1. Adaptive Grids towards Interactive Tourist Map Deformation
Ph.D. Defense
Pio Claudio
Adviser: Prof. Sungeui Yoon

2. Outline Introduction Approach Summary and Future Work Tourist Maps
Metro Transit-Centric Visualization for City Tour Planning
A Content-Aware Non-Uniform Grid for Fast Map Deformation
Summary and Future Work

3. Tourist Maps Close-up maps Overview map POI annotations
Points-of-Interest
(POI) list
Metro map
Streets
visitseoul.net

4. Tourist Map Functions Map Information Route Planning POI Discovery
Are tourists satisfied with the map at hand?
[Yan and Lee; Current Issues in Tourism 2015]

5. Tourist Map Functions Map Information
Route Planning
POI Discovery
Tourist Map Functions Map Information
Provide essential information (digestible)
Highlight significant elements
Remove clutter
eng.bigbustours.com/paris/route-map.html

6. Tourist Map Functions POI Discovery
Map Information
Route Planning
POI Discovery
Tourist Map Functions POI Discovery
Show POI locations
Updated POI information (online)
Major POI are larger
Minor POI are smaller

7. Tourist Map Functions Route Planning
Map Information
Route Planning
POI Discovery
Tourist Map Functions Route Planning
Schematic layout of routes (octilinear)
Memorable route representations
How to reach POIs from route

8. Tourist Maps: Going Digital
Rise of mobile services and social media applications
Personalization
Updated information
Interactivity

9. Research Statement
Given an original map layout and a task, optimize the deformation of topological networks for task-based optimal viewing
In this thesis, case is focused on optimizing tourist map layouts

10. Map Information
Route Planning
POI Discovery
Contributions
Propose a holistic, dynamic interactive map application combining the three functions
Metro Transit-Centric Visualization for City Tour Planning
Enable scalable transitions for changing functional map views through fast grid deformations
A Content-Aware Non-Uniform Grid for Fast Map Deformation

11. Outline Introduction Approach Summary and Future Work Tourist Maps
Metro Transit-Centric Visualization for City Tour Planning
A Content-Aware Non-Uniform Grid for Fast Map Deformation
Summary and Future Work

12. Metro Transit-Centric Visualization for City Tour Planning
Presented at EuroVis 2014
Computer Graphics Forum 2014

13. Goal Holistic visualization technique
Provides digestible info
POI discovery along metro map
Effective route planning from octilinear metro layout
Dynamic and interactive map application

14. Preview Lisbon

15. INPUT: Tourist Destinations
Approach
Destinations Summary
Map Warping
INPUT: Tourist Destinations
INPUT: Metro Map
Octilinear Layout

16. Hierarchical Clustering
Framework
Trip Websites
POI Data
Octilinear Layout
Map Warping
Visual Worth
Run-time Map
Hierarchical Clustering

17. Determining Significant Regions: Visual Worth
Kernel Density Estimation
POI position
POI rank (rank r)
POI proximity to metro- stations (proximity ρ)
: POI
Visual Worth
high
low

18. Octilinear Layout Computation
Mixed-Integer Programming [Nöllenburg et al. 2011]
Apply variable edge lengths according to visual worth
- more space to significant regions
Input
Uniform
Octilinear
Variable 18

19. Hierarchical Clustering
Framework
Trip Websites
POI Data
Octilinear Layout
Map Warping
Visual Worth
Run-time Map
Hierarchical Clustering

20. Results
Default zoom level
Zoomed-in view

21. Results Prague

22. Outline Introduction Approach Summary and Future Work Tourist Maps
Metro Transit-Centric Visualization for City Tour Planning
A Content-Aware Non-Uniform Grid for Fast Map Deformation
Summary and Future Work

23. A Content-Aware Non-Uniform Grid for Fast Map Deformation
Work under submission

24. Personalizing maps [Ballatore et al. Communications of the ACM 2015]
Map Personalization
Web & mobile services customized to each user
Web maps
different tasks, different maps
Apply deformation to create (transitions for interactive) maps
“Map morphing”
Personalizing maps [Ballatore et al. Communications of the ACM 2015]

25. Map Morphing Examples Tourist map ↔ Metro map
Map morphing: making sense of incongruent maps. [Reilly et al. GI 04]

26. Map Morphing Examples Street map ↔ Metro map
Original Map (zoomed-in)
Warped Map (zoomed-out)
Map warping for the annotation of metro maps [Bottger et al. CG&A 08]

27. State-of-the-Art Optimization of Maps (1/2)
Drawing Road Networks with Focus Regions [Haunert et al. TVCG 11]
Deform roads by optimization
Road edges as input
𝛿= 𝐸 𝑖 ′ − 𝑇 𝑖 𝐸 𝑖 2
More
Edge count
Less
Slower
Speed
Faster

28. State-of-the-Art Optimization of Maps (2/2)
Drawing Road Networks with Mental Maps [Lin et al. TVCG 14]
Overlaid uniform grid used as medium to deform roads
Instead of road edges, grid edges are input
𝛿= 𝐸 𝑖 ′ − 𝑇 𝑖 𝐸 𝑖 2
Finer
Subdivision
Coarser
More
Edge count
Less
Slower
Speed
Faster
Higher
Accuracy
Lower

29. Contributions Adaptive grid for fast deforming maps for varying tasks
Introduce support edges to preserve quad shapes
Implement optimization method in GPU
Demonstrate in different applications

30. Framework
Applications
Non-uniform grid
Optimization

31. Non-uniform Grid Benefit Challenge Adaptive subdivision
Consider significant areas
Less quads, less edges = faster performance
Challenge
Cracks may not preserve quad shapes
cracks

32. Non-uniform Grid Address Cracks - Support Edges
Regularize grid
Quad level of neighbors have at most difference of 1
Support edges
Quads with smaller neighbors are triangulated
cracks
support edges

33. Non-uniform Grid Address Cracks - Support Edges
Non-uniform grid w/o support edges
Non-uniform grid w/ support edges

34. Framework
Applications
Non-uniform grid
Optimization

35. Optimization Objective Formulation
Similar to uniform grid deformation
Grid edges as input
Including support edges
Minimize total residue 𝛿
Solve using conjugate gradient method
Iterative, fast
𝛿= 𝐸 𝑖 ′ − 𝑇 𝑖 𝐸 𝑖 2

36. Optimization Stable Optimization
As matrix size increases, results become unstable
Apply association
𝐴 𝑇 𝐴𝑥= 𝐴 𝑇 𝑏
𝐴 𝑇 𝐴𝑥 = 𝐴 𝑇 𝑏
Original
Unstable
Stable
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain [Shewchuk]

37. Optimization GPU Implementation
Residue , Edge Count 
As residue decreases, GPU shows a slower growth rate

38. Framework
Applications
Non-uniform grid
Optimization

39. Application: Destination Maps
Maps that show a sketch of a simplified route to a destination
Automatic generation of destination maps [Kopf et al. SIGGRAPH Asia 2010]
Drawing road networks with mental maps [Lin et al. TVCG 2014]

40. Application: Destination Maps Result
20x10
40x20
80x40
Ours

41. Application: Destination Maps Result
Residue , Edge Count 
As residue decreases, ours shows a slower growth rate

42. Application: Destination Maps Result

43. Application: Mental Maps
Deform map to conform to a specified shape pattern
Drawing road networks with mental maps [Lin et al. TVCG 2014]

44. Application: Mental Maps Result
20x20
40x40
80x80
Ours

45. Application: Mental Maps Result
Residue , Edge Count 
As residue decreases, ours shows a slower growth rate

46. Application: Mental Maps Result

47. Application: Focus Region Maps
Selected regions are enlarged for highlighting purposes
Drawing road networks with focus regions [Haunert et al. TVCG 2011]
Interactive focus maps using least-squares optimization[Van Dijk et al. IJGIS 2014]

48. Application: Focus Region Maps Result
Road-edge
Uniform grid
Non-uniform grid

49. Application: Focus Region Maps Result
Residue , Edge Count 
As residue decreases, ours shows a slower growth rate

50. Application: Focus Region Maps Result

51. Map Information
Route Planning
POI Discovery
Summary
Propose a holistic, dynamic interactive map application combining the three functions
Enable scalable transitions for changing functional map views through fast grid deformations
Combining these approaches in a total solution package results in an interactive, dynamic, personalized map application

52. Future Work
Integrate with smart city sensors to enable real- time information with real-time visualizations
Time-sensitive updates
Route recommendation
Gamification

53. Publications Full Papers Articles
A Content-Aware Non-Uniform Grid for Fast Map Deformation, under submission, 2016.
Metro Transit-Centric Visualization for City Tour Planning, Computer Graphics Forum, 2014.
View-Dependent Representation of Articulated Models, WSCG, 2013.
Cache-Oblivious Ray Reordering, (secondary author) ACM Transactions on Graphics, 2010.
Articles
Tourist Map Visualization, under submission, 2016.
Octilinear Layouts for Metro Map Visualization, International Conference on Big Data and Smart Computing, 2014.

54. Questions, Comments?

56. Determining Popular Regions
Focus +
Context
Graphical Fisheye Views of Graphs. Sarkar et al.
Wider spaces to popular regions
Which are popular regions?

57. Map Warping Input Warped Map
Put tourist map elements in a single map space
Map warping
Use the metro stations as control points
Solve for affine transformation parameters
Apply transformation and interpolation to original map points
Input
Warped Map

58. Hierarchical Clustering
Framework
Trip Websites
POI Data
Octilinear Layout
Map Warping
Visual Worth
Run-time Map
Hierarchical Clustering

59. Hierarchical Clustering
Displaying all tourist destinations will clutter the map
Display only relevant destinations at a given view configuration (visual worth)
Run a hierarchical clustering algorithm [Goldberger2008]

60. Runtime Map
Determine a graph cut which displays largest clusters fitting the view window
Display top N rated clusters (visual worth)

61. Vienna

62. Recent works apply evaluations like A/B testing and rating.
Spatially Efficient Design of Annotated Metro Maps [Wu et al., EuroVis13]
Drawing Road Networks with Mental Maps [Lin et al., TVCG 14]
Recent works apply evaluations like A/B testing and rating.

63. Results: User Study

64. Optimization Objective Formulation
Quad preservation objective
𝛿 0 = 𝐸 𝑖 ′ − 𝑇 𝑖𝑗 𝐸 𝑗 ′ 2
𝛿 1 = 𝐸 𝑖 ′ − 𝑇 𝑖𝑗 𝐸 𝑗 ′ 2
𝛿 2 = 𝐸 𝑖 ′ − 𝑠 𝑖 𝐸 𝑖 2
Application specific objectives
Road preservation:
Road scaling:
𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝛿= 𝑖 𝑛 𝑤 𝑖 𝛿 𝑖

65. Optimization Conjugate Gradient Method
Solves
Time complexity
𝑂 𝑚 𝑘
m: non-zero entries in A
k: condition number
In the normal equation form
𝑂 𝑚 𝑘 2 =𝑂 𝑚𝑘
𝐴𝑥=𝑏
𝐴 𝑇 𝐴𝑥= 𝐴 𝑇 𝑏

66. Overlap Control Common Approaches Shrinking Boundaries
Non-uniform Grid Smoothing
High Resolution Mesh

67. Common Approaches Overlap Control
Rewind & constrain [Van Dijk et al. IJGIS2014]
P(0)
P(1)
P(t)
Optimize
Rewind
Constrain
P(t) = (1-t)P(0)+tP(1)
!!! Modify objective matrix !!!!
Scale [Tiddeman C&G2001]
P(0)
P(1)
P(s)
Optimize
Scale
P(s) = (1-s)P(0)+sP(1)

68. Common Approaches Overlap Control
Laplacian smoothing [Lin et al. TVCG 2011]
Fast and easy to implement
Procrustes projection [Dwyer et al. GD 2009]
inverted tri X
target shape Y
X’1 X1 Y1 X0 X2 Y2 Y0
X’2
X’0
𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑖 𝑛 𝑋 𝑖 − 𝑠 𝑌 𝑖 𝑇+𝑡 2

69. Overlap Control
Shrinking Boundaries

70. Shrinking Boundaries Move to centroid Laplacian smoothing
Overlap Control
Shrinking Boundaries
Laplacian smoothing
∆ 𝑥 𝑖 = 𝑗∈ 𝑖 ∗ 𝑤 𝑖𝑗 𝑥 𝑗 − 𝑥 𝑖
𝑤 𝑖𝑗 =1/𝑣𝑎𝑙𝑒𝑛𝑐𝑒(𝑖)
Move to centroid

71. - Not good for boundary vertices
Overlap Control
Shrinking Boundaries
Laplacian smoothing
∆ 𝑥 𝑖 = 𝑗∈ 𝑖 ∗ 𝑤 𝑖𝑗 𝑥 𝑗 − 𝑥 𝑖
𝑤 𝑖𝑗 =1/𝑣𝑎𝑙𝑒𝑛𝑐𝑒(𝑖)
Move to centroid
- Not good for boundary vertices

72. Shrinking Boundaries - Fix
Overlap Control
Shrinking Boundaries - Fix
Laplacian smoothing for boundary vertices
Project Laplacian to vertex normal
∆ 𝑥 𝑖 = 𝑛 𝑖 𝑛 𝑖 𝑇 𝑗∈ 𝑖 ∗ 𝑤 𝑖𝑗 𝑥 𝑗 − 𝑥 𝑖
𝑤 𝑖𝑗 =1/𝑣𝑎𝑙𝑒𝑛𝑐𝑒(𝑖)
Linear Anisotropic Mesh Filtering [Taubin 2001]

73. Shrinking Boundaries - Fix
Overlap Control
Shrinking Boundaries - Fix
20x10
40x20
80x40

74. Non-uniform Grid Smoothing
Overlap Control
Non-uniform Grid Smoothing
T-junction vertices
Tail pulls the centroid of three neighbors
Solution: disregard tail contribution

75. Non-uniform Grid Smoothing
Overlap Control
Non-uniform Grid Smoothing

76. Overlap Control
Hi-Res Mesh
Laplacian Smoothing and Scaling methods cannot produce a solution
Try techniques to loosen overlaps and find a solution for high res mesh
Mass-spring Model

77. Hi-Res Mesh - Mass-spring Model
Overlap Control
Hi-Res Mesh - Mass-spring Model
After every iteration if there is overlap, find a relaxed solution
𝛿= 1 2 𝑘 𝑣′ 𝑗 − 𝑣′ 𝑖 − 𝑣 𝑗 − 𝑣 𝑖 2
𝑣 𝑖 = 𝑥 𝑖 , 𝑤/𝑜 𝑜𝑣𝑒𝑟𝑙𝑎𝑝 &𝑝𝑟𝑒𝑣𝑋[𝑖], 𝑤/ 𝑜𝑣𝑒𝑟𝑙𝑎𝑝

78. Hi-Res Mesh - Mass-spring Model
Overlap Control
Hi-Res Mesh - Mass-spring Model
20x20
40x40
80x80