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

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

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

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]

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

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 www.visitmoscow.co.uk

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 www.phosphorart.com/multimap-abbey-road/

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

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

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

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

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

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

Preview Lisbon

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

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

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

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

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

Results Default zoom level Zoomed-in view

Results Prague

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

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

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]

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

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]

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

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

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

Framework Applications Non-uniform grid Optimization

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

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

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

Framework Applications Non-uniform grid Optimization

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

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]

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

Framework Applications Non-uniform grid Optimization

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]

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

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

Application: Destination Maps Result

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

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

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

Application: Mental Maps Result

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]

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

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

Application: Focus Region Maps Result

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

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

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.

Questions, Comments?

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

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

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

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]

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

Vienna

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.

Results: User Study

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

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

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

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)

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

Overlap Control Shrinking Boundaries

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

- 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

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]

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

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

Non-uniform Grid Smoothing Overlap Control Non-uniform Grid Smoothing

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

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

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