数字图像中的Delta复合体。近似图像对象
Delta Complexes in Digital Images. Approximating Image Object Shapes
摘要：
在数字图像的计算拓扑中，单纯形在近似图像对象形状时被Delta集代替。为了简单起见，单纯形和Delta集被限制在欧几里得平面上。平面单形可以是顶点、线段或填充三角形。在图像形状的研究中，平面Delta集是有序单纯复形的序列。基本方法是通过将包含形状的图像区域分解为称为Delta复合体的Delta集合的组合来近似图像形状。这种方法的图像形状的动机是容易与三角洲复盖的形状可以测量和比较。一些直接相关的形状分析的基本结果也给出了在三角洲复杂的逼近。
英文摘要：
In a computational topology of digital images, simplexes are replaced by Delta sets in approximating image object shapes. For simplicity, simplexes and Delta sets are restricted to the Euclidean plane. A planar simplex is either a vertex, a line segment or a filled triangle. In this study of image shapes, a planar Delta set is a sequence of ordered simplicial complexes. The basic approach is to approximate an image shape by decomposing an image region containing the shape into combinations of Delta sets called Delta complexes. This approach to image shapes is motivated by the ease with which shapes covered by Delta complexes can be measured and compared. A number of basic results directly related to shape analysis are also given in the context of Delta complex proximities.
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