Are edges incomplete?

We address the problem of computing a general-purpose early visual representation that satisfies two criteria. 1) Explicitness: To be more useful than the original pixel array, the representation must take a significant step toward making important image structure explicit. 2) Completeness: To support a diverse set of high-level tasks, the representation must not discard information of potential perceptual relevance. The most prevalent representation in image processing and computer vision that satisfies the completeness criterion is the wavelet code. In this paper, we propose a very different code which represents the location of each edge and the magnitude and blur scale of the underlying intensity change. By making edge structure explicit, we argue that this representation better satisfies the first criterion than do wavelet codes. To address the second criterion, we study the question of how much visual information is lost in the representation. We report a novel method for inverting the edge code to reconstruct a perceptually accurate estimate of the original image, and thus demonstrate that the proposed representation embodies virtually all of the perceptually relevant information contained in a natural image. This result bears on recent claims that edge representations do not contain all of the information needed for higher level tasks.