1 stella x. yu 1,2 jianbo shi 1 robotics institute 1 carnegie mellon university center for the...
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Stella X. Yu 1,2 Jianbo Shi 1
Robotics Institute1
Carnegie Mellon UniversityCenter for the Neural Basis of Cognition2
Understanding Popout through Repulsion
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Questions to Be Asked
When can popout be perceived? What grouping factors are needed to bring about popout?
What grouping criteria can capture most popout phenomena?
What is popout?
finding patterns finding outliers
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Observation: Popout by Feature Similarity
Similarity grouping assumes that groups are characterized by unique features which are homogeneous across members. Segmentation is then a feature discrimination problem between different regions.
Feature discrimination only works when the similarity of features within areas confounds with the dissimilarity between areas, illustrated in the above examples of region segmentation, contour grouping and popout.
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Observation: Popout by Feature Contrast
When feature similarity within a group and feature dissimilarity between groups are teased apart, the two aspects of grouping, association and segregation, can contribute independently to perceptual organization.
In particular, local feature contrast plays an active role in binding even dissimilar elements together.
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ContextualGrouping
Model: Popout as Contextual Grouping
Attraction measures the degree of feature similarity. It is used to associate members within groups.
Repulsion measures the degree of feature dissimilarity. It is used to segregate members belonging to different groups.
Contextual grouping consists of dual procedures of association and segregation, with coherence detection and salience detection at the two extremes of the spectrum.
association segregation
RepulsionAttraction
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Representation: Relational Graphs
G=(V, E, A, R) V: each node denotes a pixel E: each edge denotes a pixel-pixel relationship A: each weight measures pairwise similarity R: each weight measures pairwise dissimilarity
Segmentation = node partitioning break V into disjoint sets V1 , V2
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Criteria: Dual Goals on Dual Measures
Maximize within-region attraction and between-region repulsion Minimize between-region attraction and within-region repulsion
Cut-off attraction is the separation cost Cut-off repulsion is the separation gain
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Criteria: Why Repulsion Help Popout?
Cost-1 – Gain-1 + Cost-2 – Gain-2 < min ( Cost-1 – Gain-1 + Gain-2, Cost-2 – Gain-2 + Gain-1)
Repulsion unites elements who have common enemies
Cut-1
Cut-2
Cut-1
Cut-2
Cost-1 + Cost-2 > min (Cost-1, Cost-2)
Attraction unites elements who have common friends
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Model: Energy Function Formulation
Group indicators
l
ll Vu
VuuX
,0
,1)(
Weight matrix
Energy function as a Rayleigh quotient
ADD RD
)deg(
)deg(,)1( 1
21 V
VXXy Change of variables
Degree matrix
Eigenvector as solutionyDyWDyy
WyyT
T
1max
Dyy
Wyy
DXX
WXXXXNassoc
T
T
t tTt
tTt
2
121 ),(
RDRAW RDR
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Interpretation: Eigenvector as a Solution
The derivation holds so long as 121 XX
If y is well separated, then two groups are well defined; otherwise, the separation is ambiguous
The eigenvector solution is a linear transformation, scaled and offset version of the probabilistic membership indicator for one group.
121)1( XXXy
stimulusSolution y
well separatedSolution yambiguous
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Interaction: from Gaussian to Mexican Hat
Repulsion
Attraction
2
2
12
1
2
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jiji ffff
ij eeW
2
2
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)(
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ji ff
e
Attraction
RDRAW RDR
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Regularization
)( WWW
A R
),( DDW R
RA
),( DDW R D D2
)()( WWW
Regularization does not depend on the particular form of .
Only D matters. To avoid bias, we choose D = I.
Regularization equalizes two partitions by:Decrease the relative importance of large attractionDecrease the relative importance of large repulsion
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Results: Popout
Stimuli Attraction +Repulsion+Regularization
Attraction to bind similar elements
Repulsion to bind dissimilar elements
Regularization to equalize
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When Can a Figure Popout
x : figure-figure connection y : figure-ground connection z : ground-ground connection Attraction: x , y , z >0 Repulsion: x , y , z <0 Coherent: attraction within a group Incoherent: repulsion within a group
Question 1: What are the feasible sets of (x,y,z) so that figure-ground can be separated as is ?
Question 2: How do the feasible sets change with the degree of regularization D = I?
x: f-f y: f-g
z: g-g
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Conditions for Popout: Normalized Cuts
Scale on x,y,z does not change the grouping results Linear or quadratic bounds on x-y
,0,,21
0,8
7,,
2
1,
8
7,1,,87
2
1,1,
2
821,21
1,,,7
811,,
2
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1
2
,1,,87,1,,2
1,0,,7
81,0max1,0,,
1
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0,,,210,,,9211
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yyx
yxyx
yyxyyy
yyxz
yy
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yy
xyy
yxz
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BackgroundSimilar
BackgroundDissimilar
No regularization Infinite regularization
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Conditions for Popout: Normalized Cuts
Repulsion(blue) greatly expands feasible regions. Regularization helps especially when within-group connection is weak.
z = 1Background
Similar
z = -1BackgroundDissimilar
No regularization Infinite regularizationRegularization = 1
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Comparison of Grouping Criteria
1,,,5.0,,,21
1,,,5.0,,,21
Cuts AverageCutsMin
yyxyyxz
yyxyyxz
Repulsion helps as well Invariance to regularization Linear bounds on x-y Narrower than Normalized Cuts
z = 1Background
Similar
Min Cuts
z = -1BackgroundDissimilar
Average Cuts Normalized Cuts
No regularizationInfinite regularization
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Results: Popout in Coherent Background
o+o+
o+
o+
o+
o+
Solution w/Attraction
Solution w/Repulsion
Stimuli
marked on Feasibility map“o”: Attraction“+”: Repulsion
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Solution withRegularizedRepulsion
Solution withRegularizedAttraction
Results: Popout in Random Background
= 0 per w = 0.05 per w = 0 per w = 0.05 per w
+
stimulus
+
No grouping w/o regularization. Repulsion helps as well. Insensitive to the degree of regularization.
o o
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Results: Popout in Random Background
Solution withRegularizedRepulsion
Solution withRegularizedAttraction
= 0 per w = 0.05 per w = 0 per w = 0.05 per w
stimulus
No grouping w/o regularization. Repulsion helps as well. Insensitive to the degree of regularization.
+ +
o o
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Results: Computational Efficiency
30 x 30 Image A: r = 1 A: r = 3 A: r = 5 A: r = 7 [A, R]: r = 1
If only attraction is allowed, much larger neighbourhood radius is needed to bring similar subregions together. When subregions are dissimilar, increasing radius does not help attraction to bring them together.
Solutions with Attraction with Repulsion
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Conclusions
Advantages of repulsion
Complementary: regularization Computational efficiency
Pairwise relationships
Attraction: similarity grouping Repulsion: dissimilarity grouping
Figure-ground organization
Coherent ground Incoherent ground
Coherent figure Attraction +Regularization
Incoherent figure +Repulsion