Local Spatial Frequency Analysis of Image Texture

Real-world scenes contain many interacting phenomena that lead to complex images which are difficult to interpret automatically. Part of this difficulty is due to the dichotomy of useful representations for these phenomena. Some effects are best described in the spatial domain, while others are more naturally expressed in frequency. In order to resolve this dichotomy, we present the combined space/frequency representation which, for each point in an image, shows the spatial frequencies at that point. This representation is useful for developing theories about many important vision phenomena, leading to deeper understanding and better algorithms. In this paper, we show how the representation can be used for the shape from texture problem and to analyze aliasing simply and naturally. The space/frequency representation should be a key aid in untangling the complex interaction of phenomena in images, allowing automatic understanding of real-world scenes.