This document introduces Information-Geometric Lenses (InfoGeoLenses) for creating multiple focus+context interfaces. InfoGeoLenses map coordinates through continuous, differentiable connection maps to integrate a focus region and its context seamlessly. Examples include the Logistic, Matsushita, and Modified Sarkar-Brown lenses. InfoGeoLenses have properties like approximating Euclidean shape near focus and allowing simple reconstruction of the original image. The document demonstrates 2D and 3D focus+context interfaces using InfoGeoLenses, such as a virtual library embedded in geometric spaces.

1. Information-Geometric Lenses for
Multiple Foci + Contexts Interfaces
Richard Nock
Frank Nielsen
CEREGMIA – UAG Sony CS Labs
France
Japan
rnock@martinique.univ-ag.fr
Frank.Nielsen@acm.org

2. Outline
F+C interfaces
Definition
Example of desirable property
InfoGeoLenses
Definition & principles
Properties
Applications
2D InfoGeoLenses
3D InfoGeoLenses

3. F+C interfaces

4. F+C Interface > Definition
Integrate a focus (magnified) region and its context in a seamless
display
Focus region
Context
(From Cockburn et al., 2007)

5. Example > Reliable perception of shapes
The Euclidean shape of a perceived disk in the F+C interface
?
Focus

6. Example > Reliable perception of shapes
The Euclidean shape of a perceived disk in the F+C interface
Sarkar-Brown ‘92
SB(0)
disk

7. Example > Reliable perception of shapes
The Euclidean shape of a perceived disk in the F+C interface
Sarkar-Brown ‘92
SB(2)
~disk

8. Example > Reliable perception of shapes
The Euclidean shape of a perceived disk in the F+C interface
Sarkar-Brown ‘92
SB(5)
disk

9. Example > Reliable perception of shapes
The Euclidean shape of a perceived disk in the F+C interface
InfoGeoLens
LOG
~disk

10. Example > Reliable perception of shapes
The Euclidean shape of a perceived disk in the F+C interface
InfoGeoLens
MAT
~disk

11. InfoGeoLenses

12. InfoGeoLenses > Definition & principles
Map each coordinate (x, y, z, …) through a “connection map”:
function
continuous,
differentiable
strictly increasing,
symmetric wrt
.
Different functions yield different InfoGeoLenses
Logistic, LOG
Matsushita, MAT
Modified Sarkar Brown, MSB
(Prop: MSB = 1st order approximation of LOG)

13. InfoGeoLenses > Definition & principles
InfoGeoLens
MSB

14. InfoGeoLenses > Definition & principles
Examples of InfoGeoLenses
MSB =
Modified Sarkar-Brown

15. InfoGeoLenses > Properties
Region near the focus is approximately Euclidean

16. InfoGeoLenses > Properties
Simple and almost lossless reconstruction of the original image
through
MSB

17. InfoGeoLenses > Properties
Simple and almost lossless reconstruction of the original image
through
Original
image
reconstructed

18. InfoGeoLenses > Properties
Simple and almost lossless reconstruction of the original image
through
MSB

19. InfoGeoLenses > Properties
Simple and almost lossless reconstruction of the original image
through
Original
image
reconstructed

20. InfoGeoLenses > Properties
Simple and almost lossless reconstruction of the original image
through
MSB

21. InfoGeoLenses > Properties
Simple and almost lossless reconstruction of the original image
through
Original
image
reconstructed

22. InfoGeoLenses > Properties
Simple construction of multiple foci+context interfaces
LOG
Voronoi
diagram

23. InfoGeoLenses > Properties
Simple construction of multiple foci+context interfaces
MAT
Voronoi
diagram

24. Applications > 2D InfoGeoLens

25. InfoGeoLenses > Demo 2D F+C interface
Virtual library (1k books) embedded in the classical
Beltrami-Klein disk, and then LOG, then MAT interface
Red dots = books; hexagons = language (English/French)

26. InfoGeoLenses > Demo 2D F+C interface

27. Applications > 3D InfoGeoLens

28. InfoGeoLenses > Demo 3D F+C interface
Virtual library (10k books) embedded in the LOG cube
Rich interaction (zoom, rotations & translations can be inside/outside)
3D representation dynamically learned from users behavior (see
Nock, Nielsen & Briys, ACM/IEEE JCDL’2013); colors = Dewey
Subjects

29. InfoGeoLenses > Demo 3D F+C interface

30. Conclusion
InfoGeoLenses inspired by Information Geometry
Definition
Example of desirable property
InfoGeoLenses useful for blending with other interfaces
Definition & principles
Properties

31. Thank you > Questions ?