The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics

Chen, Jun

Bibliographic data

Monograph

Persistent identifier:: 856566209

Author:: Chen, Jun

Title:: The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics

Sub title:: May 23 - 25, 2001, Bangkok, Thailand

Scope:: VI, 434 Seiten

Year of publication:: 2001

Place of publication:: Pathumthani, Thailand

Publisher of the original:: AIT

Identifier (digital):: 856566209

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: THREE LEVEL HIERARCHICAL QUALITATIVE DESCRIPTIONS FOR DIRECTIONS OF SPATIAL OBJECTS. Han CAO, Jun CHEN, Daosheng Du

Document type:: Monograph

Structure type:: Chapter

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 21 riAL OBJECTS 1 ¡rsity, ing I relation often use id to determine the of objects' abstract qualitative direction econd one with line ded into two stages, 3tion and reasoning ner. So the cardinal and described in a inference direction iy cannot consider :tor in determining 3n extended spatial is an improved ssed method and into nine direction utheast (SE), south JW), and same (O). get object falls, the target is described station of the target but there still exist distinguished with ction-relation matrix bor code for empty are empty or not. In ptures intersections ghboring boundary the value of the bits1-8 capture the i, bottom-right, right, spectively. Every bit mber: 69833010 records a 0 if the corresponding boundary part does not intersect with the target object and a 1 if the target object intersects with the boundary. Bits have values multiple by the powers of 2, from 2° to 2 8 . The neighbor code is the sum of nine bit numbers. It ranges from 0 to 510. Nine of these neighbor codes are arranged in the same topological organization as the direction-relation matrix. This structure yields the deep direction-relation matrix (Goyal, 2000). However neighbor codes method is not cognitively plausible to describe detailed directions and the computation process of neighbor codes is not necessary so complicated between all six pair of objects (area and area, area and line, area and point, line and line, line and point, point and point). Such as point and point object, we need not to record the tiles' boundary by calculating their neighbor codes at all. Because of the different need in small-scale space and large-scale space, spatial objects may change their dimensional representation from a polygon to a point; direction relations between two objects need to describe at different levels of detail. infinite. If the object is finite and its boundary is well defined within the data window, then this is a closed object (Shekhar, 1999). We can use open object to model the directions between extended objects by converting the calculation of directional relationships to the calculation of topological relationships between objects. In order to test the direction of object B related to object A, we use 4I matrix to test into which direction tile B falls (Equ.1-9). The union of all the nine tiles overlapping with target object B is the direction region where B is located with reference object A. In fact, the eight open rectangles can be transformed into close ones according to the maximum and minimum X, Y coordinates of target object, as shown in Fig. 1a. ôNW A Ç\dB ôNW a Ç]B° NW/V\dB NW/[\B° (1) In this paper we propose a three level hierarchical qualitative direction description model of spatial objects. The first one is the direction description with point object as a reference, the second one with line object as a reference, and the third one with area object as a reference. In each level, direction models is again divided into two stages, the first one is the primary direction description and reasoning model, and the second one is the detailed description and reasoning model with distance relation of objects and topological relation between object and direction tile’s boundary as a refiner. In our primary direction description, direction relation is converted into topological model; such a representation is based on n intersection model. First we use projection-based method to obtain the MBR of reference object and partition the space around it into nine direction tiles. We present each direction tile as a spatial object, then we get eight open rectangles N, NE, E, SE, S, SW, W, NW, and one close rectangle O based on the MBR of reference object. In each direction tiles, we use 4I topological matrix to calculate the direction relation. The union of all the nine tiles that overlap with target object is the direction region where the target object is located with reference object. So we can describe direction with a unified topological model. For the object meeting with direction tiles boundary, we use extended detailed boundary topological-relation matrixes to record every sixteen-boundary element. And by integrating object’s distance relation in our detailed reasoning model, we can inference direction relation more accurately. The rest of the paper is organized as follows: Section 2 uses 4I topological matrix to define our primary direction description model. Section 3 discusses direction relation inference and gives an example to show the effect of object's distance relation in direction reasoning. In order to distinguish more different direction relations, Section 4 presents our detailed direction relation matrix to record the topological relation between object and direction tile’s boundary. Section 5 outlines a framework for direction relation description using line object as a reference object. Section 6 describes the direction relation description model with point object as a reference. Section 7 concludes with comments. 2. MODELING DIRECTION BETWEEN EXTENDED OBJECTS USING 4I TOPOLOGICAL MATRIX R H A, B dN A V\ 5B 3N a Ç\B° N/ f] dB N a °C\B° (2) dNE A f]3B 8NE a D B" NE À ° D dB NE/f}B° (3) R Wa,B dW A Ç\dB 3W A Ç]B° w/^dB w/ïïb° (4) ^A.B dO A f) dB 0/ f]8B dO A (T B° o A °CiB° (5) R Ea,B 8E a Ç)dB E/PiÔB dE A fl B° E A °CiB° (6) ôsw a r\ôB ôsw a n b" sw/ftdB sw A °f]B° dS A f] dB dS A C\B° S A °C\dB S/C\B° (7) (8) r se a ,b dSE A fl dB dSE A f)B° SE/ f| dB SE/f]B° (9) nw a Na^| Ëlf A nw a N A ne a • nw a N A ne a W A if > ' No a | W A wêq ; E A W A ss Ea 05 , > S A SE a SW A S A se a swv ^S A se a (a) (b) (c) For the direction relations between spatial objects with area object as a reference, we use projection-based models with neutral zone modeling direction relation (Fig 1). Given two objects A and B, we want to decide the direction of target object B related to the reference object A. First we obtain the MBR of object A and partition the plane around it into nine direction tiles based on the MBR of object A. We represent each direction tile as a spatial object. Eight of nine direction tiles (NW A , N A , NE A , E A , SE a , S a , SW a , W a ) are open rectangles. 0 A is close object. Here open objects mean those geometries whose boundaries are partially defined, or extending beyond the data window, or Fig. 1 the 8-directions model with area object as reference From the 4I topological matrix, we have tree rules: Rule 1. For one direction region, If there are no none-empty intersections or only ana is not empty in the 4I matrix, then the target object is not in this direction region. For example, B is not in the direction region NW A (Fig 1a). Rule 2. For one direction region, If the intersection of ° na

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