ie, Integrat-
Techniques
nd Machine
01.1944, 14-
Jo, Florida,
y Models to
onstruction,
Vol.14, n?2,
, Perceptual
ion and de-
n aerial im-
1derstanding
Kaufmann,
988
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ty of Photo-
R. Debrie,
o-adaptative
ational Con-
10, ITALY,
Fusion of
)etect Man-
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derstanding,
May 1993
COLOUR AERIAL IMAGE SEGMENTATION USING A BAYESIAN HOMOGENEITY PREDICATE AND MAP
KNOWLEDGE
F. Quint
S. Landes
Institute for Photogrammetry and Remote Sensing
University of Karlsruhe
76128 Karlsruhe, Germany
quint@ipf.bau-verm.uni-karlsruhe.de
Commision Ill, Working Group 2
KEY WORDS: Colour, Aerial, Image, Model, Vision, Colour Aerial Image, Aerial Image Segmentation, Bayesian Model
ABSTRACT
In this article we present a homogeneity predicate for segmentation purposes. It is based on the probability of a pixels to fulfill
the model assumptions for a region. For some practical relevant models, a closed formula for this probability is given. The
homogeneity predicate is used in a region growing procedure to segment colour aerial images. In this application, estimates for
the position of initial seed regions and the model type to be used are extracted from topographical maps.
KURZFASSUNG
In diesem Artikel wird ein Homogenitätsprädikat für die Segmentierung von Bildern vorgestellt. Es beruht auf der Wahrschein-
lichkeit für einen Bildpunkt, daB er den getroffenen Modellannahmen entspricht. Für einige praxisrelevante Modelle kann eine
geschlossene Formel zur Berechnung dieser Wahrscheinlichkeit angegeben werden. Das Homogenitáatsprádikat wird in einem
Fláchenwachstumsverfahren zur Segmentierung von Farbluftbildern verwendet. Schátzwerte für anfángliche Kristallisations-
punkte des Fláchenwachstumsverfahrens und die zu verwendenden Modelle werden aus Karten gewonnen.
1 INTRODUCTION
Segmentation of images into physically meaningful regions is
one of the most often addressed problems in computer vision
literature. The periodically appearing review articles give a
good overview of the domain, see e.g. (Haralick and Shapiro,
1985), (Pal and Pal, 1993).
Haralick and Shapiro (Haralick and Shapiro, 1985) catego-
rize the different segmentation procedures according to the
control algorithm they use, in:
e measurement space guided spatial clustering,
e region growing,
e spatial clustering and
e split and merge schemes.
In (Pal and Pal, 1993) the different image segmentation tech-
niques are reviewed according to the used homogeneity pre-
dicate. It is made distinction between:
e gray level thresholding,
e iterative pixel classification,
e surface based segmentation,
e segmentation of colour images,
e edge detection based approaches and
e methods based on fuzzy sets.
The method presented in the current article is a region
growing scheme. As homogeneity predicate we use the
a-posteriori probability for the features of an image pixel to
fulfill an a-priori model of a region. Similar approaches for
the homogeneity predicate, embedded in different segmenta-
tion schemes have also been made in (Silverman and Cooper,
1988), (LaValle and Hutchinson, 1995).
In section 2 we describe our model assumptions. A closed for-
mula for calculating the probability of homogeneity is derived
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
in section 3. After a brief look at computational issues in sec-
tion 4, we give in section 5 an example for a simple, planar
model. Finally we show how the developed procedure can be
used for segmenting colour aerial images. Initial seed regions
for the region growing scheme and information on the model
type to be used are extracted from map knowledge.
1.1 Segmentation procedure
Our definition of segmentation follows (Pavlidis, 1977): it
is the partition of the image in pairwise disjunct regions R,,
which, in their union cover the whole image. In order to assign
a pixel to a region, it must fulfill two conditions:
e it must be neighbour with at least one other pixel of
the region (connectedness condition)
e a homogeneity predicate between the pixel and the re-
gion must evaluate to true (homogeneity condition)
We implement our segmentation procedure as a region
growing scheme: For each pixel of the image which is not
already marked as belonging to a region and which is neigh-
bour to at least one region a homogeneity predicate is tested.
The pixel is marked as belonging to the region for which the
tested predicate evaluates to true. The procedure stops when
all pixels are assigned to a region. ;
The homogeneity predicate is calculated using the a-posteriori
probability of a pixel for belonging to the current region. This
probability is calculated according to a model described in the
following section. We calculate the a-posteriori probability for
all regions, which the pixel is neighbouring. The homogeneity
predicate evaluates to true for the region with the highest
probability.
2 THE MODEL
2.1 Image formation
For simplicity of expression, we will call the quantities forming
the image light intensities. The presented scheme however is
