Trajectory-Based Morphological Operators: A Model for Efficient Image Processing

Table 1

Characteristics of the algorithms based on classical mathematical morphology versus the morphological trajectory model.

	Classical morphology	Morphological trajectory model
Application space	Finite group of pixels as a discretization of Euclidean space	2D Euclidean space (extensible to 𝑛-D Euclidean space)
Objects	Based on a complete image	Based on the boundary of each object (discrete/continuous)
SEs	Group of pixels	Geometric representation of the frontier
Method	On each pixel it operates in a neighborhood environment defined by the SE	The minimum distance of the SE center is calculated in a direction ^→𝑣 on a trajectory defined by Γ(𝑘)
Result	Erosion/dilation as group of pixels	Frontier points of the erosion/dilation operation