estimated. 
In this paper we explore the matching problem based on featu- 
res. For feature extraction we use the point operator proposed 
by Fórstner (1987, 1989). The points selected in the different 
images have to be matched e.g. to solve the problem of point 
transfer or the problem of DTM reconstruction. Today image 
analysis and matching are based on pyramids and some strate- 
gies, which guide the process usually from coarse to fine resolu- 
tion (for examples cf e.g. Ackermann and Hahn, 1991). For the 
analysis of the single image, tracking of features through scale 
space is proposed by Bergholm (1987).The scale space Witkin 
(1983) is a kind of an image pyramid which consists of an infi- 
nite number of smoothed image levels. The characteristic of this 
representation is that the scale (smoothness) parameter is conti- 
nuous which is of benefit for tracking. In the matching case, 
e.g. in DTM reconstruction, it is usual to work with standard 
image pyramids, almost with a Gaussian image pyramid. The 
smoothing levels of this pyramids are fixed and the spatial 
resolution between two consecutive levels decreases from the 
bottom to the top of the pyramid. In this case not the tracking 
idea is dominant but the questions due to approximate values, 
efficiency of the algorithm and reliability of matching are ad- 
dressed. 
The concept of this investigations and according to this the 
organization of the paper is as follows: (1) We want to find out 
characteristics of the point operator in scale space. This implies 
questions due to the tracking of the point location of the interest 
point from fine to coarse and vice versa. Moreover the signifi- 
cance of the selected features in scale is important. The example 
used in section 2 is a synthetic image. (2) The scale space 
tracking of features in real images is discussed in section 3. 
Influences due to physical (illumination, etc.) and geometric 
(perspective projection) aspects can be observed. Mainly the 
consequences for the image location of the features and for the 
stereo displacements are of interest. For the synthetic image as 
well as for the real images we want to restrict ourself to one 
dimension. The one-dimensional real signals are taken from a 
epipolar stereo pair. 
1.1 RELATED WORK 
Related work which has not been addressed up to now mainly 
concerns the representation and reasoning about features in scale 
space. Since the early days of computer vision it was quite clear 
that high-level processes need and have to use a lot of different 
knowledge for reasoning. For low-level processes such as edge 
detection a common belief was that they are simply data driven 
without use of explicit knowledge. This assessment today chan- 
ges. A lot of operators for edge detection have been proposed in 
parts but research has clearly demonstrated that the edge detec- 
ted by these techniques do not give satisfying results (Lu and 
Jain, 1992; Bergholm, 1987). Because of this the role of reaso- 
ning in low level processing comes into the center of interest. 
As one of the first Witkin (1983) analyzed thoroughly the be- 
havior of edges in scale space. He reflected work of Marr 
(1982), who argued "that physical processes act on their own 
intrinsic scales". A scale-structured representation, called the 
interval tree, he introduced to describe contours over scale. This 
organization characterizes the information over a broad range of 
scale, that means, between a coarse resolution level with a small 
number of edges and a fine resolution level with usually signi- 
ficantly more edges. This organization is expected to be useful 
Witkin for matching or object reconstruction tasks. The sym- 
bolic image description over scale is generated by the zero- 
crossings of a Laplacian of Gaussian (LoG) convolved image, in 
which the Gaussian c is addressed as scale. Three typical edge 
behaviors in Gaussian scale space were observed by researchers: 
(1) The locations of edges in filtered images using different 
scale parameters can (and in general will) be different. (2) in 
scale space zero crossing occurring at finer scales can disappear 
at coarser scales. (3) Spurious edges are those that occur at a 
coarser scale but have no corresponding edges at a finer scale. 
For more details cf. Lu and Jain (1992). This two authors pre- 
sented the most sophisticated algorithm up to now, called RESS, 
which stands for reasoning about edges in scale space. The 
knowledge about edge behavior in scale space is explicitly 
formulated in 35 rules and is used in RESS to select proper 
scale parameters, to correct dislocation of edges (1), to recover 
missing edges (2), and to eliminate noise or false edges (3). The 
separation of significant edge information from noise mainly has 
been also the aim of Bergholm (1987) in his multiscale tracking 
procedure, called edge focusing, as well as Canny (1986), who 
proposed a multiscale edge detector. 
Finally we want to address the work of Heikkilà (1989), which 
has some similarity to our investigation because he used also 
the Fórstner point operator. In the one-dimensional case the 
point operator coincides with an edge detector. The estimated 
point position locates the edges with subpixel accuracy, at least 
in theory. Therefore the estimation of the edge location in scale 
space will be interesting. In the paper of Heikkilä the properties 
of the operator by varying the scale parameter of the integrating 
window are investigated. The integration works on the squared 
gradient image. Consequently the interest operator is a nonlinear 
edge operator. So far this is presumably the main difference to 
other edge operators like the linear LoG operator mentioned 
before. Our interest is not the problem of a varying window 
size. We investigate the behavior of the operator applied to a 
series of Gaussian smoothed images. In the 2 D case the opera- 
tor can be formulated as 
[XG,. * f) VG, * f) * G, (1) 
With o, the scale space image of f(x,y) is generated, whilsto, 
is responsible for the size of the weighting in the window. the 
dyadic product vv" indicates the nonlinearity of the operator. If 
C, is constant and o, varies mainly the following characteristic 
for edges can be observed: 
With increasing c, the number of edges decreases, i.e. the 
edges fuse or disappear with coarser scale o,. Just invert is the 
situation when the scale space parameter c, varies and o, is 
constant: 
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