1XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Modelling Cartographic Relations for Categorical Maps Moritz Neun and Stefan Steiniger University of Zürich, Department of Geography Swiss National Science Foundation Project: DEGEN {neun,

2XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Outline 1.Motivation 2.Introducing Relations 3.Modelling Horizontal & Vertical Relations 4.Outlook

3XXII International Cartographic Conference, A Coruña, July 9-16th, Motivation

4XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Thematic (Categorical) Maps Most research in generalization on topographic maps  majority of maps are of thematic nature (categorical, GIS, facilities, networks, POI...)  focus on thematic maps with polygons in a generic approach Examples: geology, land-use, statistics, administration

5XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Motivation Generalization should preserve the typical and emphasise specifics.

6XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Motivation Generalization should preserve the typical and emphasise specifics.

7XXII International Cartographic Conference, A Coruña, July 9-16th, Introducing Relations

8XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 What is considered as a relation?

9XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 What is considered as a relation?

10XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 What is considered as a relation?

11XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 What is considered as a relation?

12XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 What is considered as a relation?

13XXII International Cartographic Conference, A Coruña, July 9-16th, Horizontal & Vertical Relations

14XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Horizontal & Vertical Relations Horizontal relations of map objects exist within one specific scale or level of detail (LOD) and represent common structural properties. horizontal relations

15XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Relation Types topologic neighbour frequency, area statistics compactness, area size, distance orientation => meso structure? Inter-thematic structure for aggregation (are blue soil classes of same familly?) => Semantic similarity Geometry Topology Structure Statistics and Density Semantics

16XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Horizontal Relations

17XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Topological Properties Topologic structure: - Island (in other polygon or background) - Island cluster - Landscape (complete tesselation) Ring model relation island island cluster landscape ring model with three levels Topologic neighbourhood Nine-Intersection Model (9IM) : e.g. overlap, touch, contain,... neigbourhood l1 l2 l3 A

18XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Structural Properties visible patterns  gestalt theory  meso structures Aproximity groupings Bsimilarity (size, shape, orientation) Cgrouping by type Dparallelism

19XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Horizontal & Vertical Relations Horizontal relations of map objects exist within one specific scale or level of detail (LOD) and represent common structural properties. horizontal relations

20XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Horizontal & Vertical Relations Horizontal relations of map objects exist within one specific scale or level of detail (LOD) and represent common structural properties. horizontal relationsvertical relations 1:25k 1:200k Vertical relations are links between single map objects or groups of map objects between different map scales and LODs.

21XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 vertical relations map object relations identity relation 1:1 simplification smoothing enlargement exaggeration collapse symbolization displacement group relation n:m aggregation (alignment, cluster) amalgamation (cluster) typification (cluster, alignment) partitioning (e.g. by alignments) LOD relations semantic similarity legend type priorities causal & logic structural neigbourhood matrix diversity configuration relations between properties of whole LODs e.g. semantic similarity or type priorities for aggregation

22XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 vertical relations map object relations identity relation 1:1 simplification smoothing enlargement exaggeration collapse symbolization displacement group relation n:m aggregation (alignment, cluster) amalgamation (cluster) typification (cluster, alignment) partitioning (e.g. by alignments) LOD relations semantic similarity legend type priorities causal & logic structural neigbourhood matrix diversity configuration relations between single map objects or groups  matching and formalisation of the geometrical, topological and semantical outcome with abstract generalization operators  abstract procedural knowledge

23XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Vertical Identity Relations 1:1 x

24XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Vertical Identity Relations 1:1 x A Coruña

25XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Vertical Group Relations n:m

26XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Enrichment of Relations

27XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Vertical Relation Properties enrich relations with additional information relation properties semantic properties statistics resistance / attraction configuration (island, landscape) containment (in, ring model) threshold level geometric properties size / position shape orientation type change topological properties neigbourhood intersection type structure change originator

28XXII International Cartographic Conference, A Coruña, July 9-16th, Outlook

29XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Using Relations Improve automated generalisation (horizontal relations) choice of appropriate algorithms more information about parameters for algorithms better evaluation of results Interpolation of intermediate scale levels (Cecconi 2003) e.g. in combination with morphing Incremental updating of lower detailed LODs (Kilpeläinen and Sarjakoski 1995) Training and use of learning algorithms (inductive, neuronal) by analyzing relations and properties (Weibel et al. 1995

30XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Thanks for your attention! Any questions, suggestions or comments? maps: Flood hazard map: China –language region map: snow depth map: soil map „Littau“: IKA, ETHZ, Switzerland

31XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Matching 1:25‘0001:200‘000

32XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Project DEGEN Purpose:data enrichment with relations modeling of enriched data exploitation of enriched data Focus: thematic vector maps Goals/Questions:types of “vertical” relations between map objects on different LODs? modelling and representing in a MRDB? matching of map objects in two LODs and acquisition relations and their attributes? management and deployment of relations? usefulness of vertical relations for the creation of intermediate LODs? usefulness of the same relations for incremental generalization?

33XXII International Cartographic Conference, A Coruña, July 9-16th, 2005 Vertical Relations vertical relations map object relations identity relation 1:1 simplification smoothing enlargement exaggeration collapse symbolization displacement group relation n:m aggregation (alignment, cluster) amalgamation (cluster) typification (cluster, alignment) partitioning (e.g. by alignments) LOD relations semantic similarity legend type priorities causal & logic structural neigbourhood matrix diversity configuration