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 
traction. 
grey level, multichannel 
image 
r 
A 
FEX 
V 
y 
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. 
3 OVERVIEW 
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 
steps: 
• 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). 
4 SCALE CHARACTERISTICS OF LOCAL 
AUTOCOVARIANCE FUNCTION 
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