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John Wilder, Jacob Feldman, Manish Singh; Shape classification based on natural shape statistics. Journal of Vision 2008;8(6):717. doi: https://doi.org/10.1167/8.6.717.
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We studied the classification of shapes into broad natural categories such as “animal” or “leaf”, which with many shapes can proceed without overt basic-level recognition. Shape representation models often make implicit assumptions about what shape structures most often occur in natural shapes, but such assumptions are not generally closely tied to real-world measurements, and not tuned to naturally occurring classes. As a step towards “naturalizing” shape representation, we collected shape statistics from a large database of real shapes drawn from several natural categories, such as animals, and leaves, focusing on shape parameters relating to skeletal and axial structure as in the Bayesian skeleton estimation framework of Feldman & Singh (2006). These statistics allow for the creation of “ecologically-informed” shape models that generalize over the many specific individual structures observed in these classes. Building on the Bayesian skeleton model, we developed a mathematical approach to shape prototypification, which allows shapes to be probabilistically classified with respect to the prototype most likely to have generated it. To investigate human shape classification, we asked subjects to classify shapes that were constructed by taking a weighted average (suitably normalized) of animal and leaf contours, resulting in shapes that were parametric mixtures of the two classes. Subjects can indeed classify such shapes, and their classifications closely track the ground truth given by the mixing proportions. We model this classification process via a Bayesian classifier that assigns a posterior shape class as a function of the shape structure, using our database of class-specific natural shape parameters to inform the priors and likelihood functions. The resulting model gives a good account of the data, and sheds light on how novel shapes can be assigned to semantically meaningful real-world categories based on knowledge of structural regularities but without overt recognition.
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