2518 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 11, NOVEMBER 2002
Existential Uncertainty of Spatial Objects Segmented From
Satellite Sensor Imagery
Arko Lucieer and Alfred Stein
Abstract—This research addresses existential uncertainty of spatial ob-
jects derived from satellite sensor imagery. An image segmentation tech-
nique is applied at various values of splitting and merging thresholds. We
test the hypothesis that objects occurring at many segmentation steps have
less existential uncertainty than those occurring at only a few steps.
Index Terms—Existential uncertainty, satellite sensor imagery, segmen-
tation, spatial objects, visualization.
I. INTRODUCTION
Object-oriented approaches to satellite sensor image processing be-
come increasingly popular with the growing amount of high-resolution
satellite imagery. Segmentation techniques can help to extract spatial
objects from an image scene. Uncertainty will be present in any seg-
mented image and can have a significant effect on further image pro-
cessing steps. Therefore, existential uncertainty is of a major impor-
tance for spatial objects, expressing the uncertainty that an object, as
identified by a segmentation procedure, exists [1].
Image segmentation is primarily used to subdivide an image into
different segments. These segments may or may not correspond to
objects as observed in the terrain. Image segmentation is in a sense
related to spectral classification, which puts pixels into classes de-
fined either a priori or during classification. Segmentation differs
from classification, however, as spatial contiguity is an explicit goal
of segmentation, whereas it is only implicit in classification. Spectral
classification of satellite sensor images applied on a pixel basis ig-
nores potentially useful spatial information between pixels. Whereas
image classification has become a routinely applied method, image
segmentation never became very popular in earth observation appli-
cations. The main reason is that the spatial resolution of satellite
sensor imagery is a prime limiting factor for segmentation [2]. In-
creasing availability of high-resolution satellite sensor imagery, such
as acquired by the IKONOS satellite, however, requires additional
attention to uncertainty in segmentation procedures.
Quantification of existential uncertainty is essential to evaluate seg-
mentation quality. Recently, probabilistic and fuzzy techniques have
been used to quantify and model uncertainty in classification proce-
dures [2], [3]. This has mainly been applied on a pixel basis, and no
attention has been given to uncertainty related to image objects.
An essential step in image segmentation is its validation. The ex-
istence of objects, however, depends on the context of a study: for ex-
ample, topographical objects may differ from geological objects or land
cover objects. In this study, we take the approach that an object with a
high existential certainty corresponds to an object as represented on a
topographic map.
Besides quantification, visualization is important to communicate
uncertainty [4], [5]. Visualization allows the user to explore uncertainty
in spatial data [6], e.g., by animation or by linked views, and to review
effects of changing parameters during segmentation.
Manuscript received December 4, 2001; revised July 5, 2002. This work was
supported by the European Commission under Project FET14189 “REV!GIS.”
The authors are with the International Institute for Geo-Information Science
and Earth Observation (ITC), 7500 AA Enschede, The Netherlands (e-mail: lu-
cieer@itc.nl; stein@itc.nl).
Digital Object Identifier 10.1109/TGRS.2002.805072
The objective of this research is to quantify and visualize existen-
tial uncertainty of spatial objects derived from high-resolution satellite
sensor imagery with a split-and-merge image segmentation algorithm.
The study is applied on an IKONOS image of an agricultural area near
Enschede, The Netherlands. A topographic map is used to validate seg-
mentation results.
II. METHODS
A. Image Segmentation Using a Split-and-Merge Algorithm
Commonly, three approaches are distinguished toward segmen-
tation: edge-based segmentation, region-based segmentation, and
split-and-merge segmentation [7]. Split-and-merge segmentation,
as applied in this study, consists of a region-splitting phase and an
agglomerative clustering phase. In the splitting phase, the image B
is initially considered as a square block of pixel values with mean
vector M
B
and covariance matrix S
B
. The dimension is determined
by the number of bands in the image; in case of IKONOS this equals
four. This block is split into four square subblocks (B
1
, B
2
, B
3
, and
B
4
), characterized by vectors of mean pixel valuesM
B
,M
B
,M
B
,
and M
B
and covariance matrices S
B
, S
B
, S
B
, and S
B
in the
subblocks. To define homogeneity, we consider a threshold 
ms
for
the mean and thresholds 
ss
for the covariance matrix. These values
are chosen in advance and kept constant during segmentation. An
image block B is homogeneous if
jM
B
M
B
j < 
ms
; for i = 1; 2; 3; 4 (1)
and
jS
B
S
B
j < 
ss
; for i = 1; 2; 3; 4 (2)
and heterogeneous if one of these equations does not apply. Hetero-
geneous subblocks are split recursively until homogeneity occurs or
until a minimum block size of one pixel is reached. The resulting data
structure is a regular quadtree. In the clustering phase, adjacent block
segments are merged if the combined segment is homogeneous. The
homogeneity rules (1) and (2) are applied in a similar way. Thresh-
olds for mean and covariance matrix are denoted by 
mm
and 
sm
,
respectively [8].
B. Quantifying Existential Object Uncertainty
The final result of a segmentation procedure depends upon the
thresholds 
ms
, 
ss
, 
mm
, and 
sm
. For various thresholds, objects of
different size emerge. Small  values lead to small objects, whereas
large values result in large objects. Some objects are insensitive to
threshold values, whereas some objects disappear beyond a particular
threshold and others expand in size. We hypothesize that objects
emerging in a uniform shape irrespective of threshold values corre-
spond to real-world objects as represented on a topographic map.
Objects disappearing at a specific threshold have a high degree of
existential uncertainty and are called “unstable objects.” Objects that
remain the same at different segmentation levels are “stable” objects
and have a low degree of existential uncertainty.
To quantify existential uncertainty in a segmentation procedure,
ranges for the splitting thresholds 
ms
and 
ss
and merging thresholds

mm
and 
sm
are chosen. These ranges are divided into n steps. At
each step, object boundaries, in the form of segment edge pixels, are
determined. At step k, these boundary pixels are assigned the value
one and nonboundary pixels the value zero and are represented on
0196-2892/02$17.00 © 2002 IEEE