The visual system is able to recognize a scene based on a sketch made of very simple features. This ability is likely crucial for survival, when fast image recognition is necessary, and it is believed that a primal sketch is extracted very early in the visual processing. Such highly simplified representations can be sufficient for accurate object discrimination, but an open question is the role played by color in this process. Rich color information is available in natural scenes, yet artist's sketches are usually monochromatic; and, black-and-white movies provide compelling representations of real world scenes. Also, the contrast sensitivity of color is low at fine spatial scales. We approach the question from the perspective of optimal information processing by a system endowed with limited computational resources. We show that when such limitations are taken into account, the intrinsic statistical properties of natural scenes imply that the most effective strategy is to ignore fine-scale color features and devote most of the bandwidth to gray-scale information. We find confirmation of these information-based predictions from psychophysics measurements of fast-viewing discrimination of natural scenes. We conclude that the lack of colored features in our visual representation, and our overall low sensitivity to high-frequency color components, are a consequence of an adaptation process, optimizing the size and power consumption of our brain for the visual world we live in.