Image edge detection is an important tool of image processing, in which edge representation and extraction with uncertainty is one of key issues. Based on the physics-like methods for image edge representation and extraction, a novel cognitive physics-based method with uncertainty is proposed. The method uses data field to discover the global information from the image and then to map it from grayscale space to the appropriate potential space. From the point of view of the field theory, the method establishes an extensible theoretical framework and unifies the existing physics-like methods. On the other hand, the method defines the ascending half-cloud to construct the internal relationship between the range of cloud uncertainty degree and the edge representation and extraction. Finally, the method achieves image edge representation and extraction with uncertainty using the cognitive physics. The time complexity of the proposed algorithm is approximately linear in the size of the original image. It is indicated by the quantitative and qualitative experiments that the proposed method yields accurate and robust result, and is reasonable and effective.