Modification in the Contour Relaxation Model
It was shown in section 2 (Figure 1) how application of the contour
relaxation resulted in partitioning of the sky region into a number of
smaller regions (resulting in false contours). We propose a modification in
the contour relaxation model in order to avoid such an image partitioning.
The modification involves introduction of a bias in the likelihood function
which suppresses the false contours formation process by adjusting the
likelihood function ratio according to the change in the region size.
The bias is modeled by the following function:
f(s)=exp(-w(<>sjk/(sjo+<>sjk)))
where sjo is the jth region size at the zeroth iteration, <>sjk is the change in the jth region at the kth iteration of the relaxation.
Instead of maximizing the ratio r(Y,Q) of the likelihood function p(Y,Q),
a new ratio r(Y,Q,s), incorporating the bias f(s) in the model is maximized,
r(Y,Q,s) = r(Y,Q) * f(s)
Where r(Y,Q) denotes the ratio of the likelihood function
p(Y,Q).