The light intensities of natural images exhibit a high degree of redundancy. Knowing the exact amount of their statistical dependencies is important for biological vision as well as compression and coding applications but estimating the total amount of redundancy, the multi-information, is intrinsically hard. The conventional approach for estimating the redundancy per pixel is to estimate the multi-information for patches of increasing sizes and divide by the number of pixels. Here, we show that the limiting value of this sequence—the multi-information rate—can be better estimated by another limiting process based on measuring the mutual information between a pixel and a causal neighborhood of increasing size around it. We explain the theoretical relationship of the two methods and compare their performance on natural images. While both methods provide a lower bound on the multi-information rate, the mutual …