Generalized hit-miss operators

The morphological operations of a hit-miss transform opening and closing are generalized in a number of ways. The new operations have been applied to a variety of binary image analysis problems that involve pattern detection and reconstruction. Generalized openings are developed by replacing erosions with hit-miss transforms. These new openings are shown to be anti-extensive idempotent and center-independent. Similarly generalized closings are developed and related to openings by duality. Additionally the hit-miss transform is further generalized by replacing the erosions with blur and rank order transforms in order to improve the robustness of pattern matches. The set of invariance properties of these new transforms can be widened by forming generalized openings from them.