Mathematical morphological operations of boundary-represented geometric objects
Mathematical morphological operations of boundary-represented geometric objects
复制标题
边界表示的几何对象的数学形态学运算
DOI：
10.1007/bf00119839
复制
发表时间：
1996
影响因子：
2
通讯作者：
R. Haralick
中科院分区：
文献类型：
--
作者：
P. K. Ghosh;R. Haralick
具有乘除功能的整数系统与具有闵可夫斯基加法和分解功能的凸对象系统之间的相似性确实惊人。这种相似性也表明了一种将两个闵可夫斯基运算统一为一个运算的计算技术。为了将乘法和除法看作一个单一的运算，有必要将整数系统扩展到有理数系统。两个Minkowski运算的统一还要求普通凸对象域必须附加逆对象或负对象的概念。更有趣的是，否定宾语的概念允许进一步的统一。一个非凸对象可以被看作是普通凸对象和负对象的混合体，从而使得对凸对象和非凸对象采用完全相同的计算技术成为可能。我们表明，如果输入多边形和多面体由它们的斜率图表示来表示，则统一技术可以很容易地理解和实现。
The resemblance between the integer number system with multiplication and division and the system of convex objects with Minkowski addition and decomposition is really striking. The resemblance also indicates a computational technique which unifies the two Minkowski operations as a single operation. To view multiplication and division as a single operation, it became necessary to extend the integer number system to the rational number system. The unification of the two Minkowski operations also requires that the ordinary convex object domain must be appended by a notion of inverse objects ornegative objects. More interestingly, the concept of negative objects permits further unification. A nonconvex object may be viewed as amixtureof ordinary convex object and negative object, and thereby, makes it possible to adopt exactly the same computational technique for convex as well as nonconvex objects. The unified technique, we show, can be easily understood and implemented if the input polygons and polyhedra are represented by theirslope diagramrepresentations.