This paper introduces a new empirical formulation of the clear-sky intensity distribution based on images acquired with a sky imager developed at the PROMES-CNRS laboratory (Perpignan, France). Both the formulation and image processing methodology are detailed and stand for key steps in the development of a high quality cloud detection algorithm. The work presented in this paper is a part of a research project which aims at improving solar plant control procedures using direct normal irradiance forecasts under various sky conditions at short-term horizon (5-30 min) and high spatial resolution (similar to 1 km(2)). Modelling the clear-sky intensity distribution in real time allows clear-sky images to be generated. These clear-sky images can then be used to remove the clear-sky background anisotropy on images and so improve cloud detection algorithms significantly. Cloud detection is essential in short-term solar resource forecasting. The new formulation is especially designed for improving performance of the existing models in the circumsolar area. When tested over more than 2200 clear-sky images, corresponding to a solar zenith angle spanning from 24 degrees to 85 degrees, the new formulation outperforms a standard approach based on the All-Weather model (Perez et al., 1993) by 15% on the whole sky and more than 20% in the circumsolar area. Application of the methodology for the real-time cloud detection purpose is discussed at the end of the paper. (C) 2015 Elsevier Ltd. All rights reserved.