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Yunfeng Li; A computational model on 3D shape recovery. Journal of Vision 2009;9(8):67. doi: https://doi.org/10.1167/9.8.67.
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© ARVO (1962-2015); The Authors (2016-present)
Last year we presented a model that could recover a 3D shape from a single 2D image by applying simplicity constraints (e.g., symmetry, planarity, maximum compactness, minimum surface). This model was tested on randomly generated polyhedra. The model' performance was very similar to the performance of human subjects. Both, the subjects and the model recover the 3D shape accurately for most shapes and most viewing directions. This model has been elaborated and now it can be applied to real images of real objects. The new model is different from the old one in several ways. First, we apply the least squares method to correct the points on the image in order to reduce the effect of noise. Second, the model applies the maximum compactness and minimum surface area constraints in a different way. Unlike the previous version, the new model computes the convex hull of the recovered 3D shape, and then computes the compactness and surface area of the convex hull. Thirdly, we derived a new likelihood function. The likelihood function is defined as the reciprocal of the rate of change of projected image when a 3D shape is rotated around its center. Finally, we are exploring whether the simplicity constraints (maximal compactness, minimum surface area and maximum planarity) can themselves be represented as a likelihood function, and whether using this combined likelihood will further improve shape recovery. We are now testing the interaction between binocular disparity and a priori constraints in 3D shape perception. The subjects view binocularly or monocularly the stereoscopic images of symmetric polyhedra, with several different slants of the symmetry plane, and with several viewing distances. We expect that binocular disparity and simplicity priors combine non-linearly in producing accurate 3D shape perception.
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