Point Feature Label Placement Bert Spaan

Overview  Introduction  Types of point labeling problems  Good and bad labeling  Complexity of point labeling problem  Algorithms and their characteristics  Results of algorithms  Demo application

What are Point Features?  Cities, mountain tops in geographical maps  Values in plots with statistical data  Nodes in graphs

Map without labeling  Maps without labels give little information  The same holds for charts and graphs

Examples Point Feature Labeling

Why automated labeling?  Label placement contributes up to half of the time needed for producing high-quality maps 1  Cartographers place 20 to 30 labels per hour 1  For some very large technical diagrams, labeling by hand is nearly impossible 1 Cook & Jones, 1990, A Prolog rule-bases system for cartographic name placement

Example Automated Labeling

Labeling Example

Labeling graphs is easy!

Good labeling is not so easy...

Two possibilities  Label Size Maximization Maximize the size of the placed labels The labeling has to be complete  Label Number Maximization Maximize the number of placed labels Labels have fixed size  Most literature focuses on Label Number Maximization, so will this presentation

Label Quality  Basic Rules 1.The placement of labels is as unambiguous as possible. Place labels close to the point features they belong to. 2.The information of the labels is legible. No or only a few labels overlap. 3.The number of omitted labels is low.  Some label position are preferred above others

Example Basic Rule 1  Avoid ambiguity

Example Basic Rule 2  Avoid overlapping labels

Example Basic Rule 3  Avoid unlabeled points

Possible Label Positions  There are lots of ways to label point features  None of them is always the best  Good labeled maps use a mixture  We focus on iso- oriented axis-parallel rectangles

Label Position Models  iso-oriented axis-parallel rectangles  Fewer possible positions lead to Easier computability Fewer solutions  The following six position models have been extensively studied:

Four-slider Model  Label has to always touch its corresponding point feature With one of its four corners Along one of its four edges Labeltje

Preferred Label Positions  Studies have shown that people tend to prefer certain label positions in favour of others

Complexity ModelDecision problemLabel number max. problem One-positionO(n log n)NP-hard Two-positionO(n log n)NP-hard Four-positionNP-completeNP-hard One-sliderO(n log n)NP-hard Two-sliderNP-completeNP-hard Four-sliderNP-completeNP-hard

Complexity  Label maximization problem is NP-hard  A heuristical approach is needed  Not always an optimal labeling Time is important, calculating an optimal labeling can take days (or years) Leaving some point features unlabeled is not always too big a problem Human cartographers can make adjustments to algorithm output

Point feature density  The density of the point features to be labeled is important  Low density Few labels will overlap Overlaps are easily resolved Optimal solution is easy to calculate  High density A lot of labels will overlap No space for moving labels around Optimal solution is difficult to calculate

Complexity (contd.)  NP-hardness isn’t always a problem When the point feature density is not too high When number of point features is not too high  Real-world problems often meet the above criteria

Simple Labeling  Random Labeling Label points in randomly, if possible  One-position Labeling  Simple & Fast  Works fine for graphs or maps with very low density

Existing Algorithms  Hirsh An Algorithm for Automatic Placement Around Point Data 1982  Christensen, Marks & Shieber An Empirical Study of Algorithms for Point-Feature Label Placement 1995  Van Kreveld, Strijk & Wolff Point Labeling with Sliding Labels 1999  Klau & Mutzel Optimal Labeling of Point Features in Rectangular Labeling Models 2003  Ebner, Klau & Weiskircher Label Number Maximization in the Slider Model 2004

Force System  Repulsive forces between labels  Method that seeks equilibrium of minumum energy  Low eqiulibrium corresponds to pleasing labeling

Local Minima  “Force has no place where there is need of skill” – Herodotus  Force systems tend to get stuck in local minima  Optimalizations and constraints are therefore needed

Example Local Minimum Blablablabla Bloblobloblo Bleblebleble Bliblibliblibli Blublublu

Simulated Annealing  Very flexible optimization method  Analogy: annealing in metallurgy Fast cooling leaves energy in material Slow cooling leaves less energy  Accepts worse intermediate configurations  Temparature Decreases Controls how the rise and fall of energy  Probability

Computational Results  Random benchmark set From: Ebner, Klau, Weiskircher, 2005, Proc. 12th Internat. Symp. On Graph Drawing, pages

Computational Results  Random benchmark set From: Ebner, Klau, Weiskircher, 2005, Proc. 12th Internat. Symp. On Graph Drawing, pages

Computational Results  Real-world benchmark set From: Ebner, Klau, Weiskircher, 2005, Proc. 12th Internat. Symp. On Graph Drawing, pages

Computational Results  Real-world benchmark set From: Ebner, Klau, Weiskircher, 2005, Proc. 12th Internat. Symp. On Graph Drawing, pages

Output of Algorithms  Java Application Ebner, Klau & Weiskircher Implements important algorithms

Questions? ?