Hybrid line simplification for cartographic generalization

Abstract

The performance of a line simplification algorithm can be different depending on the shape characteristics of the line data. Methodologies for segmenting a line feature into homogeneous sections and simplifying the segments with a proper algorithm are of great importance in linear generalization. This study proposes a methodology for segmenting and simplifying linear features based on the quantitative characteristics of a line. We analyzed the performance of existing simplification algorithms based on the geometrical attributes of line shapes. The analyzed data was used as a criterion for segmenting line data and selecting simplification algorithms appropriate for each segment. Then, we implemented segmentation and hybrid line simplification on topographic map data with a 1:1000 scale. To evaluate the performance of this methodology, visual and statistical assessments were implemented. As a result, this hybrid approach preserves more of the shape characteristics and produces less positional errors than the individual application of existing algorithms.

Introduction

Recently, the location-based service industry has grown quickly and the utilization of digital maps on the Internet and in mobile environments has become ubiquitous. Cartographic generalization is an indispensable technique for transferring or changing scale of digital maps in these environments (Jones and Ware, 2005). Line simplification is one of the most important operators in cartographic generalization (Li and Openshaw, 1993). Since the 1960s, innumerable simplification algorithms have been developed in the cartographic generalization and pattern recognition area: the Douglas–Peucker algorithm (Douglas and Peucker, 1973), the sleeve-fitting algorithm (Zhao and Saalfeld, 1997), the Lang algorithm (Lang, 1969), the Reumann–Witkam algorithm (Reumann and Witkam, 1974), the Visvalingam–Whyatt algorithm, (Visvalingam and Whyatt, 1993) simplification based on turning angle functions (Rangayyan et al., 2008) and many other algorithms. It is well known that the performance of a line simplification algorithm depends on the shape characteristics of the line feature (Balboa and Lopez, 2009). Thus, segmenting the line feature into homogeneous sections and applying appropriate algorithms and parameters depending on the shape characteristics of a section are important for improving the performance of the simplification National Geographic Information Institute (NGI), 1995, Visvalingam and Williamson, 1995, Richardson and Mackaness, 1999, Richardson and Mackaness, 1999, Dutton, 1999, Lopez and Balboa, 2008.

Although countless segmentation and simplification methodologies for linear features have been developed, little research has been done to investigate simplification options by using a quantitative analysis of the effects of various algorithms based on the shape of line features. It is also a shortcoming of these studies that they mainly depend on the subjective knowledge of experts to determine the subsections in a line feature and to identify the appropriate algorithms or parameters. Moreover, the generalization quality is evaluated merely by a visual or qualitative assessment in many cases (Skopeliti and Tsoulos, 1999, Chen and Chen, 2005, Mustiere, 2005, Balboa and Lopez, 2008, Balboa and Lopez, 2009, Lopez and Balboa, 2008).

In this paper, we propose a new methodology for segmenting and simplifying linear features based on the quantitative characteristics of a line. Three key points emerge as potential contributions of this study. First, we present a segmentation method based on a quantitative analysis of the performances of the simplification algorithms according to the shape characteristics of the linear features. Second, we propose a hybrid simplification method that applies different simplification algorithms for these segments in order to produce the least positional error. Third, we analyze the visual aspects and displacements between the original line data and the simplified line for a qualitative and quantitative evaluation of the proposed methodology.

This paper consists of five sections. In Section 2, the processes of segmentation and simplification proposed in this study are described in detail. Section 3 shows the results of tests applying these processes to a cartographic line data set. In Section 4, visual and statistical assessments of the results are presented. Finally, the conclusions of this study and possible future work are presented in Section 5.