The Curve Indicator Random Field: Curve Organization Via Edge Correlation

Can the organization of local edge measurements into curves be directly related to natural image structure? By viewing curve organization as a statistical estimation problem, we suggest that it can. In particular, the classical Gestalt perceptual organization cues of proximity and good continuation—the basis of many current curve organization systems—can be statistically measured in images. As a prior for our estimation approach we introduce the curve indicator random field. In contrast to other techniques that require contour closure or are based on a sparse set of detected edges, the curve indicator random field emphasizes the short-distance, dense nature of organizing curve elements into (possibly) open curves. Its explicit formulation allows the calculation of its properties such as its autocorrelation. On the one hand, the curve indicator random field leads us to introduce the oriented Wiener filter, capturing the blur and noise inherent in the edge measurement process. On the other, it suggests we seek such correlations in natural images. We present the results of some initial edge correlation measurements that not only confirm the presence of Gestalt cues, but also suggest that curvature has a role in curve organization.