Current Retinex-based image enhancement methods with fixed scale filters cannot adapt to situations involving various depths of field and illuminations. In this paper, a simple but effective method based on adaptive full-scale Retinex (AFSR) is proposed to clarify underwater images or videos. First, we design an adaptive full-scale filter that is guided by the optical transmission rate to estimate illumination components. Then, to reduce the computational complexity, we develop a quantitative mapping method instead of non-linear log functions for directly calculating the reflection component. The proposed method is capable of real-time processing of underwater videos using temporal coherence and Fourier transformations. Compared with eight state-of-the-art clarification methods, our method yields comparable or better results for image contrast enhancement, color-cast correction and clarity.