L10- Map labeling algorithms
L10 – Map labeling algorithms
NGEN06(TEK230) –
Algorithms in Geographical Information Systems
by: Sadegh Jamali (source: Lecture notes in GIS, Lars Harrie)
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L10- Map labeling algorithms
Background
• Labels are an essential aspect of maps.
For example, on maps for mobile applications, it is
necessary to label roads, landmarks, and …. to help
users understand their location and the environment.
• The labels should be easy to read and should follow
basic cartographic rules.
• The cartographic rules are analytically defined and
implemented in computer programs.
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L10- Map labeling algorithms
Aim
 to provide some basics of algorithms for
automated map labelling.
Content
1. Basic cartography theory
2. Label placement by combinatorial optimization
3. Label placement by slider model
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L10- Map labeling algorithms
1. Basic cartography theory
Generally, there are two things
that are important for labels:
• proper font type and size
• good position.
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L10- Map labeling algorithms
Font type and size
Figure. The two main font families (From Jenny et al. 2008).
Example of Sans Serif family: Verdena and Frutiger
Font size: at least 12 points.
Note: to distinguish between different label types, you could use
wide letter spacing, varying font size and bold/italic style.
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L10- Map labeling algorithms
Label position
To be good positioned, the labels should:
1) not overlap
2) not obscure other map objects
3) placed in a good position relative to the referent.
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L10- Map labeling algorithms
Preferred positions for point labels
Slocum et al. (2005)
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L10- Map labeling algorithms
Preferred positions for line labels
Slocum et al. (2005)
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L10- Map labeling algorithms
Preferred positions for area labels
Slocum et al. (2005)
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L10- Map labeling algorithms
2. Label placement by combinatorial
optimization
Label placement can be defined as a
combinatorial optimization problem.
To find the optimal combination of placement a
cost function (f) is created.
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L10- Map labeling algorithms
Cost function
The best solution: the solution with the smallest cost.
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L10- Map labeling algorithms
Challenge!
But the search space is LARGE!
For example, for n point labels with 6 possible placement
of each label, the possible number of combinations is 𝟔𝒏 .
This is not a feasible approach even for small numbers
of labels.
So how to find the best possible solution?
we can adopt an iterative improvement
algorithm.
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L10- Map labeling algorithms
Iterative improvement algorithm
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can be illustrated as a search process
on the surface of a landscape
each position = a specific configuration,
i.e., a solution, with an elevation
representing the “cost” of the solution
moves around to find the lowest
position on the landscape
can be realized by a slope descending
algorithm
slope descending may be terminated at
local lowest positions
simulated annealing allows moving towards both lower (better) and
upper (worse) neighboring positions, where a worse position is
accepted with a probability decreasing over time
the probability is controlled by a parameter denoted as temperature,
which decreases over time and thus forms a number of temperature
stages
by accepting worse positions with a decreasing probability, simulated
annealing may escape from a local optimal position and reach the
global optimal position (Russell and Norvig 1995).
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L10- Map labeling algorithms
Combinatorial optimization schema
1) Labels are initially placed at the position with best
placement properties.
2) Create a cost function to reflect cartographic
requirements and aesthetic principles.
3) Start an optimization using the simulated annealing
schema. For each iteration a label is randomly selected.
4) Run the process until a minimum of the cost function
is found.
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L10- Map labeling algorithms
3. Label placement by slider model
In the combinatorial optimization: a fixed number of positions
are allowed.
Slider model: much more positions are allowed (leads to
enhanced cartographic quality of the labels).
Constraints:
1) labels should be legible
2) each label should be properly associated to the
feature that it describes (i.e. feature and its label
are not separated).
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L10- Map labeling algorithms
Slider Model (Zhang and Harrie(2006a,b))
Phases:
1) all possible positions for the label are computed.
2) the candidate positions are reduced according
to conflict detection.
3) finally a position is selected from the reduced
candidate set to label the feature.
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L10- Map labeling algorithms
Slider Model: point labeling algorithm
Input data: a point set (to be labeled) and
other feature classes (acting as obstacles)
Algorithm workflow:
1. Select a point sequentially from the point set, and
create four rectangular boxes around the point (“range
boxes”).
Figure: (a) The top range box of a point feature.
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L10- Map labeling algorithms
The workflow:
2. Select the range boxes of a point feature sequentially, and
search for the obstacles in conflict with this box.
3. For each conflicting obstacle, compute the intersection
between the obstacle and the range box. If any intersection
exists, reduce the range box using the intersection.
Figure: (b) The reduced range boxes (left
and bottom) of a point feature in conflict
with a line feature.
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L10- Map labeling algorithms
Reduction of a range box:
depends on the location and size of the intersection
between the range box and the obstacle.
Suppose the point 𝑷(𝒙𝒑 , 𝒚𝒑 ) is to be labelled, and a range
box RB is attached to the point P
If there is an object O (label or cartographic feature) that overlaps
the range box RB, then the intersection I has the properties:
where MBR is the minimum bounding box function.
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L10- Map labeling algorithms
Then the range box RB will be reduced to a new range box RBnew
as follows (if it is a top or bottom range boxes; left and right range
boxes are treated similarly):
Figure: Reduce a range box in conflict with an obstacle
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L10- Map labeling algorithms
The workflow:
4. select a position to place the label inside the reduced range
box according to position preference.
5. Go back to step 1) to deal with the next point’s labelling.
The computational complexity: O (nk+nm)
Step 2): O (nk)
n: the number of point features to be labeled
k: the number of obstacles
Step 3): O (nm)
m: the average number of conflicting obstacles for each point to be labeled
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L10- Map labeling algorithms
Slider Model: line labeling algorithm
Steps:
1) search for all the long line segments along a
line as candidate positions.
2) Candidate positions along each segment are
reduced to a part of the original positions,
without conflict to any obstacles.
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L10- Map labeling algorithms
Input data: a line set (to be labeled) and several feature classes
(acting as obstacles)
Algorithm workflow:
1. Select a line sequentially, and create its generalized version
using the Douglas-Peucker algorithm.
2. Search for segments long enough for label placement.
3. Search for the longest segment.
4. Create a range box with orientation along the longest segment.
5. Search for obstacles in conflict with the range box, and shrink
the range box according to conflict detection.
6. If the reduced range box is long enough, then reduce its size to
the size of corresponding label text, shrinking its two sides
towards the centroid. Otherwise, search for the second longest
segment, then go back to step 4) to find a labelling position for
the line.
7. Go back to step 1) to deal with the next line’s labelling.
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L10- Map labeling algorithms
The computational complexity: O (nk+nm)
n: the number of line features to be labeled
k: the number of obstacles
m: the average number of conflicting obstacles for
each line to be labeled.
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L10- Map labeling algorithms
A case study
Figure: Labels placed automatically by the slider
method (source: National Land Survey of Finland)
Note: only one label is created for each road feature. So the
routine for merging the road segments was successful in this
case study.
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