Image matting and segmentation, which are used to extract a foreground object from the background, are primary techniques for digital image and video editing. In digital matting, the transparency of the foreground object is considered, while segmentation performs a rigid extraction of the object. Recently, several algorithms for matting and segmentation problems have been proposed and have provided high-quality results. In this paper, we propose a unified formulation for image matting in the framework of the method of Quantification IV based on a review of the previous studies from this framework. Our method also utilizes discriminative information provided by a user (a few strokes drawn by the user). The experimental results show a favorable matting performance.