Combining Local and Global Cues for Closed Contour Extraction

We address the problem of extracting the simple closed contours that bound the salient objects in a natural image[4]. The method proposed in this paper falls in the category of contour grouping methods, which search for the optimal cycle of local oriented primitives (e.g. edgels, line segments) forming the boundary. The first stage of processing in our method extracts from the image a sparse graph representation of the oriented structure in the image. Local oriented edges detected in the image are grouped locally into subpixellocalized line segments of variable length. As in prior work, each of the resulting segments forms a vertex in our association graph, and each edge in this graph represents a grouping hypothesis between specified endpoints of two segments. Contour grouping algorithms are generally based upon classical Gestalt cues such as proximity, good continuation and similarityWhile prior methods [1, 2] have approximated these local cues as independent and modelled the marginals parametrically, we use EM to learn Gaussian mixture models for the 4-dimensional likelihoods, which allows us to capture small dependencies between the cues. Our sparse graph is then formed by representing only the k outgoing edges with highest likelihood for each vertex. Algorithms for computing closed contours are generally based upon these 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. A main contribution of our paper is a novel, effective method for 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 develop and test this method using global colour contrast cues in both a greedy constructive search for closed contours, and in the final ranking of closed contours. We adopt a regression approach: learn a regressor that will predict the distance of a candidate path from ground truth based on both local and global cues. We take a nonparametric approach to the regression problem, binning the local cue fl (ck) and global cue fg (ck), and then estimating the mean ε̂l and ε̂g and variance σ2 l and σ2 g of predicted error for each. Assuming independence between the local and global cues, the least-squares error prediction εML (ML for normal distributions) is then given by