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Nathaniel R. Twarog, Edward H. Adelson, Marshall F. Tappen; Segmenting 2D Shapes using 3D Inflation. Journal of Vision 2011;11(11):851. doi: 10.1167/11.11.851.
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© ARVO (1962-2015); The Authors (2016-present)
Given an arbitrary 2D silhouette, human observers can readily segment it into parts; these same observers generally agree on whether a segmentation looks correct, suggesting a regularity in how humans perceive 2D parts. As a result, considerable work has been done to understand what drives this part segmentation. Hoffman and Richards proposed the Minima Rule, in which endpoints of part boundaries are located at local minima of negative curvature. The rule succeeds at explaining many segmentation phenomena, but has many well-known limitations, including a lack of systematic rules for pairing boundary endpoints and numerous exceptions. Later models, such as the Shortcut Rule and Necks and Limbs, have added auxiliary rules to patch these holes, but they lack the simplicity of the original Minima rule, require careful parameter tweaking, and still contain significant exceptions. We propose a new approach which is both simple and effective, and largely parameter free. Rather than working directly on the 2D contour of the silhouette, we construct a 3D shape that fits the contour, using a simple inflation algorithm that we call Puffball. Puffball places spheres along the medial axis of the silhouette; the union of these spheres is smooth, fills the original silhouette, and gives an intuitive result. This inflation exhibits natural breakpoints, marked by creases of negative curvature on the top of the inflated shape. Bridging these breakpoints across the silhouette using the medial axis results in an intuitive part segmentation on numerous shapes, even those which foiled previous approaches. Also, these part boundaries can be ranked in strength to create a hierarchy of parts. Thus, our part segmentation algorithm begins and ends in 2D, but by moving our analysis to 3D, we arrive at an approach which is simpler, more intuitive, and far more reliable.
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