This paper provides a theoretical characterization of monotonically connected image surface regions, called slope regions. The characterization is given by several topological properties described in terms of critical points relative to the region. We formally prove the necessary and sufficient conditions that a region needs to satisfy to be a slope region. We also provide a prototype of slope regions which is general and contains, as particular cases, the prototypes studied and published in previous conference papers.

中文翻译：

---

表征斜坡区域

本文提供了单调连接的图像表面区域的理论表征，称为斜率区域。表征由几个拓扑属性给出，这些拓扑属性根据相对于该区域的临界点进行描述。我们正式证明了一个区域成为斜坡区域需要满足的充要条件。我们还提供了一个斜坡区域的原型，它是通用的，并且包含在以前的会议论文中研究和发表的原型作为特殊情况。