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.

多数图像可近似视作分块均匀的拼接色块。各色块于过渡区域相接，此类过渡区域呈现模糊的带状几何形态。这类边界有时会模糊消散，随后又重新显现，进而形成可部分融合相邻色块的‘衔接通道’。此类结构在绘画技法专著中已有广泛探讨。素描创作中亦存在类似效果（轮廓模糊、衔接通道）。过渡区域的特征包括宽度、锐度与幅度——此处幅度指两侧色块间的对比度。此外，过渡区域还具备多样的纹理结构。我们针对此类过渡现象提出一套形式化理论。图像可被理解为过渡区域的叠加组合。可通过对过渡区域的选择性处理实现图像风格的调整。该理论在形式上与图像处理领域的技术术语‘边缘（edges）’理论相似，但二者语义存在本质差异。我们将该理论作为一套形式化框架，旨在以结构化的方式，对‘边缘质感（edge qualities）’——这一由画家使用、与图像处理中‘edge’的含义毫无关联的术语——展开有理有据的探讨。