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We are surrounded by surfaces that we perceive by visual means. Understanding the basic principles behind this perceptual
process is a central theme in visual psychology, psychophysics, and computational vision. In many of the computational models
employed in the past, it has been assumed that a metric representation of physical space can be derived by visual means. Psychophysical
experiments, as well as computational considerations, can convince us that the perception of space and shape has a much more
complicated nature, and that only a distorted version of actual, physical space can be computed. This paper develops a computational
geometric model that explains why such distortion might take place. The basic idea is that, both in stereo and motion, we
perceive the world from multiple views. Given the rigid transformation between the views and the properties of the image correspondence,
the depth of the scene can be obtained. Even a slight error in the rigid transformation parameters causes distortion of the
computed depth of the scene. The unified framework introduced here describes this distortion in computational terms. We characterize
the space of distortions by its level sets, that is, we characterize the systematic distortion via a family of iso-distortion
surfaces which describes the locus over which depths are distorted by some multiplicative factor. Given that humans' estimation
of egomotion or estimation of the extrinsic parameters of the stereo apparatus is likely to be imprecise, the framework is
used to explain a number of psychophysical experiments on the perception of depth from motion or stereo.
Received: 9 January 1997 / Accepted in revised form: 8 July 1997 相似文献