Boundaries, Transitions and Passages

Many pictures are approximately piecewise uniform quilts. The patches meet in transitional areas that have a vague, ribbon-like geometry. These borders may occasionally get lost and sometimes pick up again, creating a 'passage' that partly blends adjacent patches. This type of structure is widely discussed in treatises on painting technique. Similar effects (lost outlines, passages) occur in drawing. The border regions are characterized by width, or sharpness and amplitude - which is the contrast between the patches on each side. Moreover, border regions have various textural structures. We propose a formal theory of such transitions. Images can be understood as superpositions of border areas. Stylistic changes can be implemented through the selective treatment of borders. The theory is formally similar to, though crucially different in meaning from, the theory of 'edges' (a technical term) in image processing. We propose it as a formal framework that enables principled discussion of 'edge qualities' (a term used by painters in a way unrelated to the use of 'edge' in image processing) in a well-structured manner.