This paper describes a robust method for estimating, in a reliable manner, the illumination distribution of a real scene from shadows in a given image. In general, shadows in a scene are caused by the occlusion of incoming light; image brightness inside shadows have a great potential for providing distinct clues to the illumination distribution of the scene. Taking advantage of this fact, we recently proposed to estimate the illumination distribution of a real scene from a single image of the scene. The proposed method has been applied successfully to real images with complex illumination distributions. Nevertheless, it was found that, under certain circumstances, the method sometimes failed to provide a correct estimate of illumination distribution. Those failures stem from the fact that the method does not take into account several factors regarding the stability of illumination estimation. The purpose of this study is to analyze how much information is obtainable from a given image about the illumination distribution of the scene. In particular, we carefully examine the source of instability of using shadows obtained from a single image for the estimation in several aspects: blocked view of shadows by the object; limited sampling resolution for image brightness inside shadows; and the appropriate light model to approximate the illumination distribution of the scene. Based on this analysis, we propose a new method that guarantees to estimate the illumination distribution of a scene in a reliable manner regardless of types of input images such as the shape of an occluding object or a camera position.