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