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Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects
Baltsavias, Emmanuel P.

International Archives of Photogrammetry and Remote Sensing,Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999
Figure 1: a) Aerial image b) Edge extraction result. Grey
level edges obtained with FEX. Observe the large number
of small edges in the textured areas, c) Texture edges from
(Shao and Forstner, 1994).
program FEX but with a newly developed filter bank. The
resulting multichannel image represents the scale charac
teristics of the local Autocovariance Function (SCAF) (cf.
Fig. 3). Thus, we apply FEX on a suitable representation of
texture instead of a grey level or color image for obtaining
texture edges.
We do not aim at a a complete representation of the tex
tures. However, we achieve a separation of neighboring
textured areas, that is sufficiently good for the interpreta
tion of aerial images.
Figure 2: Extension of FEX by the scale characteristics of
the local autocovariance function (SCAF).
After a normalization step, we combine the pyramid levels
for all three texture features in a multichannel image (sec
tion 4.4).
In the second step, we extract the texture edge (section5)
using the multichannel scheme known from our feature ex
grey level, multichannel
segmented image
e.g. 5 levels for Laplacian Pyramid p ... negative Hessian of
autocovariance function
SCAF... scale characteristics
of autocovariance function
Figure 3: Process to obtain SCAF (scale characteristics of
the local autocovariance function) and the texture segmen
tation from a grey level or multichannel image using FEX.
We want to give an overview of the individual steps of our
texture edge extraction scheme (cf. Fig.3).
First, we derive the scale characteristics of the local auto
covariance function, (cf. section 4). This is the basic step
of our approach. These characteristics are derived in two
• the strength, direction and anisotropy of the texture are
derived from the square gradient of the image function
(4.2). They characterize the form of the local autocor
relation function. This way we obtain three features of
the image texture at the highest resolution.
• the spatial frequency of these features is then deter
mined using a Laplacian pyramid (4.3).
This section explains in detail the steps for derivation of the
scale characteristics of the local autocovariance function.
4.1 Stochastic image model
To characterize the textures we have used the following im
age model.
Starting from a fully partitioned image (I = (J™ x Si) into
m segments Si, we assume that the ideal image function
within the segments is a weak stationary process f t (r, c) ~
N(m,Ci), where m — const and Q is the covariance
matrix of the image pixels within the segments (r rows, c
columns). We assume the covariance matrix to be repre
sentable by a p. d. covariance function C(Ar, Ac), thus