In this paper, results of phychovisual studies of the human visual system are discussed and interpreted in a mathematical framework. The formation of the perception is described by appropriate minimization problems and the edge information is found to be of primary importance in visual perception. Having introduced the concept of edge strength, it is demonstrated that strong edges are of higher perceptual importance than weaker edges (textures). We have also found that smooth areas of an image influence our perception together with the edge information, and that this influence can be mathematically described via a minimization problem. Based on this study, we have proposed to decompose the image into three components: (i) primary, (ii) smooth and (iii) texture, which contain, respectively, the strong edges, the background and the textures. An algorithm is developed to generate the three-component image model and an example is provided in which the resulting three components demonstrate the specific properties as expected. finally, it is shown that the primary component provides a superior representation of the strong edge information as compared with the Laplacian-Gaussian Operator scheme which is a popular edge extraction method.