Statistical analysis of space-varying morphological openings with flat structuring elements

The statistical behavior of a special type of morphological operation, the space-varying opening, is analyzed and investigated. The major distinction between the space-invariant morphological operation and the space-varying one is that the structuring element corresponding to each position in the space-invariant operation is the same, but the structuring element corresponding to each position in the space-varying operation may be different. A regular statistical analysis method, which was originally designed for the analysis of the space-invariant opening, is applied and generalized to the analysis of the space-varying one. For the filtering of a noisy step edge, some comparative analytic results are obtained revealing that edge-preserving ability can be improved by the use of the space-varying opening.