Terrain Generalization with Multi-Scale Pyramids Constrained by Curvature

Article excerpt

Introduction

Expert cartographers generalize terrain for 3D maps by removing unnecessary and visually distracting details, and accentuating important landforms, while preserving characteristic terrain features and typical landforms. However, generalization methods for 3D maps are most often technology driven, i.e., they are often not targeted at cartographic generalization, but intend to reduce the amount of terrain details in order to achieve responsive frame rates when rendering terrain in video games and other interactive environments. Such methods may introduce artifacts, such as artificial edges and flat triangle structures, or overly smoothed mountain ridges and valleys.

3D maps most often depict terrain in a central perspective projection, compressing terrain features in the background. The terrain compression increases with the distance to the viewer: the foreground is depicted at a large scale, while the background is rendered at a considerably smaller scale. This results in an excessively detailed background, especially when using high-resolution terrains. Such highly detailed representations are often visually inefficient because the main landforms are not clearly discernable due to the many distracting details. The dense details generate disturbing visual noise, which obscures macro topography--it is impossible to see the forest for the trees. Hence, the level of terrain generalization must seamlessly increase with the distance to the viewer.

Cartographic generalization is an inherently visual task. A graphical environment is required for adjusting the generalization parameters in a trial-and-error approach to the spatial resolution of the terrain, the landscape features and the purpose of the map. A problem plaguing authors of 3D maps, however, is the currently available software for generalizing terrain, which sometimes is difficult to comprehend and control, or does not offer a WYSIWYG preview mode for interactive manipulation in real-time.

The research presented in this article aims at making a contribution to the solution of these problems. Visually disturbing details are to be removed from digital terrain, while sharp edges and mountain ridges are to be retained. The goal is to preserve the characteristic appearance of a terrain, and to seamlessly adjust the amount of generalization from foreground to background. We are aiming at a generalization method that is easy to comprehend and control by authors of 3D maps, and provides feedback in real time.

For our prototype, an equalizer metaphor was chosen as basis for the user interface. In audio engineering, the equalizer filter is used to alter the frequency response of an audio source. Most users should be familiar with equalizers from audio playback software and physical audio equipment. Terrain Equalizer, a free and open-source software application, was developed, integrating the presented generalization method and its related user interface.

Related Work

In this overview of related research, we concentrate on cartographic generalization aiming at improving the visual effectiveness to generate clear and legible maps. Generalization methods to improve data storage or to accelerate rendering, analysis or transmission of terrain data are not treated here, neither is the generalization of representations derived from terrain models, such as contour lines.

Filtering, Smoothing and Denoising

The term filtering is understood in the context of signal processing, i.e., the application of an operator (the filter) that removes frequency components from the signal (the terrain). Such filters are known from image processing, and can be applied to gridded terrain models. Low-pass filters remove high-frequency details, whereas high-pass filters emphasize discontinuities. While high-pass filters are rarely applied to digital terrain (Weibel and Heller 1991), low-pass filters are the simplest and thus most commonly used filters (Li 2008). …