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Yun Shi, Tadamasa Sawada, Yunfeng Li, Zygmunt Pizlo; Recovering a 3D shape from a single 2D image of a generalized cone. Journal of Vision 2011;11(11):56. doi: 10.1167/11.11.56.
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© ARVO (1962-2015); The Authors (2016-present)
Human observers perceive 3D shapes very accurately even from single 2D images. However, recovering a 3D shape from a single 2D image is an ill-posed problem. There exist infinitely many 3D interpretations of the 2D image. In order to solve this problem, a priori constraints about the 3D shape are required. In our prior studies (Li, Pizlo, & Steinman, 2009; Sawada, 2010), we proposed a computational model that recovers 3D shapes from single 2D images using the following constraints: 3D mirror-symmetry, maximum 3D compactness, minimum surface area and maximum planarity of contours. Note that even though most objects in our everyday life are mirror-symmetric, their parts are adequately represented by generalized cones (GC), which are characterized by translational, rather than mirror symmetry. In this study, we propose a computational model which recovers shapes of 3D GCs from single 2D images. Our GCs are produced by swiping a planar closed curve (cross section) along a planar axis with the following constraints: all cross sections in a given GC have the same shape, but not necessarily constant size. Each cross section is perpendicular to the tangent of the axis. With these constraints, a single 2D orthographic image of a GC determines the 3D shape up to one unknown parameter – aspect ratio. The aspect ratio of the recovered GC is selected by maximizing a weighted average of 3D compactness and surface area. Performance of this model will be compared to the performance of the subjects in a 3D shape adjustment task.
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