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Yunfeng Li, Tadamasa Sawada, Meng Yi, Longin Jan Latecki, Zygmunt Pizlo; 3D symmetry correspondence from 2D images of objects. Journal of Vision 2011;11(11):73. doi: https://doi.org/10.1167/11.11.73.
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Last year we presented a model that recovered a 3D scene containing symmetric 3D shapes from a perspective image (Catrambone et al., 2010). The 3D recovery was applied to an “organized” image. In particular, the model was given information about which pairs of 2D curves in the image represent pairs of 3D symmetric curves. This is called “symmetry correspondence problem”. This problem is fairly easy to a human observer, but the underlying computational mechanisms remain unknown. Symmetry correspondence problem is ill-posed. Specifically, we have recently proved (Sawada et al., 2010) that any pair of 2D curves has one or more 3D symmetric interpretations. Therefore, pixel-based or edge-based algorithms will usually fail to detect real 3D symmetry. Here, we present a new computational method which uses higher-level features and which is based on a priori constraints. This method was tested with images of indoor scenes containing furniture, like chairs, and tables. The analysis of an image begins with detecting edges of approximately rectangular objects and grouping the edges into one of three groups corresponding to three different vanishing points (see Hedau et al., 2009). One vanishing point corresponds to the mirror symmetry of the object. The next step is to detect ‘C’ or ‘S’ curves that consist of two “L” junctions. Such curves, being higher order features, are not accidental. Two ‘C’ or ‘S’ shapes are considered to be symmetric if the lines connecting the corresponding “L” junctions pass through the vanishing point. After detecting all symmetric ‘C’ and/or ‘S’ shapes, the algorithm forms a list of corresponding (symmetric) edges. Several additional processes, like the computation of the distances between the corresponding edges and removing possible outliers, were applied to remove spurious (false) correspondences. The algorithm was tested on tens of real images and shown to be robust for non-degenerated views.
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