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Jacob Feldman, Manish Singh, Vicky Froyen, Seha Kim, Sung-Ho Kim; Integrated Bayesian estimation of 3D shape and figure/ground. Journal of Vision 2011;11(11):1039. doi: 10.1167/11.11.1039.
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Shape (both 2D and 3D) and figure/ground organization have usually been treated as disparate topics, but the representation of contour shape and the assignment of border ownership (figure/ground) are well-known to be intimately related. In this work we present Bayesian techniques for estimating them jointly in an integrated fashion. In previous work, we have developed a framework for Bayesian estimation of the shape skeleton, that is, for identifying the skeletal (medial-like) structure that best “explains” a given shape as the outcome of a stochastic growth-like process. Here we generalize this computational framework to encompass multiple contours with unknown border ownership, building upon two premises supported by empirical findings: (1) that skeletal structure tends to “draw” border ownership, and (2) that border ownership can vary along the length of a contour depending on local geometry. In the expanded framework, the computational goal is to estimate not just a single skeleton but a set of skeletons that, collectively, best explain the ensemble of image contours, including the figural polarity at each contour point. In the maximum a posteriori (MAP) estimate, each contour point is perceptually “owned” by the side whose skeletal structure best explains it; that is, contours are owned by their apparent interiors. Moreover, by expanding the data to be explained to include T-junctions, the MAP interpretation can encompass depth differences, resulting in an estimate of the 3D (nonplanar) structure of each skeleton. These 3D skeletons can then be “inflated” to recover a rudimentary estimate of 3D shape based on estimated skeletal structure. The result is an integrated Bayesian estimate of 3D shape and f/g together, which accounts for key perceptual intuitions and agrees with a variety of psychophysical data.
Supplemental details and figures can be found at ruccs.rutgers.edu/~jacob/demos/shape.html.
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