In visual display devices such as LCD devices with backlight illumination, the backlight typically consumes most of device battery power. In the interest of displaying a given pixel pattern at a minimized backlight level, the pattern can be transformed while maintaining image quality, with a transform determined from pixel luminance statistics. Aside from, or in addition to such minimizing, a transform also can be used for image enhancement, for a displayed image better to meet a visual perception quality. In either case, the transform preferably is constrained for enforcing one or several display attributes.