Viewpoint Selection Viewpoint Selection Based on Fechner Based on Fechner Type Information Type Information Quantities for 3D Quantities for 3D

ObjectsObjects††

S.Oba††

T.Ikai††

S.Aoki T.Yamashita††††

††M.Izumi K.Fukunaga

††††

††

†† Osaka Prefecture UniversityOsaka Prefecture University

Panasonic Mobile & System Engineering Panasonic Mobile & System Engineering Co. , Ltd.Co. , Ltd.

Related WorkRelated Work

Previous study Shannon Entropy

Mathematical approach

Algorithms for selecting good view Viewpoint EntropyViewpoint Entropy )(zH

)(

)(log)(

)()(

)(2 zA

tA

zA

tAzH

zTt

Assumption of good viewLargeness of number of visible faces

Uniformity of each visible face

)(zT : all visible face from a viewpoint t : face

)(tA : visible area of face t

)(

)()(zTt

tAzA

where

Basic idea of our approachBasic idea of our approach

Characteristics Psychophysical approach

Selecting a representative view

Fechner lawFechner law

Candidate of good view for user

Polyhedral object Triangular Mesh of curved object

Representative view

Unrepresentative view

Assumptions Representative view in which

amount of visible areas is large

amount of changes of curvature is large

Fechner type information quantityFechner type information quantity

Fechner type information quantity

1log2

qI

: physical quantity

: design parameter

q

Psychophysical law

Fechner lawThe relationship between stimulus

and sensory response is logarithmiclogarithmic

brightnebrightnessss

e.g.

e.g.

human

02logQ

QR : sensory response

: stimulus amount

RQ

lower limit of stimulus amount

0Q

Fechner law

:

Face Type Shape Information QuantityFace Type Shape Information Quantity

Information of one face

Shape information quantity

provides information of one of faces

implies face information of 3D object in the brain

Face type shape information quantity

1log2

ff

SI

physical quantity

2S3S1S

area

q S area = light stimulus amount

Viewpoint information quantityviewpoint information

quantityInformation of

total visible faces

Face Type Viewpoint Information QuantityFace Type Viewpoint Information Quantity

receivesreceives

)(2 1

)(log),()),((cos)(

zTt f

tSztztgz

)0(0)(

)1(1)(

xxg

xxg

step function

step function

Viewpoint hemisphereViewpoint hemisphere

where Face type viewpoint information quantity

viewpoint

Edge Type Shape Information QuantityEdge Type Shape Information Quantity

12 cos

loge

e

LI

Edge type shape information quantity

Relationship between viewpoint and edge line

visible face

invisible face

II

Ivisible face

visible face

L : length of edge

: extended curvature

viewpointviewpoint

ZZ

Edge Type Viewpoint Information QuantityEdge Type Viewpoint Information Quantity

Edge Edge II type viewpoint information quantity type viewpoint information quantity

)(

)),('(cos)),((cos)(zUu

I zugzugz

1)(cos

)(log),(cos 2 u

uLzu

e

visible face

visible face

I

: all visible edge from a viewpoint

)(zU

normal vector

normal vector

Z' extended

vectorZ

Edge Type Viewpoint Information QuantityEdge Type Viewpoint Information Quantity

visible face

invisible face

II

Edge Edge IIII type viewpoint information quantity type viewpoint information quantity

)(

),(cos)),((cos{2

1)(

zUuII zuzugz

1)(cos

)(log)},('cos)),('(cos 2 u

uLzuzug

e

normal vector

normal vector

Z' : all visible edge from a viewpoint

)(zUZ

Experimental Result ( Polyhedral object )Experimental Result ( Polyhedral object )

min

max

EntropyEntropy

We show results of Face , Edge I , Edge II , and Entropy

Representative view

Unrepresentative view

Edge IEdge I Edge IIEdge IIFaceFace

Experimental Result ( Curved Object )Experimental Result ( Curved Object )

FaceFace Edge IEdge I Edge IIEdge II EntropyEntropy

We show results of Face , Edge I , Edge II , and Entropy

min

maxRepresentative view

Unrepresentative view

A novel approach for viewpoint selection

ConclusionsConclusions

Future workMore More discussionsdiscussions on the difference among algorithms on the difference among algorithms

• Fechner type information quantity

• Shape information quantities

• Viewpoint information quantities

Selecting representative views which have local maximum values of each viewpoint information quantity.

Fechner law

Face typeEdge type

Face typeEdge typeEdge type

III