Reconstruction

Two formulae:

• In general, no smallest shape containing a given pixel $\mathbf{x}$ $\Rightarrow$ we take a limit of gray levels as shapes decrease

 

 

• $u(\mathbf{x})\geq \lambda \Leftrightarrow \exists$ superior shape $S$ at level $\lambda$ containing $\mathbf{x}$ such that if $I$ is an inferior shape at level $\lambda, I\subset S \Rightarrow \mathbf{x}\not\inI$. This gives a reconstruction of $[u\geq\lambda]$.

Summer School on Mathematical Problems in Image Processing, Trieste, Italy, September 4th-18th 2000