Contour grouping: Ecological statistics, generative models and ideal observers

Abstract

While the Gestalt laws of perceptual grouping were originally conceived as qualitative principles, the contemporary view is quantitative, treating perceptual organization as a problem of statistical inference. Here we consider the problem of contour grouping within this modern framework. In particular, we use a contour tracing technique to study the statistics of proximity, good continuation and similarity cues for contour grouping in natural images. Statistical modeling of the proximity cue indicates that it is by far the most powerful of the three cues, and follows a scale-invariant power law in close agreement with prior psychophysics. The approximate independence of the three cues leads to a simple Bayesian model for contour inference which, when combined with global cues and priors, can be used for the inference of bounding contours from natural images. This generative model of contour grouping also allows naturalistic contours to be synthesized and used as stimuli in controlled psychophysical experiments. We employ the methodology of Field et al. (1993), in which human observers are presented with images containing random fields of oriented elements. The observer's task is to detect a stochastic sequence of elements generated by the natural contour model. Interpreting human performance is difficult without an ideal observer model, i.e. a benchmark that reflects the inherent difficulty of the task. Unfortunately, the computational complexity of the problem precludes a direct simulation of the ideal observer. Here we describe an alternative method that uses two sub-optimal machine observers to derive bounds on ideal observer performance. Using this technique, we find human efficiency to be in the 25–50% range, declining as a function of the number of elements on the contour. The proximity cue appears to be more efficiently exploited than good continuation cues, consistent with our finding that proximity provides more information in the natural environment. ElderJ.H.KrupnikA.JohnstonL.A.(2003). Contour grouping with prior models, IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(25), 661–674. ElderJ.H.GoldbergR. M.(2002). Ecological statistics of Gestalt laws for the perceptual organization of contours. Journal of Vision, 2(4), 324–353, http://journalofvision.org/2/4/5/, DOI 10.1167/2.4.5. FieldD. J.HayesA.HessR. F.(1993). Contour integration by the human visual system: Evidence for a local “association field.” Vision Research, 33, 173–193.