Next: Results for thin network
Up: Roads Extraction using a
Previous: Data model for extracting
The different movements defining the proposal
Simulation of Candy model
RJMCMC dynamics :
adding, deleting, moving segments in the image. The movements (the
transition kernels) need to guarantee :
- the irreducibility, the aperiodicity and the
reversibility of
the Markov chain
- the computation of the acceptance ratio must be possible
Some movements :
birth and death of a free segment
birth and death of a simple connected segment
birth and death of a double connected segment
modifying the orientation of a single or simple connected segment
modifying the length of a single or simple connected segment
modifying the position of a single connected segment
modifying the position of a simple connected segment
Example of the acceptance ratio
Birth and death of a free segment :
.
Let be Pn the probability to choose the birth of a free segment
and Pm the probability to choose to kill one.
The acceptance ratio is :
![\begin{displaymath}R=\frac {f(S^{\prime})Q(S^{\prime} \rightarrow S)}{f(S)Q(S \rightarrow S^{\prime})}
\end{displaymath}](img63.gif) |
(22) |
We have :
![\begin{displaymath}Q(S^{\prime} \rightarrow S)=P_{m} \times \frac{1}{n_{d}+1}
\end{displaymath}](img64.gif) |
(23) |
nd is the number of free segments in the configuration S.
And :
![\begin{displaymath}Q(S \rightarrow S^{\prime})=P_{n} \times \frac{1}{\nu(T)} \times
\frac{1}{2\pi(l_{max}-l_{min})(w_{max}-w_{min})}
\end{displaymath}](img65.gif) |
(24) |
We obtain :
![\begin{displaymath}R=\frac{P_{m}}{P_{n}} \times \frac{2\pi\nu(T)(l_{max}-l_{min})(w_{max}-w_{min})}{n_{d}+1} \times \frac{f(S \cup \zeta)}{f(S)}
\end{displaymath}](img66.gif) |
(25) |
Realizations of the Candy model
Figure:
Realizations of the prior model with different densities :
a)
b)
a)
![\includegraphics[width=8cm]{/u/biotite/0/ariana/rstoica/DOCS99/FIGURES/PRIOR/prior_25.eps}](img67.gif) |
b)
![\includegraphics[width=8cm]{/u/biotite/0/ariana/rstoica/DOCS99/FIGURES/PRIOR/prior_50.eps}](img68.gif) |
|
Statistics of the Candy model
Figure 10:
Statistics of the segments
|
Next: Results for thin network
Up: Roads Extraction using a
Previous: Data model for extracting
Radu Stoica
2000-04-17