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New Geomatics Technologies and Applications

Least squares regression model for generalization of multiple lines

(Case study: Zerivar Lake)

1*
Jalil Jafari , Amir Gholami 2

1 Faculty of geodesy and geomatics engineering, K.n.toosi University, Tehran, Iran

2 Faculty of Planning and Environmental Sciences, Tabriz University, Tabriz, Iran
* J.jafarikntu@yahoo.com

Abstract: The most basic linear regression model, also known as the base model for Linear Regression, is LS (Least
Squares) Regression. LS regression is a statistical technique for minimizing the sum of square differences between
observed and predicted values. With the help of LS, it is possible to fit the best line to the features in the field of feature
generalization. The aim of this summarization is to maintain the geometry and area while reducing the details. In this
research, the least squares regression was used to generalize multiple lines with the aim of minimizing the distance from
the main line. In order to study the proposed model, after its implementation on different shapes, the multi-lines of Zerivar

Lake were summarized and the results of the proposed model were compared with the common Douglas-Poker and
Viswalingam methods. To evaluate the results, the indices of area differences, mean curvature similarity, similarity of the
angle changes, and the corrected median Hausdorff distances were used. Based on the first three metrics, the proposed
model performed around 12 to 14 percent better. However, the corrected Hasdroff distance index shows that it performed
about 5 meters worse than the other approaches, which is indicative of the fact that it did not depend on the feature's

initial points.

Keywords: LS, Cartography, Generalization, Summarization

1. Introduction
Along with the increase in the volume of data and spatial information, storage, transmission, processing and display of
features and spatial information has become a major and pervasive challenge in cartography and in particular, the spatial
information system [1]. Also, GIS software's graphical interface can't carry all the specifics needed to view small-scale maps,
and large volumes of spatial data make data storage, transmission, and processing difficult.

1