Combining Local and Global Cues for Closed Contour Extraction

Abstract

Algorithms for computing closed contours are generally based upon local Gestalt cues relating pairs of oriented elements, and a Markov assumption to then group these elements into chains. Without additional global constraints, these algorithms generally do not perform well on general natural scenes. Such global cues could include symmetry, shape priors or global colour appearance. A key challenge is to combine these local and global cues in a statistically optimal way. Here we propose a novel, effective method for rigorously combining local and global cues, both at the stage of forming new closed contour hypotheses, and at the stage of evaluating and ranking these hypotheses. We also demonstrate the importance of promoting the diversity of hypotheses. We evaluate our results on a standard public dataset, and demonstrate a substantial performance improvement over prior methods.

Shape from Contour: Computation and Representation

“…One option is to measure the grouping likelihoods between all pairs of edges on an object (Geisler et al 2001) and invoke a transitivity assumption: If edge A groups to edge B, and edge B groups to edge C, then edge A also groups to edge C. This rule will generally lead to unordered sets of edges that do not respect the 1D nature of contours. An alternative is to measure the grouping likelihoods only between successive pairs of edges on the contour (Elder & Goldberg 2002) and invoke a Markov assumption: The likelihood of the contour is given by the product of the likelihoods of each local pairwise association between adjacent edges (Zucker et al 1977, Sha'ashua & Ullman 1988, Elder & Zucker 1996a, Williams & Jacobs 1997, Movahedi & Elder 2013, Almazen et al 2017. This assumption respects the 1D nature of the contour but greatly simplifies the probabilistic model: The local pairwise grouping probabilities are now sufficient statistics for computing maximum probability contours.…”

“…What computational mechanisms are involved in harnessing global cues such as closure to solve these complex grouping problems? Some models for global contour extraction based on the Markov assumption discussed in Section 3.3 incorporate closure by explicitly searching for closed cycles of local elements (Elder & Zucker 1996a, Mahamud et al 1999, Stahl & Wang 2008, Levinshtein et al 2010, Movahedi & Elder 2013. It should be noted, however, that the statistical structure of a cycle is more complex than a Markov chain, as closure induces global statistical dependencies between the local elements, and hence there is a mismatch between the first-order Markov model used by these methods and the goal of recovering closed contours.…”

The role of global cues in the perceptual grouping of natural shapes

“…Although this Markov assumption has been used by computer vision algorithms to extract global contours from complex natural images (Elder & Zucker, 1996), there are a number of reasons to be skeptical that it represents a complete model of human perceptual grouping. First, it has been noted that these algorithms can fail in some cases where the human visual system seems to have little trouble (Movahedi & Elder, 2013). Second, the distribution of intrinsic distances between high-curvature events on natural contours has been shown to be incompatible with the Markov assumption (Ren, Fowlkes, & Malik, 2008).…”