Maximum A Posteriori Texture Boundary Detection

Imagine we have observed some pixel intensities $x^{n},n=1,...,N$ along a scanline. We denote these observations by a vector $X$. We wish to find the position $c$ on the scanline for which the posterior probability of the sets of texture descriptors $S=\{ s_{i}\mid i=1,..,I\}$ on both sides are maximum. If we assume a prior texture for both sides then, the a posterior probability of $S$ on both sides given the observation vector $X$ and the prior textures $T_{1}$ and $T_{2}$ be expressed as follows.

$$\begin{array}{c} \max_{c}P(S_{1},S_{2}\mid X,T_{1},T_{2})=\m... ...{c},T_{1})\, P(S_{2}\mid X_{c+1}^{N},T_{2})\right\} \end{array}$$ (1)

These probability terms can be calculated in an efficient way along the vector of observations using a recursive algorithm as demonstrated in the following.