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Yun Shi, Yunfeng Li, Zygmunt Pizlo; Extracting shapes from objects. Journal of Vision 2013;13(9):447. doi: https://doi.org/10.1167/13.9.447.
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Shape is one of the most important characteristics of objects, which allows us to identify them and recognize their functions. The conventional view has been that all objects have shapes, although there has been no agreement about what shape is. Here we propose a new definition of shape according to which shape refers to all spatial regularities of the object. By regularities we mean self-similarities or redundancies. This view of shape is rooted in Hochberg & McAlister’s (1953), as well as Attneave’s (1954) approaches, and has recently been formalized by Feldman and Singh (2005). This latter formalism allows one to measure the description length (DL) of a curve, which represents the information content (complexity) of the curve. In order to switch from "describing a curve" to "extracting the curve’s shape", we modify the method proposed by Feldman and Singh in two ways. First, we define the complexity of a curve as the sum of the complexity of a regular representation η of the curve (the curve’s shape), and the complexity of noise, which is the proportion of the original curve not captured by η. The shape η is the one that minimizes the total description length of the curve as represented by the sum of these two components. Second, our approach naturally allows one to include conventional symmetries such as mirror, rotational and translational and to treat them the same way as all other spatial regularities. In a sense, this second part of our theory resembles Leeuwenberg’s (1971) ideas behind his Structural Information Theory. These two elaborations are the key to generalizing the new definition of shape to 3D natural objects.
Meeting abstract presented at VSS 2013
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