Accuracy Improvement by Compound Discriminant Functions for Resembling Character Recognition Takashi NAKAJIMA, Tetsushi WAKABAYASHI, Fumitaka KIMURA,

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1 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 Rights / 著作権関連情報 copyright 2000IEICE

Tetsushi; Kimura, Fumitaka; M 電子情報通信学会論文誌.

2 Accuracy Improvement by Compound Discriminant Functions for Resembling Character Recognition Takashi NAKAJIMA, Tetsushi WAKABAYASHI, Fumitaka KIMURA, and Yasuji MIYAKE ETL9B % 98.00% 0.69% ETL9B 1. 1] 3] 4] 5] ETL9B Faculty of Engineering, Mie University, Tsu-shi, Japan 1 3] 3] (9) (10) (13) projection distance 4] 2 D II Vol. J83 D II No. 2 pp

3 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 X X X X X =1 (2) subspace method 7] ], 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

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.

4 2 2 Fig. 2 Decision boundary of modified projection distance. α = (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 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) Φ 1 1 X 625

= 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.

5 2000/2 Vol. J83 D II No. 2 Φ 2 Φ 3 X M 1 Y 2 M Y X 0 2 gcpd(x) 2 =(1 δ)gpd(x)+δg 2 2 cpd(x) (0 < = δ < = 1) (7) 3] (6) ] 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 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)

(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 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 ] ] C 3 C = JIS 1 ETL9B 12] ] 3. 1 ETL9B ] 10 3 Table 3 The way to apply each discriminant functions. A B C D E F G H I J K ETL9B k 40 α 0.05 k 2 δ ETL9B A K

7 2000/2 Vol. J83 D II No % 3 B 20 k 60 α 0.1 k 5 δ % 93.46% 4 5 5], 13] Fisher 14] 13] k =0 ETL9B B 98.00% C 98.69% 4 Table 4 Recognition rate for - and -. (%) Table 5 Recognition rate for 24 pairs of resembling characters. (%) Table 6 Recognition rate for 3036 classes. (%) A B C D E F G H I J K δ k α 628

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.

8 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) δ (δ =1) (δ =0) δ 5 δ δ (δ =1) (δ =0) δ k α 15], 16] (D) (E) 6 (a) (b) (c) a b c 6 (c) (b) (c)

9 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 B C D E F G H I J K 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) X Y Y X 8 9 X Y X Y 7 SPARC station 10 hypersparc 125 MHz 4. ETL9B % 93.46% % 98.00% 0.69% ETL9B 1]

8 Example of characters recognized by Modified projection distance, misrecognized by Compound modified projection distance. 9 Fig.

10 2] ] D-II vol.j80-d-ii, no.10, pp , Oct ] vol.24, no.1, pp , Jan ] D-II vol.j78-d-ii, no.11, pp , Nov ] F. Kimura, Y. Miyake, and M. Shridhar, Relationship among quadratic discriminant functions for pattern recognition, Proc. 4th IWFHR, pp , Dec ] E. Oja, Subspace Method of Pattern Recognition, Reserch Studies Press, England, ] ] PRL82-79, ] D-II vol.j81-d-ii, no.6, pp , June ] D.G. Keehn, A note on learning for Gaussian properties IEEE Trans. Inf. Theory, vol.it-11, no.1, pp , Jan ] 63 D ] Yang DENG D-II vol.j79-d-ii, no.5, pp , May ] 12 pp ] 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 , Jan ] 2 PRMU97-228, Feb (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

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.

11 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 = ) 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} 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

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.

12 ME ME 633

On the Limited Sample Effect of the Optimum Classifier by Bayesian Approach he Case of Independent Sample Size for Each Class Xuexian HA, etsushi WAKA

Journal Article / 学術雑誌論文ベイズアプローチによる最適識別系の有限標本効果に関する考察 : 学習標本の大きさがクラス間で異なる場合 (< 論文小特集 > パターン認識のための学習 : 基礎と応用 On the limited sample effect of bayesian approach : the case of each class 韓, 雪仙 ; 若林, 哲史