If there are multiple salience maps obtained as a result of different threshold operations, how can final results be obtained for each object in the image based on entropy?
It is possible to do what you want using the neighbourhood approach to selecting salient subimages. The trick is to start with an image $X$ of interest, select a point $x$ of interest in $X$ and find the neighbourhood of the selected point using entropy as the feature of the selected point Sx$ and finding all points near the selected point, where each neighbourhood point $y$ a particular entropy such that the difference between the entropy of $x$ and the entropy of $y$ is less than or equal to a preset threshold, i.e.,
Let $\Phi(x)$ equal the entropy of $x$ in an image $X$ and compute $\Phi(y)$ (entropy of $y$ in Image $X$). Select $th$ (threshold), a real number. Let $N_{x,th}$ denote the neighbourhood of $x$ defined by
\[
N_{x,th} = \left\{d((\Phi(x),\Phi(y) < th: y\in X\right\}.
\]
Let $P(X), P(Y)$ denote the family of all subsets in $X, Y$, respectively. Let $Y$ be a second image. Then let the mapping $f: P(X\mapsto Y$ be defined by
\[
f(N_{x,th}) = N_{y,th}: d((\Phi(x),\Phi(y) < th.
\]
That is, the neighbourhood $f(N_{x,th})$ found in $Y$ will be salient with respect to entropy, since the entropy of $x$ in image $X$ will be close to the entropy of $y$ in image $Y$. This is so, since $f$ maps a neighbourhood in $X$ to a neighbourhood in $Y$ containing points with entropy levels similar to the entropy levels of points in the neighbourhood $N_{x,th}$ in image $X$.
This a start on the answer to the question for this thread.
This explains the solution precisely and very well.. Thank you so much
Dear Haris Ahmad Khan,
The approach to finding salient subimages that I suggested in my post, is part of what is known as the topology of digital images using a proximity space approach. For more about this, see
J.F. Peters, Topology of Digital Images. Visual Pattern Discovery via Proximity Spaces, Springer, 2014:
http://www.amazon.ca/Topology-Digital-Images-Discovery-Proximity/dp/3642538444
For more about the near sets approach in studying such things as digital images, you may find the following web page interesting:
http://en.wikipedia.org/wiki/Near_sets
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