Journal Article / 学 術 雑 誌 論 文 混 合 識 別 関 数 による 類 似 文 字 認 識 の 高 精 度 化 Accuracy improvement by compoun for resembling character recogn 中 嶋, 孝 ; 若 林, 哲 史 ; 木 村, 文 隆 ; 三 宅, 康 二 Nakajima, Takashi; Wakabayashi, Tetsushi; Kimura, Fumitaka; M 電 子 情 報 通 信 学 会 論 文 誌. D-II, 情 報 システム, II-パターン The transactions of the Institute o Communication Engineers. D-II. 2000 http://hdl.handle.net/10076/11112 Rights / 著 作 権 関 連 情 報 copyright 2000IEICE
Accuracy Improvement by Compound Discriminant Functions for Resembling Character Recognition Takashi NAKAJIMA, Tetsushi WAKABAYASHI, Fumitaka KIMURA, and Yasuji MIYAKE ETL9B 24 98.69% 98.00% 0.69% ETL9B 1. 1] 3] 4] 5] ETL9B Faculty of Engineering, Mie University, Tsu-shi, 514 8507 Japan 1 3] 3] (9) (10) (13) 2. 2. 1 projection distance 4] 2 D II Vol. J83 D II No. 2 pp. 623 633 2000 2 623
Table 1 1 Derived and compared compound discriminant functions. 2000/2 Vol. J83 D II No. 2 1], 2] 3] X X X X M 0 (1) 6] gss(x) 2 =1 {X T Φ i} 2 (2) 1 2 Fig. 1 Decision boundary of projection distance. gpd(x) 2 = X M 2 {(X M) T Φ i} 2 (1) X M Φ i i k 2 1 2 X 2 1 2 X X X X =1 (2) subspace method 7] 2. 2 5], 7] (1) (2) g 2 mpd(x) = X M 2 g 2 mss(x) =1 (1 α)λ i (1 α)λ i+ασ 2 {(X M)T Φ i} 2 (3) (1 α)λ i (1 α)λ i + ασ 2 {XT Φ i} 2 (4) α 0, 1] σ 2 modified projection distance method modified subspace method α =0 α =1 624
2 2 Fig. 2 Decision boundary of modified projection distance. α =0 2 2 2 1 1 (3) 8], 9] (4) 10] 2. 3 pseudo Bayes discriminant function 5] g pb (X) { =(N + N 0 +1)ln 1+ 1 } N 0σ 2 g2 mpd(x)] + ln ( (1 α)λ i + ασ 2) 2lnP (ω) α = N0 N + N 0 (5) N M P (ω) ω α 0, 1] σ 2 X N 0 Fig. 3 3 3 Component of compound projection distance. σ 2 M σ 2 P (ω) 11] 5] 2. 4 compound projection distance ] 2 M T Y {M T Φ i}{y T Φ i} G 2 cpd(x) = M = M 2 M 1 M T M {M T Φ i} 2 Y = X M 1 (6) M 1, Φ i i M 2 (6) 1. 3 3 1 2 Φ 1 1 X 625
2000/2 Vol. J83 D II No. 2 Φ 2 Φ 3 X M 1 Y 2 M Y 3.3 1 1 X 0 2 gcpd(x) 2 =(1 δ)gpd(x)+δg 2 2 cpd(x) (0 < = δ < = 1) (7) 3] (6) 2. 2. 5 ] 2 M T Y γ i{m T Φ i}{y T Φ i} G 2 cmpd(x) = γ i = M T M (1 α)λ i (1 α)λ i + ασ 2 M = M 2 M 1 γ i{m T Φ i} 2 Y = X M 1 (8) α =0 α =1 Y M g 2 cmpd(x) =(1 δ)g 2 mpd(x)+δg 2 cmpd(x) (9) 2. 6 2 1 ] 2 D T Y {D T Φ i}{y T Φ i} G 2 css(x) = D =Ψ 1 Φ 1 D T D {D T Φ i} 2 Y = X Φ 1 (10) D T Y γ i{d T Φ i}{y T Φ i} G 2 cmss(x) = γ i = D T D (1 α)λ i (1 α)λ i + ασ 2 D =Ψ 1 Φ 1 γ i{d T Φ i} 2 Y = X Φ 1 (11) Φ i i Ψ 1 1 D 2 (10) 1], 2] gcss(x) 2 =(1 δ)gss(x)+δg 2 2 css(x) (12) gcmss(x) 2 =(1 δ)gmss(x)+δg 2 2 cmss(x) ] 2 (13) 2. 7 626
G cpb (X) =(N + N 0 +1) { ln 1+ 1 } N 0σ 2 G2 cmpd(x)] N 0 = αn (1 α) (14) 2 24 Table 2 Pairs of resembling characters (24 pairs). g cpb (X) =(1 δ) g pb (X)+δG cpb (X) (15) 2. 8 3] 2 ] 2 2 3 ] C 3 C =5 5 2 10 3. JIS 1 ETL9B 12] 196 13] 3. 1 ETL9B 3036 24 48 2 13] 10 3 Table 3 The way to apply each discriminant functions. A B C D E F G H I J K ETL9B 10 9 10 k 40 α 0.05 k 2 δ 0.1 3. 2 3036 ETL9B 200 20 20 40 160 3 A K 3 3036 20 627
2000/2 Vol. J83 D II No. 2 5 20 99.91% 3 B 20 k 60 α 0.1 k 5 δ 0.1 3. 3 24 2 4 24 5 4 5 92.45% 93.46% 4 5 5], 13] Fisher 14] 13] k =0 ETL9B 3036 6 B 98.00% C 98.69% 4 Table 4 Recognition rate for - and -. (%) 71.50 80.50 76.00 90.25 74.50 83.25 80.25 89.50 67.75 79.50 75.00 89.00 73.25 83.50 79.25 87.25 76.25 84.00 80.25 89.75 71.50 80.50 69.00 87.25 62.25 73.00 5 24 Table 5 Recognition rate for 24 pairs of resembling characters. (%) 89.18 92.51 92.16 93.37 89.18 92.45 92.04 93.32 92.35 93.46 89.18 88.27 84.52 6 3036 Table 6 Recognition rate for 3036 classes. (%) A 96.93 B 98.00 C 98.69 D 98.72 E 98.90 F 97.89 G 98.61 H 98.63 I 98.79 J 98.73 K 98.89 4 5 δ k α 628
Fig. 6 6 Breakdown of misrecognition. 4 δ Fig.4 Coefficiant δ v.s. recognition rate (for resembling character pairs). 5 Fig. 5 δ Coefficiant δ v.s. recognition rate (for total classes). 5 6 4 δ (δ =1) (δ =0) δ 5 δ δ 0.5 0.8 (δ =1) (δ =0) δ k α 15], 16] (D) (E) 6 (a) (b) (c) a b c 6 (c) (b) (c) 1337 80 629
2000/2 Vol. J83 D II No. 2 7 Fig. 7 Example of characters recognized by Compound modified projection distance, misrecognized by Modified projection distance. 7 Table 7 Processing time. ms/ /s A 86.2 11.6 B 96.8 10.3 C 117.7 8.5 D 124.7 8.0 E 179.0 5.6 F 93.9 10.6 G 125.9 7.9 H 117.5 8.5 I 167.0 6.0 J 130.7 7.7 K 188.2 5.3 8 Fig. 8 Example of characters recognized by Modified projection distance, misrecognized by Compound modified projection distance. 9 Fig. 9 Example of characters misrecognized both by Modified projection distance, and Compound modified projection distance. (a) (b) (c) 7 8 9 7 X Y Y X 8 9 X Y X Y 7 SPARC station 10 hypersparc 125 MHz 4. ETL9B 1 24 2 92.45% 93.46% 3 98.69% 98.00% 0.69% ETL9B 1] 1989. 630
2] 1998. 3] D-II vol.j80-d-ii, no.10, pp.2752 2760, Oct. 1997. 4] vol.24, no.1, pp.106 112, Jan. 1983. 5] D-II vol.j78-d-ii, no.11, pp.1627 1638, Nov. 1995. 6] F. Kimura, Y. Miyake, and M. Shridhar, Relationship among quadratic discriminant functions for pattern recognition, Proc. 4th IWFHR, pp.418 422, Dec. 1994. 7] E. Oja, Subspace Method of Pattern Recognition, Reserch Studies Press, England, 1983. 8] 45 2816 1970. 9] PRL82-79, 1982. 10] D-II vol.j81-d-ii, no.6, pp.1205 1212, June 1998. 11] D.G. Keehn, A note on learning for Gaussian properties IEEE Trans. Inf. Theory, vol.it-11, no.1, pp.126 132, Jan. 1965. 12] 63 D-439. 13] Yang DENG D-II vol.j79-d-ii, no.5, pp.765 774, May 1996. 14] 12 pp.31 34 1996. 15] F. Kimura, K. Takashina, S. Tsuruoka, and Y. Miyake, Modified quadratic discriminant functions and the application to Chinese character recognition, IEEE Trans. Pattern Anal. & Mach. Intell., vol.pami-9, no.1, pp.149 153, Jan. 1987. 16] 2 PRMU97-228, Feb. 1998. 1. 1 2 (6) 1 M 1 i Φ i 1 2 k 2 M 2 2 M 2 M 1 1 n k 2 { (X M 1) T } 2 { } =C (M2 M 1) T Φ i Φi (A 1) C = 1 { (M2 M 1) T Φ i } 2 (A 2) X M 1 K-L { } X M 1 = (X M1) T Φ i Φi (A 3) (X M 1) T ] { } = (X M1) T Φ i Φ T i = C C j=k+1 j=k+1 { (M2 M 1) T Φ j } Φj { (X M1) T Φ i } {(M } 2 M 1) T Φ j Φ T i Φ j { }{ } = C (M2 M 1) T Φ i (X M1) T Φ i { (X M1) T } 2 = (A 4) {(M 2 M 1) T Φ i}{(x M 1) T Φ i} {(M 2 M 1) T Φ i} 2 ] 2 (A 5) 631
2000/2 Vol. J83 D II No. 2 {(M 2 M 1) T Φ i} 2 = M 2 M 1 2 =(M 2 M 1) T (M 2 M 1) {(M 2 M 1) T Φ i}{(x M 1) T Φ i} =(M 2 M 1) T Φ iφ T i (X M 1) =(M 2 M 1) T (X M 1) (A 5) X M 1 M 2 M 1 = M { Y T } M T Y {M T Φ i}{y T Φ i} 2 = M T M {M T Φ i} 2 = Y ] 2 (A 6) (6) 2. 3] {(X M 1) T Φ i} 2 g cm(x) = + µ (E T Φ i) 2 E = {(X M 1) T } (A 7) b µ (A 1) 3] i >k b>λ i (b =3.5,λ i =10 2 10 3 ) 1 {(X M 1) T Φ i} 2 {(X M 1) T Φ i} 2 + {(X M 1) T Φ i} 2 = = 1 b + 1 b {(X M 1) T Φ i} 2 {(X M 1) T Φ i} 2 + 1 b X M 1 2 X M 1 2 ] {(X M 1) T Φ i} 2 λ i λ i+b {(X M1)T Φ i} 2 1/b 2 E Φ 1 Φ k 1 b = 1 b (E T Φ i) 2 = (E T Φ i) 2 (E T Φ i) 2 (E T Φ i) 2 = 1 b ET ] Φ iφ T i E = 1 b ET E = 1 b T T (X M 1)(X M 1) T = 1 b {(X M1)T } 2 T = 1 b {(X M1)T } 2 1/b 2 11 3 29 7 28 9 11 632
60 62 3 10 10 11 48 53 58 10 1 3 ME 35 40 43 53 ME 633