Morphological Modeling of Position-Based Spatial Relationships

Spatial information plays a very important role in image understanding. Fuzzy mathematical morphology provides an effective basis for extracting binary and ternary spatial relationships by creating a fuzzy landscape where the value at each point corresponds to the relationship degree according to its position with respect to the reference object(s). We improve existing morphological approaches in terms of flexibility and efficiency while also obtaining more intuitive results. Our morphological definitions are sensitive to relative visibility of areas based on partial occlusions, and can also cope with the cases where some objects extend significantly differently relative to others. We show the effectiveness of the proposed definitions using synthetic and real images.