Zhilin Li

A Voronoi-based 9-intersection model for spatial relations

Models of spatial relations are a key component of geographical information science (GIS). Efforts have been made to formally define spatial relations. The foundation model for such a formal presentation is the 4-intersection model proposed by Egenhofer and Franzosa (1991). In this model, the topological relations between two simple spatial entities A and B are transformed into pointset topology problems in terms of the intersections of As interior and boundary with Bs interior and boundary. Later, Egenhofer and Herring (1991) extended this model to 9-intersection by addition of another element, i.e. the exterior of an entity, which is then defined as its complement. However, the use of its complement as the exterior of an entity causes the linear dependency between its interior, boundary and exterior. Thus such an extension from 4- to 9-intersection should be of no help in terms of the number of relations. This can be confirmed by the discovery of Egenhofer et al. (1993). The distinction of additional relations in the case where the co-dimension is not zero is purely due to the adoption of definitions of the interior, boundary and exterior of entities in a lower dimensional to a higher dimension of space, e.g. lines in 1-dimensional space to 2-dimensional space. With such adoption, the topological convention that the boundary of a spatial entity separates its interior from its exterior is violated. It is such a change of conventional topological properties that causes the linear dependency between these three elements of a spatial entity (i.e. the interior, boundary and exterior) to disappear, thus making the distinction of additional relations possible in such a case (i.e. the co-dimension is not zero). It has been discussed that the use of Voronoi-regions of an entity to replace its complement as its exterior in the 9-intersection model would solve the problem (i.e. violation of topological convention) or would make this model become more comprehensive. Therefore, a Voronoi-based 9-intersection model is proposed. In addition to the improvement in the theoretical aspect, the Voronoi-based 9-intersection model (V9I) can also distinguish additional relations which are beyond topological relations, such as high-resolution disjoint relations and relations of complex spatial entities. However, high-resolution disjoint relations defined by this model are not purely topological. In fact, it is a mixture of topology and metric.

Quantitative measures for spatial information of maps

The map is a medium for recording geographical information. The information contents of a map are of interest to spatial information scientists. In this paper, existing quantitative measures for map information are evaluated. It is pointed out that these are only measures for statistical information and some sort of topological information. However, these measures have not taken into consideration the spaces occupied by map symbols and the spatial distribution of these symbols. As a result, a set of new quantitative measures is proposed, for metric information, topological information and thematic information. An experimental evaluation is also conducted. Results show that the metric information is more meaningful than statistical information, and the new index for topological information is more meaningful than the existing one. It is also found that the new measure for thematic information is useful in practice.

An Algorithm for the Generation of Voronoi Diagrams on the Sphere Based on QTM

the bubble structure of the cells) (Roos, 1991; Gold, 1992; Gold In order to efficiently store and analyze spatial data on a global and Condal, 1995; Gold and Mostafavi, 2000), and computa

Effects of JPEG compression on image classification

With the improvement of spatial resolution, data volume has become an increasingly significant concern, as the shear volume of data is expensive and inefficient in terms of data transmission, processing and storage. As a result, many image compression methods are in use. JPEG is one of the most popular methods. Indeed JPEG has become an industrial standard and has been implemented in many remote sensing image processing systems. This paper aims to experimentally evaluate the effects of JPEG compression on image classification. A scene of SPOT multispectral images was used. The image was compressed by JPEG at various compression levels (or using compression quality factors). All the compressed images are classified using the maximum likelihood classifier (MLC) of supervised classification and ISODATA of unsupervised classification. The classified result using the original (uncompressed) image was used as the benchmark. From the results, it can be found that there could be a significant decrease in image quality when compression is over 35‐fold. As a result, the accuracy of image classification is dramatically deteriorated. However, when the compression ratio is smaller than 35‐fold, the deterioration of classification accuracy is linear.

Reality in time-scale systems and cartographic representation

Abstract This paper is an attempt to provide a view point for the formalisation of knowledge in cartographic representation. What is supposed to be reality in the world is dependent on time and scale. So, there are different levels of reality, from low to high. Cartographic representation is a graphical record of reality at a particular location in the time-scale system. The problem of the transformation of reality in both scale and time dimensions in this time-scale system is also briefly discussed.

Basic Topological Models for Spatial Entities in 3-Dimensional Space

In recent years, models of spatial relations, especially topological relations, have attracted much attention from the GIS community. In this paper, some basic topologic models for spatial entities in both vector and raster spaces are discussed.It has been suggested that, in vector space, an open set in 1-D space may not be an open set any more in 2-D and 3-D spaces. Similarly, an open set in 2-D vector space may also not be an open set any more in 3-D vector spaces. As a result, fundamental topological concepts such as boundary and interior are not valid any more when a lower dimensional spatial entity is embedded in higher dimensional space. For example, in 2-D, a line has no interior and the line itself (not its two end-points) forms a boundary. Failure to recognize this fundamental topological property will lead to topological paradox. It has also been stated that the topological models for raster entities are different in Z2 and R2. There are different types of possible boundaries depending on the definition of adjacency or connectedness. If connectedness is not carefully defined, topological paradox may also occur. In raster space, the basic topological concept in vector space—connectedness—is implicitly inherited. This is why the topological properties of spatial entities can also be studied in raster space. Study of entities in raster (discrete) space could be a more efficient method than in vector space, as the expression of spatial entities in discrete space is more explicit than that in connected space.

Morphological Transformation for the Elimination of Area Features in Digital Map Generalization

For the graphic representation of spatial data (e.g. a map), if the scale of the representation is reduced, then some area features will become too small to be represented, i.e. they need to be eliminated. This elimination procedure is part of the so-called generalization process. This paper describes some techniques in digital map generalization for this procedure, which employ several operators developed in mathematical morphology, a science of shape, form and structure. The techniques include three steps. These involve a process to reduce the size of every area feature using an erosion operator (leading to the disappearance of those small area features which need to be eliminated), a process to recover the size and shape of every area feature that has just been eroded, and a process to simplify the boundaries of recovered area features so as to suit the representation at a smaller scale. The models used in these techniques provide a mathematical basis for area elimination in digital generalization of m...

Algebraic Models for Feature Displacement in the Generalization of Digital Map Data Using Morphological Techniques

Feature displacement is one of the many operations (or operators) in map-data generalization. It has become a priority item on the research agenda. This paper describes some algebraic models (or mathematical models) for this operation. These models are based on the operators developed in mathematical morphology, which is a science dealing with form, shape, and structure of objects. Feature displacements can be classified into two groups, i.e., feature translation and feature modification. For the first type, a set of structuring elements (key elements in morphological operators) are developed. Using this set of structuring elements, the two basic morphological operators, i.e., dilation and erosion, can be used for translating features in any of the eight directions, freely. Translation of features in other directions can be achieved by a combination of these eight directions. For the second type of feature displacement, a number of models have been developed to suit different cases, i.e., an area feature ...

Mathematical Morphology in Digital Generalization of Raster Map Data

This paper discusses the potential application of mathematical morphology techniques in digital generalization of raster map data. A review of existing generalization operators and morphological operators is conducted so that an insight into their relationships can then be made. The potential applications of morphological tools in digital map generalization of raster map data is discussed and problems associated with such an application are also identified. In particular, four application areas—elimination, combination, line simplification and displacement—are successfully demonstrated and the results show that morphological operators could be very important tools for generalisation purposes.

Using raster quasi‐topology as a tool to study spatial entities

The study of spatial entities needs a model that is not only fully observable and controllable, but also computable. Euclidean topology on R2 is a usually used tool for this study, but it has the following two weaknesses. First, there exists some phenomenon of human perception of the spatial entity that cannot be simulated by it. Second, its observation of the basic geometric properties (interior, exterior, boundary) of the spatial entity lacks computability so that the model based on it lacks computability and cannot be directly used to practical systems. Consequently, in this paper, we present another tool for studying spatial entities – raster quasi‐topology on R2 and then compare the two tools.