Relations between the statistical regularities of natural images and the response properties of the early visual system

Natural images are not random; instead, they ex- hibit statistical regularities. Assuming that our vision is designed for tasks on natural images, computation in the visual system should be optimized for such regularities. Recent theoretical investigations along this line have provided many insights into the visual response properties in the early visual system. In this article we review both the known statistical regularities of natural images, the extent to which low-level vision might be adapted to them, and the recent development in theoretical models to explain this relationship. Natural images are highly variable. When we look at the texture of natural surfaces like tree bark, we immediately recognize it as such in spite of large variations in the actual images that fall on our retina. In order to accomplish this feat, our visual system must be able to pool the natural range of variability and to recognize an image as an instance of the same image type. Thus an important part of vision involves capturing the statistical variation of natural images. At the same time, natural images are very specific. We know how different they are from random images. The characteri- zation of their statistical regularities has been an important research topic in science and engineering fields. We can state its ultimate goal as developing a probability model that generates images indistinguishable from natural images. We are still far from this goal, although our knowledge of natural images has been increasing. An important motivation of such an investigation is to better understand how our visual system codes visual information. Information theory states that the most statistically efficient codes are those that best capture the statistical regularities of the data. Because biological systems are under strong evolutionary pressure, it is hypothesized that the codes they use are highly efficient. Furthermore, knowledge of the statistical regularities of the data allows the system to perform important visual tasks such as finding interesting features and filling in missing information. More generally, the questions we need to answer are: what are the computational objectives of the early visual system, what are the computationally relevant biological constraints, and to what extent can the response properties be explained in relation to the statistical regularities of their input. In this article we address side by side what we know about the statistical regularities of natural images and how the early visual system (low-level vision) can be explained in terms of them (recent reviews on this subject can be found