© 2021, The Author(s).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.