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.诸多图像近似呈现分段均匀的拼贴布块结构。这些块体在过渡区域相接，这类区域呈现出模糊的缎带状几何形态。此类边界有时会变得模糊消失，有时又会重新显现，进而形成可将相邻块体部分融合的“通道”。这类结构在绘画技法的专业论著中被广泛讨论。类似的效果（轮廓消失、过渡通道）也可见于素描创作中。边界区域的特征包括宽度，或是锐度与振幅——其中振幅指的是边界两侧块体之间的对比度。除此之外，边界区域还具备多样的纹理结构。我们针对这类过渡区域提出了一套形式化理论。图像可被理解为各类边界区域的叠加组合。可通过对边界区域的选择性处理来实现风格上的变换。该理论在形式上与图像处理领域中的“边缘（edges，专业术语）”理论相似，但二者的语义存在本质差异。我们将该理论作为一套形式化框架提出，其可让我们以结构化的方式，对“边缘质感（edge qualities）”展开严谨的讨论——该术语为画家所用，其含义与图像处理领域中“edge”的用法毫无关联。