Virtual double-sided image probing: A unifying framework for non-linear grayscale pattern matching

This paper focuses on non-linear pattern matching transforms based on mathematical morphology for gray level image processing. Our contribution is on two fronts. First, we unify the existing and a priori unconnected approaches to this problem by establishing their theoretical links with topology. Setting them within the same context allows to highlight their differences and similarities, and to derive new variants. Second, we develop the concept of virtual double-sided image probing (VDIP), a broad framework for non-linear pattern matching in grayscale images. VDIP extends our work on the multiple object matching using probing (MOMP) transform we previously defined to locate multiple grayscale patterns simultaneously. We show that available methods as well as the topological approach can be generalized within the VDIP framework. They can be formulated as particular variants of a general transform designed for virtual probing. Furthermore, a morphological metric, called SVDIP (single VDIP), is deduced from the VDIP concept. Some results are presented and compared with those obtained with classical methods.