THE SUFFICIENT AREA CONDITION OF AN OBJECT FOR A SPOT- DETECTOR 
F. Cheng* and Ph. Hartl 
Institute for Navigation, University of Stuttgart, Stuttgart, Germany 
KEY WORDS: SPOT-pixel, spatial resolution 
ABSTRACT: 
Some objects can not be found or identified on a SPOT-image due to their too small areas. An Object on the ground 
must be large enough so that it can be detected vertically by a SPOT-detector and recorded as a complete pixel in a 
SPOT-image. This condition, defined as the sufficient area condition, has been not studied yet. In this paper the 
condition is theoretically analysed and quantitatively calculated. It may be expressed as follows: 1) the area of an object 
on the ground must include an ellipse, whose long axis e, is in the direction with the greatest ground slope € and 
equal to 2R/ cos€ , and whose short axis e, is horizontal and equal to 2R; 2) if the ground is smooth (€ =0), the 
ellipse becomes a circle with the radius R. Here R is the diagonal length of a SPOT-image's pixel: 10/2 m or 20/2 m. 
1. INTRODUCTION 
Some objects can not be found or identified on a SPOT- 
image due to their too small areas. How large should the 
area of an object on the ground be, so that it can be 
detected at least by a SPOT-detector? Many people 
have met such a question in their works, especially in 
classifying or identifying objects on satellite images. 
Some of them hope to use satellite data with smaller pixel 
size or higher spatial resolution in order to obtain better 
results (Begni 1988, Dowman et al 1989, Moore et al 
1989, Jensen et al 1993, Manavalan et al 1993, Cheng et 
al 1995, Hartl et al 1995). 
There are two types of SPOT-images: vertical and oblique 
viewing images. Here only the former is discussed. The 
area of an object on the ground, which makes the object 
to be vertically detected at least by a SPOT-detector and 
be recorded as a complete pixel in a SPOT-image, is 
defined as the sufficient area condition. This paper shows 
the study of the condition and gives its mathematical 
expression. 
2. THE SUFFICIENT AREA CONDITION 
ON THE SMOOTH GROUND 
2.1 Position change of grids 
The figure 1 shows a square grid, which represents the 
corresponding area of a SPOT-detector on the smooth 
ground. Here we call it a SPOT-detector-grid (G- side 
length; d- diagonal length). Suppose that there is a 
circular object C, with the radius R on the ground. On 
the object a Cartesian coordinate system oxy is set up, 
whose origin o is at the center of the object and whose y- 
axis points north. Suppose that the center of a SPOT- 
detector-grid (p) is just overlapped with the object's center 
and f,, f,, ...f, are the eight neighbour grids of the grid 
p (figure 2). In this situation the object can be detected at 
"Present address: Company for applied Remote Sensing 
(GAF), 80636 Munich, Germany 
36 
least by a complete SPOT-detector-grid, if its radius R 
meets the following condition: 
gaz 1 
2 t (1) 
This is a special situation. But it may be supposed that 
the grids' position shown in the figure 2 is the original 
position. The position of the grids on the ground generally 
changes after a revolving period of the satellite. The 
figure 3(1) shows such a change. The grids have left the 
original position in a new revolving period. We may only 
consider the position change of the grid p instead of all 
the grids, because the relative position between the 
different grids is fixed. The position change of the grid p 
shown in the figure 3(1) can be resolved into a shift and a 
turn around the origin o. i) The grid p shifts first from o to 
p' and then ii) it turns around o from p' to p" (figure 3(2)). 
In fact any position change of the grids can be resolved 
as above. 
Suppose that the grid p shifts first from the original 
position (0,0) to an other position (xp, yp) (figure 4(1)). The 
shift amount is equal to the distance between the two 
points. We define X as the component of this distance 
on the x-axis and Y as its component on the y-axis. Then 
the following equalities are tenable: X =Ixp| and Y =lypl. 
In the situation shown in the figure 4(1) the object C, can 
be detected by a complete SPOT-detector-grid, if its 
radius R meets: 
a: 22 ap 
R=] Cre ++) | (2) 
See the figure 4(2). The grid p turns around o in the 
next revolving period of the satellite. Then R should 
meet: 
2 
[ a ie. ti 
R= (X3 cos p + +3) sin p | + 
2 
are) X42) si 
( 3 cos p — ( +2) sin p 
2 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996 
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