This article presents a reformulation of the Grey Edge framework for colour constancy. Colour constancy is the ability of a visual system to perceive objects` colours independently of their scenes` illuminants. Colour constancy algorithms try to estimate the colour of an illuminant from image values. This estimation can later be used to correct the image as though it were taken under a white illuminant. The modification presented allows the framework to incorporate image-specific filters instead of the commonly used edge detectors. A colour constancy algorithm is proposed using PCA and FastICA linear component analyses methods for the construction of such filters. The results show that the proposed method improves the accuracies of the Grey Edge framework algorithms whilst on the other hand, achieving comparable accuracies with the state-of-the-art methods, but improving their time efficiencies.