, pp , June 965. [29] R. Bellman, R. Kalaba, and L. Zadeh, Abstraction and pattern classification, J. Math. Anal. Appl., Vol. 3, pp. -7, Jan [30] Krzysztof J. Cios, Inho Shin and Lucy S. Goodenday, Using Fuzzy Sets to Diagnose Coronary Artery Stenosis, IEEE Computer, pp , Mar. 99. [3] Yannis A. Tolias, and Stavros M. Panas, A Fuzzy Vessel Tracking Algorithm for Retinal Images Based on Fuzzy Clustering, IEEE Trans. Med. Imag., Vol. 7, No. 2, April 998 6

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彩色地图中道路的识别和提取

彩色地图中道路的识别和提取 9310016, i ii Abstract This thesis is on the researching of recognizing the roads in map image by computer. Based on the theory of Pattern Recognition, there is a method to be discussed, which can recognize