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During the evolution from cogni tive radio to cognitive networks, the environ ment cognition extended from wireless envi ronments to network and user environments. To understand the basic theory of Local MultiDomain Cognition （LMDC）, and to provide a theoretical basis for further study in cooperative multidomain cognition and ini tiative multidomain cognition, the LMDC is investigated in this paper. A Local Sin gleDomain Cognitive （LSDC） approach is first proposed based on multidimensional edge detection theory. This approach can divide the parameter space that describes the sin gledomain environment into different areas, and can represent each area with an identifier. Using this as a foundation, the singledomain environment is extended to multidomain en vironments, and an LMDC approach is pre sented to describe the LMDC environment. The paper concludes by introducing two ex amples and the corresponding analysis to il lustrate the feasibility of the proposed LMDC approach.