Hierarchical topology-preserving simplification of terrains (original) (raw)
Computational methods for simplification and generalisation of Digital Terrain Modelling
Istituto per la Matematica Applicata -Consiglio Nazionale delle Ricerche Storage, manipulation and rendering of huge data sets are frequently required in spatial data handling and need memory and processing resources beyond the available ones, especially in real-time or interactive environments. Thus it is necessary to define data models which use the minimum amount of data for retrieving the maximum of information possible, and modelling issues have to be considered in addition to traditional hardware or software optimisation problems.
Terrain complexity and reduction of topographic data
Journal of Geographical Systems, 1999
Digital terrain data are useful for a variety of applications in mapping and spatial analysis. Most available terrain data are organized in a raster format, among them being the most extensively-used Digital Elevation Models (DEM) of the U.S. Geological Survey. A common problem with DEM for spatial analysis at the landscape scale is that the raster encoding of topography is subject to data redundancy and, as such, data volumes may become prohibitively large. To improve e½ciency in both data storage and information processing, the redundancy of the terrain data must be minimized by eliminating unnecessary elements. To what extent a set of terrain data can be reduced for improving storage and processing e½ciency depends on the complexity of the terrain. In general, data elements for simpler, smoother surfaces can be substantially reduced without losing critical topographic information. For complex terrains, more data elements should be retained if the topography is to be adequately represented. In this paper, we present a measure of terrain complexity based on the behavior of selected data elements in representing the characteristics of a surface. The index of terrain complexity is derived from an estimated parameter which denotes the relationship between terrain representation (percentage surface representation) and relative data volume (percentage DEM elements). The index can be used to assess the required volume of topographic data and determine the appropriate level of data reduction. Two quadrangles of distinct topographic characteristics were examined to illustrate the e½cacy of the developed methodology.
Topological Landscapes: A Terrain Metaphor for Scientific Data
IEEE Transactions on Visualization and Computer Graphics, 2000
Scientific visualization and illustration tools are designed to help people understand the structure and complexity of scientific data with images that are as informative and intuitive as possible. In this context the use of metaphors plays an important role since they make complex information easily accessible by using commonly known concepts. In this paper we propose a new metaphor, called "Topological Landscapes," which facilitates understanding the topological structure of scalar functions. The basic idea is to construct a terrain with the same topology as a given dataset and to display the terrain as an easily understood representation of the actual input data. In this projection from an n-dimensional scalar function to a two-dimensional (2D) model we preserve function values of critical points, the persistence (function span) of topological features, and one possible additional metric property (in our examples volume). By displaying this topologically equivalent landscape together with the original data we harness the natural human proficiency in understanding terrain topography and make complex topological information easily accessible.
Visualizing Multifolded and Multifaulted Terrain Geometry Using Computer Graphics
Geoinformatics
The POLYPLI software makes it possible to visualize the geometry of stratified terrain which have been deformed by numerous fold and fault events in a quick and efficient way. Strata deformation is carried out by simple geometric transformations which affect the various material points. These transformations simulate the displacements which are registered in similar folding. Faults are simulated in a similar way.Stratigraphy , fold profiles wavelength amplitudes and orientations of the various fold phases and of the various faults are interactively defined by the user.POLYPLI can represent unconformities and deformations which simultaneously affect a previously deformed basement and its sedimentary cover. POLYPLI provides a new type of help for structural analysis : its provides a good approximation to the topology of intricate deformations such as those which are commonly observed in basement located metasedimentary terrains. Run under UNIX operating system, POLY-PLI is very interactive and easy to use because of a multiwindow presentation which can input most data with the mouse.
Representation and Visualization of Terrain Surfaces at Variable Resolution
The Visual Computer, 1997
We present a new approach for managing the representation of discrete topographic surfaces at variable resolution, which is based on a unified model encoding a history of either refinement or simplification of a triangulation decomposing a plane domain. An efficient data structure is proposed, which is obtained by interpreting the model containing all triangles of the history as a cell complex embedded in three-dimensional space. A major feature of the model is the ability to provide efficiently a representation of the surface at resolution variable over the domain, according to an application-dependent threshold function. Experimental results on real world data are presented, and applications to flight simulation are discussed.
Visualization of Large Terrains Made Easy
Visualization, 2001. VIS'01. Proceedings, 2001
We present an elegant and simple to implement framework for performing out-of-core visualization and view-dependent refinement of large terrain surfaces. Contrary to the recent trend of increasingly elaborate algorithms for large-scale terrain visualization, our algorithms and data structures have been designed with the primary goal of simplicity and efficiency of implementation. Our approach to managing large terrain data also departs from more conventional strategies based on data tiling. Rather than emphasizing how to segment and efficiently bring data in and out of memory, we focus on the manner in which the data is laid out to achieve good memory coherency for data accesses made in a top-down (coarse-to-fine) refinement of the terrain. We present and compare the results of using several different data indexing schemes, and propose a simple to compute index that yields substantial improvements in locality and speed over more commonly used data layouts. Our second contribution is a new and simple, yet easy to generalize method for view-dependent refinement. Similar to several published methods in this area, we use longest edge bisection in a top-down traversal of the mesh hierarchy to produce a continuous surface with subdivision connectivity. In tandem with the refinement, we perform view frustum culling and triangle stripping. These three components are done together in a single pass over the mesh. We show how this framework supports virtually any error metric, while still being highly memory and compute efficient.
This chapter reviews recent development in terrain generalisation. The focus is put on cartographic generalisation where the terrain representation is adapted with consideration to the aesthetics and legibility of the map for a specific purpose. Generalisation methods apply to traditional terrain representations (spot heights, contours, hypsometric colours, shaded relief) but also to grid and triangulated surface generalisation. First, issues related to relief representation on maps at different scales are discussed. As generalisation requires knowledge about the terrain morphology, several approaches focusing on the classification of terrain features according to morphometric or topological criteria were developed. Cartographic generalisation methods are reviewed with consideration to conflicts between terrain representations and other object type data on the map. In the second part, three case studies illustrating previous developments are presented. First, a generalisation method for hypsometric map production is described where important valleys and mountain ridges are accentuated to improve the representation. Second, a method selecting features represented by isobaths and answering specific constraints of nautical charts is presented. The third case study is a generalisation method which takes into account other objects of the map such as buildings and rivers.
VARIANT---processing and visualizing terrains at variable resolution
Proceedings of the fifth ACM international workshop on Advances in geographic information systems - GIS '97, 1997
We describe VARIANT (VAriable Resolution Interactive ANalysis of Terrains), a prototype system for processing and visualizing terrains at variable resolution, which is based on a multiresolution terrain model, called a Multi-Triangulation (MT).
Presented at the 19th ICA Meeting …, 1999
It is believed that Web-based visualisation of spatial information could be greatly enhanced through the use of dynamic or 'onthe-fly' map generalisation. This involves dynamically deriving scale-and theme-dependent displays from a single detailed dataset, thus eliminating the need to maintain duplicate datasets at different resolutions. Dynamic generalisation also prevents the generation of cartographically-poor maps that result from the display of spatial information at a considerably different resolution from that at which it was captured. The implementation involves combining automated generalisation and symbolisation techniques together in a simple rule-base to produce a virtual map of central Edinburgh in which both the level of detail and the symbology is dynamically tailored to a user-specified scale and map theme (tourist or topographic maps). The paper explores the inherent differences between the generalisation of a virtual map and that of a paper map, and also considers issues such as those arising from the relationship between map scale, map theme and utility. The research demonstrates that it is possible to achieve effective results using a limited number of simple mechanisms, and argues that the true potential of dynamic generalisation lies in two main areas -firstly, in an ability to narrowly-define the map theme, thus enhancing map clarity and more closely matching user requirements; and secondly, in using control over the map scale as a gateway to other types of map use and other themes.
Large Scale Topographic Maps Generalisation and Visualization Based on New Methodology
Geodetski List, 2015
Integrating spatial data from different sources results in visualization which is the last step in the process of digital basic topographic maps creation. Sources used for visualization are existing real estate cadastre database orthophoto plans and digital terrain models. Analogue cadastre plans were scanned and georeferenced according to existing regulations and used for toponyms. Visualization of topologically inspected geometric primitives was performed based on the ''Collection of cartographic symbols for scales 1:500 and 1:2500''-regulations applied in Republic of Croatia, since Federation of Bosnia and Herzegovina does not have prescribed regulations. In addition to integrating different spatial data, it is necessary, prior to the visualization step, to perform the generalization step (depending on basic topographic map scale, partial or complete generalization is applied). This paper describes the process of generalization and visualization of data collected and processed in accordance with the topographic data model from the Federal Administration for Geodetic and Property Affairs.
An Algorithm for the Visualization of a Terrain with Objects
Computer Graphics and …, 1997
The article describes a method for object and terrain visualization by means of the combination of two algorithms, one for terrain data and one for objects. Our purpose is to generate, efficiently and rapidly, aerial images of terrain with objects such as houses, ...
Encyclopedia of Environment and Society
We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description ts to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We de ne a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusion-transparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization.
Qlod: A data structure for interative terrain visualization
This work focuses on the use of hierarchical structures to interactively visualize terrains. Our purpose is to achieve real time three-dimensional visualization of terrain models obtained from a geographic information system. These models can represent a broad area of the Earth's surface with detailed information, thus yielding very large datasets. For this reason, it is necessary to use a compatible structure to store and query this data. In this paper, we present a new data structure which combines advantages of different structures provided in the literature. We also discuss an implementation of these ideas and a series of tests, drawing several conclusions from them.
A discrete approach to compute terrain morphology
Computer Vision and …, 2009
We consider the problem of extracting morphology of a terrain represented as a Triangulated Irregular Network (TIN). We propose a new algorithm and compare it with representative algorithms of the main approaches existing in the literature to this problem. The new algorithm has the advantage of being simple, using only comparisons (and no floating-point computations), and of being suitable for an extension to higher dimensions. Our experiments consider both real data and artificial test data. We evaluate the difference in the results produced on the same terrain data, as well as the impact of resolution level on such a difference, by considering representations of the same terrain at different resolutions
Earth Surface Processes and Landforms, 2018
Morphological analysis of landforms has traditionally relied on the interpretation of imagery. Although imagery provides a natural view of an area of interest (AOI) images are largely hindered by the environmental conditions at the time of image acquisition, the quality of the image and, mainly, the lack of topographical information, which is an essential factor for a correct understanding of the AOI's geomorphology. More recently digital surface models (DSMs) have been incorporated into the analytical toolbox of geomorphologists. These are usually high-resolution models derived from digital photogrammetric processes or LiDAR data. However, these are restricted to relatively small areas and are expensive or complex to acquire, which limits widespread implementation. In this paper, we present the multi-scale relief model (MSRM), which is a new algorithm for the visual interpretation of landforms using DSMs. The significance of this new method lies in its capacity to extract landform morphology from both high-and low-resolution DSMs independently of the shape or scale of the landform under study. This method thus provides important advantages compared to previous approaches as it: (1) allows the use of worldwide medium resolution models, such as SRTM, ASTER GDEM, ALOS, and TanDEM-X; (2) offers an alternative to traditional photograph interpretation that does not rely on the quality of the imagery employed nor on the environmental conditions and time of its acquisition; and (3) can be easily implemented for large areas using traditional GIS/RS software. The algorithm is tested in the Sutlej-Yamuna interfluve, which is a very large low-relief alluvial plain in northwest India where 10 000 km of palaeoriver channels have been mapped using MSRM. The code, written in Google Earth Engine's implementation of JavaScript, is provided as Supporting Information for its use in any other AOI without particular technical knowledge or access to topographical data.
Morphology-driven simplification and multiresolution modeling of terrains
Workshop on Advances in Geographic Information Systems, 2003
We propose a technique for simplification and multiresolution modeling of a terrain represented as a TIN. Our goal is to maintain the morphological structure of the terrain in the resulting multiresolution model. To this aim, we extend Morse theory, developed for continuous and differentiable functions, to the case of piecewise linear functions. We decompose a TIN into areas with uniform
Analytic Generalization of Topographic Data and Terrain Models
2005
Map generalization is an important and complex field in classic cartography, but even more so in digital cartography. This field is in the forefront of research and application in the academic and applied cartographic world, and has been so for several years. The main goal of most of the current research is to develop generalization applications, automated if possible, for the creation of topographic maps from existing spatial databases. This goal has not been fully realized, and the digital solutions offered so far have had limited influence to this complicated process. A research was designed to develop analytic generalization procedures for topographical data and terrain models. In the following paper a methodology dealing with the generalization of topographic data is presented. The methodology is based on the four following major processes: spatial analysis, classification, selection, and simplification.