Boundary ownership by lifting to 2.1D

This paper addresses the “boundary ownership” problem, also known as the figure/ground assignment problem. Estimating boundary ownerships is a key step in perceptual organization: it allows higher-level processing to be applied on non-accidental shapes corresponding to figural regions. Existing methods for estimating the boundary ownerships for a given set of boundary curves model the probability distribution function (PDF) of the binary figure/ground random variables associated with the curves. Instead of modeling this PDF directly, the proposed method uses the 2.1D model: it models the PDF of the ordinal depths of the image segments enclosed by the curves. After this PDF is maximized, the boundary ownership of a curve is determined according to the ordinal depths of the two image segments it abuts. This method has two advantages: first, boundary ownership configurations inconsistent with every depth ordering (and thus very likely to be incorrect) are eliminated from consideration; second, it allows for the integration of cues related to image segments (not necessarily adjacent) in addition to those related to the curves. The proposed method models the PDF as a conditional random field (CRF) conditioned on cues related to the curves, T-junctions, and image segments. The CRF is formulated using learnt non-parametric distributions of the cues. The method significantly improves the currently achieved figure/ground assignment accuracy, with 20.7% fewer errors in the Berkeley Segmentation Dataset.