Importance-Driven Focus of Attention and Meister Eduard Gröller 1 1 Vienna University of...
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Importance-Driven Focus of Attention and Meister Eduard Gröller 1 1 Vienna University of Technology, Austria 2 University of Girona, Spain 3 University of Bergen, Norway Ivan Viola 1,3 , Miquel Feixas 2 , Mateu Sbert 2
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Transcript of Importance-Driven Focus of Attention and Meister Eduard Gröller 1 1 Vienna University of...
Importance-DrivenFocus of Attention
and Meister Eduard Gröller1
1 Vienna University of Technology, Austria
2 University of Girona, Spain
3 University of Bergen, Norway
Ivan Viola1,3, Miquel Feixas2, Mateu Sbert2
Ivan Viola 2
Goal
Input: known and classified volumetric data
High level request: show me object X
Output: guided navigation to object X
Ivan Viola 3
Focusing Considerations
Characteristic view
Emphasis of focus object
Guided navigation between characteristic views
Ivan Viola 4
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
char
acte
ristic
vie
wpo
int e
stim
atio
nin
tera
ctiv
e fo
cus
of a
ttent
ion
Framework
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
char
acte
ristic
vie
wpo
int e
stim
atio
nin
tera
ctiv
e fo
cus
of a
ttent
ion
Ivan Viola 5
Characteristic Views
OverviewAll objects are visible
Visibility of objects is balanced
Characteristic view of focus objectHigh visibility for focus object
If possible other objects also visible
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Ivan Viola 6
Characteristic View Estimation
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
I(vi,O) = p(o j|vi) log∑j
mp(o j|vi)p(oj)
...
...
information-theoretic framework for optimal viewpoint estimation
o2
object selection by user
v
o1
o2
o3
object-space distance weight
o2
up-vector information
cha
ract
eri
stic
vie
wp
oin
t est
ima
tion
view rating
Ivan Viola 7
View rating
v1
v2
v3
v4
v5
v6
v7
v8 o1
o2
o3
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
For every view For every object
Ivan Viola 8
View Rating
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
VisibilityHigh
Low
Location in imageIn image center
Outside center
Distance to the viewerObject close to the viewer
Far from the viewer
Ivan Viola 9
r
r0 r1 r2
o1
o
Visibility Computation
α(o0,r2)
αr
α(o1,r1)
α(o0,r0)
α(o
),( 1 rov )),(1( 00 ro ),(. 11 ro),( 0 rov ),( 00 ro
),(. 20 ro))),(),((1( 100 rovro
o0 = object 0 o1 = object 1r = rayr0 = sub-ray 0 r1 = sub-ray 1 r2 = sub-ray 2
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Ivan Viola 10
Visibility Computation
x
xrovov ),()( 11
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Ivan Viola 11
View Rating Weights
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
object-space distance weight
image-space weight
Ivan Viola 12
Characteristic Viewpoint Estimation
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
I(vi,O) = p(o j|vi) log∑j
mp(o j|vi)p(oj)
...
...
information-theoretic framework for optimal viewpoint estimation
o2
object selection by user
v
o1
o2
o3
object-space distance weight
o2
up-vector information
cha
ract
eri
stic
vie
wp
oin
t est
ima
tion
view rating
characteristic views
Ivan Viola 13
Characteristic Views
OverviewAll objects are visible
Visibility of objects is balanced
Characteristic view of focus objectHigh view rating (visibility) for focus object
If possible other objects also visible
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Ivan Viola 14
Obtaining Characteristic Views
Sets of views and objects are random variables
Views V=(v1, v2, v3, ... , vn)
Objects O=(o1, o2, o3, ... , om)
View rating (visibility, weights)Information channel between V→O
Conditional probability p(oj|vi)
Mutual information between V and O expresses degree of dependance
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Ivan Viola 15
Obtaining Characteristic Views
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Viewpoint mutual information is dependance between vi and O
High values = high dependance Small number of objects
Low average visibility
Low values = low dependance Maximum objects visible
Object visibility is balanced
Minimal VMI determines the best view
Ivan Viola 16
Probability Transition Matrix
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
p(v1)
p(v2)
p(v3)
...
p(vn)
p(o1) p(o2) p(o3) p(om)...
p(o1|v1) p(o2|v1)
p(o1|v2)
...
...
p(om|vn)...
...
p(om|v1)
p(o1|vn)
probability of the viewpoint
marginal probability of the object
view rating of object oj from viewpoint vi
Ivan Viola 17
Viewpoint Mutual Information
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Degree of correlation vj↔O
j j
ijiji op
vopvopOvI
)(
)|(log)|(),(
p(v1)
p(v2)
p(v3)
...
p(vn)
p(o1) p(o2) p(o3) p(om)...
p(o1|v1) p(o2|v1)
p(o1|v2)
...
...
p(om|vn)......
p(om|v1)
p(o1|vn)
Ivan Viola 18
Characteristic Views
OverviewAll objects are visible
Visibility of objects is balanced
Characteristic view at focus objectHigh view rating for focus object
If possible other objects also visible
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Ivan Viola 19
Incorporating Importance
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
j j
ijiji op
vopvopOvI
)(
)|(log)|(),(
j
kkk
jj
ijiji
oimop
oimop
vopvopOvI
)()(
)()(
)|(log)|(),(
importance distribution
o1 o2 o3
Ivan Viola 20
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Resulting Characteristic Viewpoints
Ivan Viola 21
inte
ract
ive
focu
s o
f atte
ntio
n
o2 o3o1
cha
ract
eri
stic
vie
wp
oin
t est
ima
tion
importance distribution
o1
o2
o3
object selection by user
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o1
o2
o3
focus discrimination
o1
o2
o3
up-vector informationv1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
I(vi,O) = p(o j|vi) log∑j
mp(o j|vi)p(oj)
...
...
information-theoretic framework for optimal viewpoint estimation
v
o1
o2
o3
object-space distance weight
cha
ract
eri
stic
vie
wp
oin
t est
ima
tion
inte
ract
ive
focu
s o
f atte
ntio
n
importance distribution
o2
object selection by user
o2
up-vector information
o1
Interactive Focus of Attention
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Ivan Viola 22
Emphasis of Focus Object
Levels of sparseness
repr
esen
tatio
n
0importance max
denseo2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
s o
f a
tte
ntio
n
Ivan Viola 23
Emphasis of Focus Object
Cut-aways to unveil internal features
Labeling to add textual information
vessels
intestinekidneys
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
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Ivan Viola 24
Guided Navigation Between Objects
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
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vie
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t e
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Decreasing importance of Object XDe-emphasis of Object X
Change to overview
Increasing importance of Object YEmphasis of Object Y
Change to characteristic view of Y
Ivan Viola 25
Refocusing
o1 o2
o3
vc
v1 v2
o1 o2
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
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vie
wp
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t e
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Characteristicview 1
Characteristicview 2
Overview
Ivan Viola 26
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
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Example - Stagbeetle
Focus view 1
Focus view 2Overview
Ivan Viola 27
Smooth Transition to Focus View
o1 o2
o3
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
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atio
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Ivan Viola 28
Example - Human Hand
Any Questions? o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
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vie
wp
oin
t e
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Ivan Viola 29
Conclusions
Focus of attention frameworkCharacteristic view estimationGuided navigationSteered by changes in importance distribution
Future WorkZooming to the focusOther smart visibility techniquesAvailable soon as plugin in volumeshop.org
Ivan Viola 31
Viewpoint Entropy [Bordoloi et al. '05]
Viewpoint Mutual Information
Comparison to Viewpoint Entropy
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
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Ivan Viola 32
Visibility Computation
v1
v2
v3
v4
v5
v6
v7
v8
importance distribution
o1 o2 o3
o1
o2
o3
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
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t e
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For overview and all focus objectsFor every viewpoint
For every object + background
Ivan Viola 33
α(o0,r2)
αr
α(o1,r1)
α(o0,r0)
α(o
Visibility Computation for Focus Object
o0 = object 0 o1 = object 1r = rayr0 = sub-ray 0 r1 = sub-ray 1 r2 = sub-ray 2
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
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0,r2)
r
α(o1,r1)
α(o
α
Ivan Viola 34
Visibility Computation
o0 = object 0 o1 = object 1r = rayr0 = sub-ray 0 r1 = sub-ray 1 r2 = sub-ray 2
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
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α(o0,r2)
αr
α(o1,r1)
α(o0,r0)
α(o
),( 1 rov ),( 11 ro),( 0 rov ),(. 20 ro)),(1( 1 rov
Ivan Viola 35
Probability Transition Matrix
o2 o3o1
importance distribution
v1
v2
v3
o1
o2
o3
visibility estimationimage-space weight
p(v1)
p(vn)
p(o1|v1)
p(om|vn)
p(o1) p(om)
...
...
...
I(vi,O) = p(oj|vi) logΣj
m p(oj|vi)p(oj)
...
...
...
information-theoretic framework for optimal viewpoint estimation
o1
o2
o3
object selection by user
v
o1
o2
o3
object-space distance weight
o1 o2
o3
v
viewpoint transformation
v
o1
o2
o3
cut-away and level of ghosting
o3o1
o2
o3
focus discrimination
cha
ract
eri
stic
vie
wp
oin
t e
stim
atio
nin
tera
ctiv
e f
ocu
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f a
tte
ntio
n
p(v1)
p(v2)
p(v3)
...
p(vn)
p(o1) p(o2) p(o3) p(om)...
p(o1|v1)p(o2|v1)
p(o1|v2)...
...
p(om|vn)...
...
p(om|v1)
p(o1|vn)
p(v1)
p(v2)
p(v3)
...
p(vn)
p(o1) p(o2) p(o3) p(om)...
p(o1|v1)p(o2|v1)
p(o1|v2)...
...
p(om|vn)...
...
p(om|v1)
p(o1|vn)
p(v1)
p(v2)
p(v3)
...
p(vn)
p(o1) p(o2) p(o3) p(om)...
p(o1|v1)p(o2|v1)
p(o1|v2)...
...
p(om|vn)...
...
p(om|v1)
p(o1|vn)
p(v1)
p(v2)
p(v3)
...
p(vn)
p(o1) p(o2) p(o3) p(om)...
p(o1|v1)p(o2|v1)
p(o1|v2)...
...
p(om|vn)...
...
p(om|v1)
p(o1|vn)
p(v1)
p(v2)
p(v3)
...
p(vn)
p(o1) p(o2) p(o3) p(om)...
p(o1|v1)p(o2|v1)
p(o1|v2)...
...
p(om|vn)...
...
p(om|v1)
p(o1|vn)
active o1
active om...
inactive
