Research on the application of relaxation technology to the extraction of linear feature from satellite image
Establishment of relaxation model
To a hazy object group in science, we often we often use the relationship among objects to reduce and eliminate the in distinction. Relaxation is a process to reduce the distinction of the probabilistic label of object using the relationship between their compatibility.
Relaxation processing goes ahead with the help of object labels. Under the suitable definition of compatibility relationship between objects labels, when relation is in use, some labels are strengthened, other are weakened, in the convenience of establishment model of the following labels are drawn.
If a=[a
1,a
2,a
3…………….a
n) represents object group A=[
l1,
l2,
l3,……….
lm} represents label group with certain explanation to objects. In terms of application of curve enhancement, object group represents every image point, the label meaning certain explanation of point represents parts of a curve with certain direction or not. Every probability P
i(
l) is corresponding to each label, and they satisfy the following conditions :
Eq.1
where P
i(
l) represents the
probability estimate of object a
i with labe
l..
Li with label represents the label group of object a
i
Two ways are used in the application of neighbour information. They are the choice of neighbour field structure and adjustment to the result of detection. Besides setting up neighbour relationship on object group, the relaxation process can also change the probability estimate by means of iteration.
Depending on compatibility coefficients, Rosenfield's article in 1976 explained the following adjustment of probability with specific deduction and discussion.
Eq.2
Where q
ik (
l) represents adjustment of probability P
ik (
l) to probability P
ik+1 (
l). It is defined as neighbour label probability weight's sum regarding compatibility coefficients as weight.
That is :
Eq.3
where coefficient d
ij represents weight coefficient when object a
i influences on object a
j and it satisfied
Sd
ij =1
Generally speaking the final probability distribution of label collections not only depends on the initial probability distribution, but also depends on the compatibility coefficient of labels. Relaxation process goes with iteration by the aid of above means until label probability reaches certain limitation.
The limitation of probability is one which represents clear signal, the limitation of probability is 0 which represents indistinctabel signal. In common conditions, the final probability should belong strictly to district (0,1).
