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During the evolution from cognitive radio to cognitive networks, the environment cognition extended from wireless environments to network and user environments. To understand the basic theory of Local Multi-Domain Cognition (LMDC), and to provide a theoretical basis for further study in cooperative multi-domain cognition and initiative multi-domain cognition, the LMDC is investigated in this paper. A Local Single-Domain Cognitive (LSDC) approach is first proposed based on multidimensional edge detection theory. This approach can divide the parameter space that describes the single-domain environment into different areas, and can represent each area with an identifier. Using this as a foundation, the single-domain environment is extended to multi-domain environments, and an LMDC approach is presented to describe the LMDC environment. The paper concludes by introducing two examples and the corresponding analysis to illustrate the feasibility of the proposed LMDC approach.