coarse DEM
ures or noise
, pronounced
! pronounced
ays found to
; problem, an
€ pairs based
feature level
lar line pairs,
n neighbour-
feature pairs
igh reliability
e refinement
n.
TION
rder operator,
string along an
with a gradient
10menon when
ch show up as
the properties
ar features are:
lley which is
rossing I(+) to
Laplacian filter
eak/valley and
alley which can
Fig. 1b. An
(GL) of the
the position of
nal rankorder
lL
(a) Linear feature string A,B,C,D along epipolar line
after applying conditional rankorder operator
|
II+1
ua jl
Li [s
FER RIT
(b) Result from convolution with gradient filter [1, -1, 0]
which indicates the position of linear features at zero crossing
Fig. 1: Linear feature detection with a gradient filter
and zero crossing
3. LINEAR FEATURES EXTRACTION BY STRING
MATCHING
After applying conditional rankorder operations to
remove minor features or noise, and a string of
pronounced linear features have been detected along
the conjugated epipolar lines, these are not always
found to correspond to each other because different
terrain situations give different reflections. To solve
this problem, an algorithm must be found to confirm
and extract the real corresponding feature pairs based
on the similarity assessment by the theory of minimum
cost sequence of error transformations (cost function
minimization).
There are two ways to assess the similarity measure by
using the cost function: distance measure approach and
conditional probability approach. The distance measure
could be the absolute differences of attributes of two
corresponding primitives, therefore, the distance
measure approach performs in a reasonable manner
with numeric attribute values and it is the reason why
we choose it as similarity measure. If the attribute
values of primitives are symbolic, such as straight or
curve for a line primitive, it is hard to justify the
assignment of the costs for different symbolic attributes,
then the conditional probability approach is more
suitable for applying [Boyer & Kak,1988].
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
The cost of error transformation is estimated in terms
of distance in characteristic space (attribute space).
The dimension of this characteristic space is determined
by the number of attributes of the primitives in the
property list. The property list consists of the attributes
of linear features such as position, amplitude and shape
of the peak/valley in intensity profile along the epipolar
line pairs [Lo,1989], and the orientation of linear
features [Kostwinder et 21,1988]. According to this
property list, a characteristic function (cost function) is
formed, which should be sensitive enough to measure
the similarity between two linear features. One
possibility is to use a string-to-string matching algorithm
which has been applied to seismic image skeletonization
[Lu,1982], bearing in mind that seismic waveforms can
more simply and more easily be defined than terrain
images. According to the reliability of attributes and
their major/minor contribution to measuring the
characteristics of linear feature, different weights are
assigned to the individual attributes in the cost
function, thus offering a criterion for correspondence
analysis.
We build up the cost function for estimation of the
"cost" of error transformation (we define the "cost" as
distance) between two peaks/valleyson R (right image)
and L (left image):
+W3*|SFp-SF, | + W,*|SBp-SB, |
The W; (the weight of attributes) can be assigned by
prior analysis or in an experiment by trial and error.
Using this cost function, we calculate the distance
d(R,L) (as a similarity measurement) between the first
linear feature of one epipolar line and all linear features
of corresponding epipolar lines, then between the
second feature and all features of corresponding
epipolar lines, and so on. For the conventional
matching strategy, the target area of the left image is
selected to search for the best match in the search area
of the right image only; the result may be different,
however, if the matching is from right to left. String
matching uses the mutual matching strategy, which
matches not only left to right but also right to left, and
then selects the minimum cost among them as the best
matching and extracts it. If we confirm the extracted
linear features again by checking the continuation of
linear features between neighbouring epipolar lines, the
reliability can be increased still more. Between
conjugated epipolar line pairs, the corresponding linear
feature can be extracted by string matching, which uses
the minimum cost as best matching. The extracted
