1. The document proposes OptWedge, an optimized visualization cue for guiding users to off-screen points of interest. 2. It develops a cognitive cost model based on how wedge shape impacts user estimation error and accounts for bias and individual differences. 3. An experiment compares user estimation accuracy for vanilla, unbiased, and biased wedge visualizations, finding optimized wedges improve accuracy for short distances.

1. OptWedge: Cognitive Optimized Guidance
toward Off-screen POIs
Shoki Miyagawa
(Mitsubishi Electric Corp.)

2. ※ POI: 2D or 3D Point-of-Interest
Guidance toward Off-screen POIs
Off-screen
POI
Display
On-screen
POI
Visualization of
Off-screen POI

3. 1. Draw human attention
to the out of view
2. Providing an additional
POI for small sized display
Applications
obstacle
destination

4. Visualization types for Off-screen POIs
[Müller+14]
1. Overview+Detail 2. Focus+Context 3. Cue-based
More space Not intuitive
Less space
Intuitive
[Miau+16]
Overview
Detailed
view
[Jo+11] [Burigat+]

5. POI
Human
Estimation
Estimation
Error
Research Question in Cue-based Visualization
Cue
To decrease an error in the users’ estimation,
1. What cue should we use?
2. How should we visualize the selected cue?

6. [Petford+19]
Comparing cues
for room-scaled
visualization vs.
Wedge Flashing Point animation
vs.
Comparing cues
for head-mounted display
[Gruenefeld+18]
vs.
Halo Wedge
Research Question in Cue-based Visualization
To decrease an error in the users’ estimation,
1. What cue should we use?
2. How should we visualize the selected cue?

7. This study uses Wedge as a cue and optimize
the shape to decrease an estimation error
Research Question in Cue-based Visualization
To decrease an error in the users’ estimation,
1. What cue should we use?
2. How should we visualize the selected cue?
• shape, color, scale, ...

8. Amodal complement enables us
to imagine the whole from the part
Wedge
POI
Display
Wedge: partially invisible
isosceles triangle
We can estimate POI
location on a invisible
vertex due to
amodal complement

9. Vanilla Wedge (VW) heuristically determined values of
shape-related parameter (𝜃, 𝑑, 𝑙)
Vanilla Wedge [Gustafson+07]
distance 𝒅
leg 𝒍
aperture 𝜽
POI
Problem
• Validity of parameter values
is unclear
• Does not consider cognitive
impact in amodal complement
• Cannot handle constraints on
displaying area

10. Our Solution: Optimization Problem
Problem
• Validity of parameter values
is unclear
• Does not consider cognitive
impact in amodal complement
• Cannot handle constraints on
displaying area
Solution
• Validity of parameter values
is clear
• Consider bias and individual
difference as cognitive impact
• Can introduce any constraint
into optimization problems
OptWedge (Optimized Wedge)
based on minimizing a cognitive cost

11. Normal distribution 𝑷
(depends on Wedge shape)
Estimated points are samples of normal distribution 𝑷(𝒃, 𝝈𝒙, 𝝈𝒚)
individual
difference 𝜎𝑥
bias 𝑏
individual
difference
σy
Proposed method
𝒙
𝒚
Estimated
point
Assumption

12. Ideal normal distribution 𝐐
(mean is on POI)
Proposed method
Normal distribution 𝑷
(depends on Wedge shape)
𝒙
𝒚
Distance from 𝑷(𝒃, 𝝈𝒙, 𝝈𝒚) to ideal normal distribution Q
Cognitive cost
e.g., Kullback-Leibler divergence

13. Proposed method
bias 𝑏
UOW (Unbiased OptWedge)
Vertex position is fixed on
POI and optimization
makes bias zero
BOW
bias 𝑏
(Biased OptWedge)
Vertex position is optimized
so as to counteract bias

14. Ex.１：Modeling cognitive cost
Ex.２：Measuring OptWedge performance
Experiment

15. • Presented 20 subjects with
375 different shapes of Wedge
• Asked subjects to estimate
POI location
• Conducted an experiment
in VR environment to reduce
a burden of input operation
10m
VR controller
ray
Ex.1: Setting

16. • The larger distance 𝑑 is,
the smaller bias 𝑏 is
• There is a trade-off error between
𝜎𝑥 and 𝜎𝑦 concerning aperture 𝜃
Ex.1: Result
𝜎𝑥
𝜎𝑥
𝜎𝑦
𝜎𝑦
𝑏 > 0
𝑏 < 0
𝑑
𝑑

17. individual difference 𝝈𝒙(𝜽, 𝒅, 𝒍)
distance 𝑑
distance 𝑑
individual difference 𝝈𝒚(𝜽, 𝒅, 𝒍)
Ex.1: Result
distance 𝑑
leg 𝑙
aperture 𝜃
bias 𝒃(𝜽, 𝒅, 𝒍)
leg 𝑙
leg 𝑙
Compared the Mean Squared Error [m2]
for polynomial regression (PR) and
Gaussian process regression (GR) models
and found GR model works better
Mean Squared Error [𝐦𝟐]
aperture 𝜃
aperture 𝜃

18. Ex.１：Modeling cognitive cost
Ex.２：Measuring OptWedge performance
Experiment

19. Ex.2 is similar to Ex.1, but..
• Showed VW/UOW/BOW
• Performed gradient descent using
VW parameter as initial point
• Considered constraints on domain
of definition and drawing area
Visualization of cognitive cost
VW
(initial point)
UOW
Constraints
𝜃[rad]
𝑙 [m]
Ex.2: Setting

20. 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1 2 3 4 5 6
W1 W2 W3
**
*
*
†
VW
UOW
BOW
**： p < 0.01
*： p < 0.05
†： p < 0.10
Distance to POI [m]
Distance to POI [m]
Ex.2: Result
Cognitive cost
Experimental value
Model prediction
UOW
BOW
VW
Mean squared error

21. 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1 2 3 4 5 6
W1 W2 W3
**
*
*
†
VW
UOW
BOW
**： p < 0.01
*： p < 0.05
†： p < 0.10
Distance to POI [m]
Experimental value
GR model prediction
UOW
BOW
VW
Cognitive cost Mean squared error
Ex.2: Result
Distance to POI [m]
UOW/BOW > VW
for short distance

22. Ex.2: Result
Cognitive cost Mean squared error
Experimental value
GR model prediction
UOW
BOW
VW
Distance to POI [m]
UOW/BOW ≒ VW
for middle distance.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1 2 3 4 5 6
W1 W2 W3
**
*
*
†
VW
UOW
BOW
**： p < 0.01
*： p < 0.05
†： p < 0.10
Distance to POI [m]

23. Our model is not accurate
for long distance
Ex.2: Result
Experimental value
GR model prediction
UOW
BOW
VW
Distance to POI [m]
Cognitive cost Mean squared error
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1 2 3 4 5 6
W1 W2 W3
**
*
*
†
VW
UOW
BOW
**： p < 0.01
*： p < 0.05
†： p < 0.10
Distance to POI [m]

24. distance VW UOW BOW
short
medium
long △
○ ○
△
△ ×
×
△ △
Q1: Why was no significant difference obtained between
VW and UOW/BOW for medium distance?
Q2: Why did the performance of BOW drop?
Ex.2: Discussion
Q1
Q2

25. Q1: Why was no significant difference obtained between VW
and UOW/BOW for medium distance?
A1: VW has high validity because an initial point is sufficient
close to an optimal point
Ex.2: Discussion
short
distance
long
distance
Initial
point
(VW)
Optimal
point(UOW)
middle
distance

26. Q2: Why did the performance of BOW drop?
A2: Model generalization performance degrades because of
a lack of data around long distance 𝑑.
distance 𝑑
leg 𝑙
aperture 𝜃
bias 𝒃 individual difference 𝝈𝒙
distance 𝑑
leg 𝑙
aperture 𝜃
distance 𝑑
leg 𝑙
aperture 𝜃
individual difference 𝝈𝒚
Ex.2: Discussion

27. We proposed OptWedge based on minimizing a cognitive cost
and designed two kinds of OptWedge including UOW/BOW
From two experiments, we can see that
• OptWedge is more effective for short distance
• Vanilla Wedge has a high validity for middle distance
• Model generalization performance degrades
for long distance (⇒ Future work)
Conclusion

29. Application for other cues
POI
聴収者
POI
POI
time
Circle
POI
透明度
POI
3D figure
Sound
Animation

30. VW
UOW
BOW
• Aperture get bigger as
distance increases for
UOW and BOW
• For BOW, model reflect a
trend that “human
underestimate a distance
to the POI”
Ex.2: Result

31. 11度：5.83cm
35度：21cm
7.15[cm]
14.67
[cm]
Long
Medium
Short
iPhone12
For the out of view
• Short : ~11°
• Medium : ~35°
• Long : 35°~
Generalizability

32. Overview+Detail
Mini-map World In Miniature (WIM)[27] Personalized Compass[28]

33. Focus+Context
Aroundplot[6]
Bird’s eye[2]
InfoRadar[1]
EyeSeeX[5]
3D
Radar[4]
EdgeRadar[3]
2D 3D

34. Halo[8] Wedge[9] ScaledArrow,
Stretched Arrow[10]
HaloDot[12]
Sparkle(LED)[11]
Cue (2D direction + distance)

35. 3D Arrow[2]
SidebARs[17]
周辺視野に矢印などの
アイコン[14]
Circle[15]
Sphere Halo, Sphere Wedge[19]
周辺視野にLED[16,18]
Bubble Bee[13]
FlyingARrow[23]
Cue (3D direction only)

36. 3D Halo, Circle Halo,
Billboard Halo[22]
Composite Wedge, Vector Boxes, Eyelight[20]
Plane Halo, Plane Wedge, PlaneArrow[21]
Wall Wedge, Flashing, Dynamic Point[4]
Cue (3D direction + distance)