Nara Women’s University

Modeling the Developmental Process　 of Depth Perception of Elementary Students

　　 　　 Naoko Yoshii, Masami Takata, Kazuki Joe

Graduate School of Humanity and Science

Nara Women’s University

Nara Women’s University

Outline of presentation

IntroductionBackground and objectives 　

Short review Recognition of two dimensional images

Experiment 　Modeling 　Conclusions

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Background

H.A.Witkin: Spatial cognition → men's sense of direction is better than that of women

Infants’ depth perception

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Objectives

To make the developmental differences in depth perception

　 　 of two dimensional images between boys and girls clear.

To construct a developmental model of depth perception

of each image by gender.

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Outline of presentation

Introduction

Background and objectives

Short review

Recognition of two dimensional images

Experiment 　Modeling

Conclusions

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Short review

First stagecreation of schema

Hock ： two-stage model

・ Create schema・ Can not manipulate schema・ Create schema・ Can not manipulate schema

Second stage

・ Can manipulate and understand schema・ Can manipulate and understand schema

manipulation of schema

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Short review

Piaget : developmental stages

・ 7,8 ~ 11 years old

　 -- development of ability to manipulate

and understand schema

・ 2 ~7 years old

-- Create schema

-- No manipulation of schema

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Short review

Hock ： two-stage model Piaget

Boys Girls

We analyzed the experimental data of each image by gender.

gray scale imagesedge images

No distinctions by gender.

color images

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Outline of presentation

Introduction

Background and objectives

Short review

Recognition of two dimensional image

Experiment 　Modeling 　Conclusions

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Experiment

Depth perception of two dimensional images--edge , gray scale, color

In the order of edge, gray scale and color

85 children ( 7 – 11 years old )

The method of paired comparison・　“　 I do not understand ” 　→　 mistake・ “ They are the same ” → 　 mistake

Age

(years)

Boys Girls

7 9 9

8 10 8

9 7 10

10 12 7

11 4 9

Table 1. Object child

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Experiment

18 images : 6 photos, each one rendered 3 different ways (edge, gray scale, and color)

20 questions about the 6 photos

Images size are 89 ㎜ × 127 ㎜

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Experiment

Nara Women’s University

Experiment

Nara Women’s University

Outline of presentation

IntroductionBackground and objectives 　

Short review Recognition of two dimensional images

Experiment 　 & 　 ResultsModeling 　Conclusions

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Experiment resultsResult of each image

Boy's graph

0.7

0.75

0.8

0.85

0.9

7 8 9 10 11Age

Correctanswer rate

EdgeGrayColor

Girl's graph

0.7

0.75

0.8

0.85

0.9

7 8 9 10 11 Age

Correctanswer rate

EdgeGrayColor

Figure 6. Boy’s graph Figure 7. Girl’s graph

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Experiment results

Accuracy by image type --edge images are low, color images are high

Boys’ accuracy and girls’ accuracy

Most accurate age

9 ~ 10 year old girls rapid development

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Results & discussions

(Q2_4) “Which is farther away, this (the eaves outside the room ) or this (the glass door in room)?’’

Figure 8. The indoor image of a kindergarten school

edge of eaves outside the room

　　　　　　　　　　　　 glass door in roomCorrect answer rate of the

color image; --seven years old ; 61.11% (boys 88.89 ％， girls 33.33 ％） --eight years old ; 94.44 ％ (boys 100 ％， girls 87.50 ％）

Correct answer rate of the color image; --seven years old ; 61.11% (boys 88.89 ％， girls 33.33 ％） --eight years old ; 94.44 ％ (boys 100 ％， girls 87.50 ％）

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Experiment results

Experiment result

The differences in development The differences in development

Construction of a developmental model Construction of a developmental model

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Outline of presentation

Introduction

Background and objectives 　Short review

Recognition of two dimension images

Experiment 　Modeling 　Conclusions

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Modeling Regression equation : y=a/x+b Obtaining constant a and constant b to minimize the

following expression.

(1)

2

1

2

11

2 ˆ

n

ii

n

ii

n

ii b

x

ayyye

Partial differentiation for constants a and b

Simultaneous equation

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Edge image:Boy‘s developmental model ： ｙ＝ -1.0281 ／ｘ＋ 0.8896 　 （ 2 ）

Girl’s developmental model ： ｙ＝ -2.0460 ／ｘ＋ 1.0578 　　 （ 3 ）

Gray scale image ： Boy’s developmental model ： ｙ＝ -1.7732 ／ｘ＋ 1.0333 （ 4 ）　　 Girl’s developmental model ： ｙ＝ -1.7210 ／ｘ＋ 1.0211

（ 5 ）　　　　 　　　

Color image ： Boy’s developmental model ： ｙ＝ -1.3522 ／ｘ＋ 1.0034 （ 6 ） Girl’s developmental model ： ｙ＝ -0.8196 ／ｘ＋ 0.9297 （ 7 ）

　（ , ｘ： age, ｙ： correct answer rate ）

117 x

Modeling

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Conclusions

Our experiment results make it clear that there is a difference in the development of depth perception of two dimensional images among boys and girls.

In the near future, using the results of this research of

age and sex,we hope to develop an effective instructional

strategy for the field of education.

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That’s all for my presentation.Thank you very much.