Texture Boundary Detection by Maximizing the distance between two textures

We can restate the problem of texture boundary detection in the context of pattern recognition. This provides us with a rich set of tools and methods to verify and analyze the results. This can be achieved by maximization of the difference between the textures on both sides of the potential boundary along the scanned observations vector $X$. This yields the best estimate of the boundary $c$ which maximizes the distance between the texture on both sides, i.e. $\max_{c}diff(T_{1},T_{2}\mid X)=\max_{c}diff(P(s_{i}\mid X,T_{1}),P(s_{i}\mid X,T_{2}))$. In the case where we look for the boundary of a known texture $T$, this maximization should be subject to the constrain that $diff(P(s_{i}\mid X,T_{1}),P(s_{i}\vert T))$ is minimum.