**A COMPARATIVE STUDY OF THE INFLUENCE OF SIMPLIFICATION
ALGORITHMS ON LINEAR FEATURES’ SHAPE AND POSITION**

L. Tsoulos, A. Skopeliti, T. Tzamakou

* National Technical
University of Athens Greece*

*lysandro@central.ntua.gr*

This
paper presents a comparative study of simplification algorithms and their
influence on two elements inherent to linear features: shape and horizontal
position. Several line simplification algorithms are evaluated, which use
different criteria for vertex rejection. Algorithms are applied to lines with
different threshold values to produce generalization results for a number of
map scales. The comparison of the results of different algorithms implies that
the number of the retained points is fixed.

The
evaluation of the results is performed
through qualitative assessment (visual comparison) and
quantitative assessment, utilizing shape distortion measures and horizontal
position displacement measures.

Shape
distortion measures are based on the description of the shape of cartographic
line utilizing a set of parameters. Recent research resulted to a number of
parameters, which describe qualitatively/quantitatively the line shape. The set
of parameters (measures) adopted have been selected from a comprehensive list
identified in the literature utilizing Principal Components Analysis - PCA.
Taking into account the PCA results and cartographic judgment, the following
measures were selected: the *“average
magnitude angularity”,* the *“error
variance”* and the *“average
angularity”*. These measures are also used for the clustering of line
segments into groups of similar complexity utilizing Cluster Analysis. The same
methodology is used for the description of the generalized lines’ shape,
leading to the objective comparison with the original lines.

Horizontal
position accuracy measures that express the generalized line displacement are
also used: distance measures (Average Euclidean distance, Hausdorff distance)
and area displacement measures (the ratio of the area between the original and
the generalized line to the length of the line etc.).

Line
shape is a critical factor in the evaluation of simplification algorithms. In
this study linear features are classified into similar shape groups before
generalization e.g. sinuous, smooth etc. This way the influence of
simplification algorithms to specific kinds of linear feature shape/character
is studied.

The aim of this study is to draw specific
conclusions on the results of each simplification algorithm and to establish a
generalization strategy, comprised of algorithms and threshold values,
appropriate for specific map scales and line features character.