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Commentaries Stability and change

By James Todd


Most people would agree that the shape of an object is one of its most perceptually important attributes, and some researchers have argued that it is the primary attribute by which observers are able to recognize objects �e.g., Biederman, 1987). Given the ubiquity of this common intuition, it is somewhat puzzling to note that the concept of ``shape' ' has no formal mathematical definition that can adequately characterize its intended meaning when used colloquially. For example, almost everyone would concur that a big sphere and a small sphere both have the same shape, yet by most of the standard measures used in geometry they are quite different. The abstract nature of the concept of shape is perhaps best revealed by the perceptual classification of biological forms �e.g., see Thompson, 1942). Consider, for example, the ability of normal individuals to identify their friends and loved ones under a variety of different viewing conditions. We are able to identify people from different vantage points, and with different facial expressions, hairstyles, make-up, or clothing accessories, such as hats or jewellery. W

Topics: geometries �i.e, Euclidean, affine, confor
Year: 2009
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