Dept. de Teoria del Senyal i Comunicacions, Univ. Politecnica de Catalunya, Barcelona.
IEEE Trans Image Process. 1995;4(8):1153-60. doi: 10.1109/83.403422.
This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.
这封通信涉及连通算子的概念。从作用于集合的算子的定义出发，展示了如何将其扩展到作用于函数的算子。通常，作用于函数的连通算子是一种变换，它扩大了由函数的平坦区域创建的空间分区。结果表明，从作用于集合的任何连通算子，都可以构造一个作用于函数的连通算子（然而，这不是生成作用于函数的连通算子的唯一方法）。此外，还以形式化的方式引入了金字塔的概念。结果表明，如果金字塔基于连通算子，则函数的平坦区域随着金字塔的层次增加而增加。换句话说，平坦区域是嵌套的。定义了重构滤波器，并介绍了它们的主要性质。最后，描述了连通算子的一些应用和使用平坦区域的示例。
