viewpoint selection based on fechner type information quantities for 3d objects † s.oba † t.ikai...
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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