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May 10, 2023 346 likes •538 views

A Handwritten Character A Handwritten Character Recognition Method Based on Recognition Method Based on Unconstrained Elastic Matching Unconstrained Elastic Matching and Eigen Eigen- -Deformations Deformations and S. Uchida H. Sakoe

SLIDE 1

A Handwritten Character A Handwritten Character Recognition Method Based on Recognition Method Based on

Unconstrained Elastic Matching Unconstrained Elastic Matching

and and Eigen

Eigen-

Deformations

Deformations

S. Uchida
H. Sakoe

Kyushu University Fukuoka, Japan

SLIDE 2

Human Interface Lab. Kyushu Univ.

Elastic Matching (EM) Elastic Matching (EM)

input reference displacement field deformation-invariant distance warped reference

SLIDE 3

Human Interface Lab. Kyushu Univ.

Unconstrained EM Unconstrained EM

A classical EM method Based on individual & local optimization of the displacement at each pixel High speed & high flexibility ! ... but, rarely employed ! (slower and less flexible constrained EMs are often employed).

SLIDE 4

Human Interface Lab. Kyushu Univ.

Overfitting by Unconstrained EM Overfitting by Unconstrained EM

reference

similar!

input reference input

discontinuity “gap”

(neglected in evaluation)

similar!

SLIDE 5

Human Interface Lab. Kyushu Univ.

Purpose and Key Idea Purpose and Key Idea

Purpose Revive unconstrained EM by relaxing the overfitting problem Key Idea Detect overfitting as the deviation from eigen-deformations

eigen-deform. not eigen-deform.

SLIDE 6

Human Interface Lab. Kyushu Univ.

Two Tasks Two Tasks

How to estimate eigen-deformations ? How to use the eigen-deformations in recognition process to detect

verfitting ?

SLIDE 7

Human Interface Lab. Kyushu Univ.

Estimation of Eigen Estimation of Eigen-

Deformations

Deformations

training patterns reference collection of displacement fields using unconstrained EM

…

Principal Component Analysis

… …

eigen-deformations

SLIDE 8

Human Interface Lab. Kyushu Univ.

Estimated 1 Estimated 1st

st Eigen

Eigen-

Deformations

Deformations

「Ａ」「Ｂ」「Ｃ」

(reference) apply positively apply negatively

SLIDE 9

Human Interface Lab. Kyushu Univ.

Recognition Using Eigen Recognition Using Eigen-

Deformations

Deformations

image distance +

min dist. discrimination reference input

…

disp. field

eigen-deform. of “A” Mahalanobis distance

SLIDE 10

Human Interface Lab. Kyushu Univ.

Recognition Rates Recognition Rates

99.07

9 2 9 4 9 6 9 8 1

1 2 3 4 5

maximum displacement (pixels) recognition rate (%)

for 500samples/category

with eigen-deform. (proposed) without eigen-deform. (conventional)

degradation due to overfitting

SLIDE 11

Human Interface Lab. Kyushu Univ.

Unconstrained vs. Constrained (1) Unconstrained vs. Constrained (1)

. 1 1 1 1 1

1 2 3 4 5

maximum displacement (pixels) computation time (ms)

unconstrained constrained

SLIDE 12

Human Interface Lab. Kyushu Univ.

Unconstrained vs. Constrained (2) Unconstrained vs. Constrained (2)

99.43% 99.12% constrained 99.07% 98.35% unconstrained with eigen-deform. without eigen-deform.

Unconstrained EM (fast) is comparable to constrained EM (slow) in recognition rate when eigen-deformations are used

SLIDE 13

Human Interface Lab. Kyushu Univ.

Conclusion Conclusion

Practical recognition method based on unconstrained EM Eigen-deformations to suppress

verfitting

Experimental results enough to encourage the revival of unconstrained EM

SLIDE 14

Human Interface Lab. Kyushu Univ.

Mahalanobis Distance Mahalanobis Distance

M

Σ

m=1

λ

c,m

1 〈 v- v , u 〉

c,m c

v : displacement field to be evaluated

c : class (“A”, “B”, ..) of reference

uc,m: m-th eigen-deformation of class c

λc,m: contribution (eigenvalue) of uc,m

SLIDE 15

Human Interface Lab. Kyushu Univ.

Piecewise Linear Unconstrained EM Piecewise Linear Unconstrained EM

input reference linear interpolation variable fixed

the mapping of each column is optimized INDEPENDENTLY

SLIDE 16

Human Interface Lab. Kyushu Univ.

Probable Overfitting Probable Overfitting

cross (fold over) gap (skip)

SLIDE 17

Human Interface Lab. Kyushu Univ.

Data Data

English capital letters from ETL6 (1100 samples / category) preprocessing

(size normalization, blurring, histogram equalization…) #101-600 average #601-1100 #1-100

reference training patterns test patterns

SLIDE 18

Human Interface Lab. Kyushu Univ.

A Handwritten Character A Handwritten Character Recognition Method Based on Recognition Method Based on

Unconstrained Elastic Matching Unconstrained Elastic Matching

and and Eigen

Eigen-

Deformations

Kyushu University Fukuoka, Japan

Elastic Matching (EM) Elastic Matching (EM)

input reference displacement field deformation-invariant distance warped reference

Unconstrained EM Unconstrained EM

A classical EM method Based on individual & local optimization of the displacement at each pixel High speed & high flexibility ! ... but, rarely employed ! (slower and less flexible constrained EMs are often employed).

Overfitting by Unconstrained EM Overfitting by Unconstrained EM

similar!

discontinuity “gap”

similar!

Purpose and Key Idea Purpose and Key Idea

Purpose Revive unconstrained EM by relaxing the overfitting problem Key Idea Detect overfitting as the deviation from eigen-deformations

eigen-deform. not eigen-deform.

Two Tasks Two Tasks

How to estimate eigen-deformations ? How to use the eigen-deformations in recognition process to detect

Estimation of Eigen Estimation of Eigen-

Deformations

training patterns reference collection of displacement fields using unconstrained EM

…

Principal Component Analysis

eigen-deformations

Estimated 1 Estimated 1st

st Eigen

Eigen-

Deformations

「 Ａ 」 「 Ｂ 」 「 Ｃ 」

(reference) apply positively apply negatively

Recognition Using Eigen Recognition Using Eigen-

Deformations

image distance +

min dist. discrimination reference input

…

eigen-deform. of “A” Mahalanobis distance

Recognition Rates Recognition Rates

99.07

9 2 9 4 9 6 9 8 1

1 2 3 4 5

maximum displacement (pixels) recognition rate (%)

for 500samples/category

with eigen-deform. (proposed) without eigen-deform. (conventional)

degradation due to overfitting

Unconstrained vs. Constrained (1) Unconstrained vs. Constrained (1)

. 1 1 1 1 1

1 2 3 4 5

maximum displacement (pixels) computation time (ms)

unconstrained constrained

Unconstrained vs. Constrained (2) Unconstrained vs. Constrained (2)

99.43% 99.12% constrained 99.07% 98.35% unconstrained with eigen-deform. without eigen-deform.

Unconstrained EM (fast) is comparable to constrained EM (slow) in recognition rate when eigen-deformations are used

Conclusion Conclusion

Practical recognition method based on unconstrained EM Eigen-deformations to suppress

Experimental results enough to encourage the revival of unconstrained EM

Mahalanobis Distance Mahalanobis Distance

M

Σ

m=1

λ

c,m

1

〈 v- v , u 〉

c,m c

v : displacement field to be evaluated

c : class (“A”, “B”, ..) of reference

uc,m: m-th eigen-deformation of class c

λc,m: contribution (eigenvalue) of uc,m

Piecewise Linear Unconstrained EM Piecewise Linear Unconstrained EM

input reference linear interpolation variable fixed

the mapping of each column is optimized INDEPENDENTLY

Probable Overfitting Probable Overfitting

cross (fold over) gap (skip)

Data Data

English capital letters from ETL6 (1100 samples / category) preprocessing

(size normalization, blurring, histogram equalization…) #101-600 average #601-1100 #1-100

reference training patterns test patterns

Misrecognitions Reduced by Present Method Misrecognitions Reduced by Present Method “L” “U” “F” “P” “N” “M” misrecognition due to “gap”

「Ａ」「Ｂ」「Ｃ」