ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
DISTRIBUTION ANALYSIS AND AUTOMATIC GENERALIZATION OF URBAN BUILDING CLUSTER 
Tinghua AI 
Section GIS Technology, 
Department of Geodesy 
Delft University of Technology, the Netherlands 
a.tinghua@qeo.tudelft.ni 
Wenping JIANG 
Department of Geographic Information Science 
Faculty of Resource and Environment Science, 
Wuhan University, P. R. China 
jwpinq@public.wh.hb.cn 
Keyworks: map generalization, building aggregation, polygon cluster, Delaunay Triangulation 
Abstract 
This paper presents a model for building cluster distribution analysis based on Delaunay triangulation skeleton. Through selective 
organization, the skeleton connection within gap area between building polygons obtains a special geometrical construction which is 
similar to Voronoi diagram with properties of spatial partitioning equally. Each building polygon is surrounded by a partitioning polygon 
which can be regarded as growth region of building seed. Based on this model, several cluster structure variables can be computed for 
building distribution analysis, such as distribution density, topological neighbor, adjacent distance, adjacent direction. Considering the 
constraints of position accuracy, statistical area balance, orgothonal characteristics in building cluster generalization, the paper gives a 
progressive algorithm of building cluster aggregation, including conflict detection (where), object (who) displacement, and geometrical 
combination operation (how).The context relationship of cluster structure is reflected through weighted distance computation, vector 
combination and other strategies. The algorithm has been realized in an active generalization system and some experiment illustrations 
are provided in the paper. 
1. INTRODUCTION 
Map generalization has to take into account spatial object 
properties in geometrical, semantic and topological aspects. The 
Objects with the same geometrical type, but different geographic 
meaning should be executed with different generalization model 
and algorithm. In recent years, the study of geo-oriented 
generalization is active, which aims at some special 
geographical categories (Poorten and Jones, 1999, Ruas 1998, 
Bader and Weibel 1999). The research on urban building 
abstract is an example. As a polygon object with human culture 
characteristics, the building has different properties in spatial 
distribution, shape structure, Gestalt nature compared with 
natural features such as soil parcel, vegetable, lake. Disjoint 
cluster distribution and orthogonal shape properties requires to 
be considered specially in building generalization. 
Building cluster generalization includes multiple level analysis 
and operation. Grouping is the first decision-making which is 
based on conflict detection, distribution pattern recognition, 
Gestalt nature cognition. The following displacement involves 
how far and what direction identification. Thirdly, the geometrical 
combination and simplification has to maintain orthogonal 
geometric nature. Three level processes require special model to 
derive such descriptions variables as distribution density, 
distribution pattern, adjacency distance, adjacency direction 
etc. Independent building simplification is active in this field and 
achieves some methods and algorithms. From the point of 
readable view, Regnauld and Edwardes (1999) discuss three 
operations for building simplification: detail removal, squaring, 
local enlargement. Lee(1999) presents some ideas on single 
building simplification focusing on shape maintenance. Based on 
divide-and-conquer idea, Guo and Ai(2000) give an algorithm to 
simplify building polygon through separating a building into 
multiple hierarchical organization of rectangle elements. For 
building cluster aggregation, Regnauld (1996) develops a 
method to classify building group applying MST model in graph 
theory. Ruas(1998) presents an algorithm of building 
displacement to resolve conflicts between building and street 
edge. These works are relative independent in the whole 
procedure of map generalization. This paper attempts to 
combine the first two issues of building generalization, 
concentrating on cluster structure displacement and aggregation 
and giving a model to support cluster analysis. 
In building cluster generalization, it is difficult to satisfy all 
constraints. Group combination which exactly maintains position 
accuracy ( no displacement) of each building may result in area 
increasing greatly, due to gap area between original buildings 
being included. The compromise strategy is to sacrifice each 
constraint partly, not respecting anyone condition completely. 
This strategy requires to handle three level operation 
interdependently. It also needs generalization model containing 
different functions to support both high level decision making and 
low level geometric operation, to answer such questions of 
where happens conflict, how to displace(direction and offset), 
how to aggregate. This paper will present one data model 
having this kind of properties to support building aggregation. 
Based on Delaunay triangulation skeleton, we will construct a 
geometrical construction which is similar to Voronoi diagram with 
properties of spatial partitioning equally. Each building polygon is 
surrounded by one partitioning polygon which can be regarded 
as the growth region of building seed. Based on this model, 
several cluster structure variables can be computed for building 
distribution analysis, such as distribution density, topological 
neighbor, adjacency distance, adjacency direction. This model 
makes use of the powerful function of Delaunay triangulation in 
spatial adjacency analysis. 
Remained contents is organized as following: The constraints in 
building polygon generalization is discussed in section 2. 
Section 3 gives the model of partitioning geometrical 
construction and some variable computation based on this model. 
A progressive algorithm of building cluster aggregation is 
presented in section 4 with experiment illustrations, and then 
some future improvements are discussed in conclusion, section 
5. 
2. CONSTRAINS OF BUILDING GENERALIZATION 
Based on geometric, topological and semantic analysis, the 
constraints of building generalization involves position accuracy 
maintenance, short space distance avoidance, the whole area 
balance maintenance, Gestalt keep in distribution structure, and 
square shape retain. The main purpose in building generalization 
is to remove spatial conflict and during the procedure to respect 
above constraints as much as possible. 
From the point of readable view, when distance between 
buildings is shorter than cognition tolerance, we may think the 
spatial conflict generating. To resolve conflict, the candidate 
operations include deletion, displacement, aggregation. Deleting 
some buildings needs to consider semantic importance and