Computational Approaches

Stages and Modules of Perceptual Computation

Perceptual computation in our visual system can be roughly divided into three stages: early vision, mid-level vision, and high-level vision. Early vision involves the extraction of elementary visual features such as edges, color, and optical flow, among others, as well as the grouping of these features into useful aggregates. Mid-level vision deals with the inference of visible surfaces or Marr's so-called 2.5-D sketch. The objective here is to infer the geometrical shapes of the visible surfaces and the occlusion relationships between them in a visual scene. High-level vision concerns reasoning about objects, their identities, structures, and locations. It also concerns global scene information such as 3-D spatial layout and illumination direction. Although the three-stage division is motivated mainly by functional considerations, these computational stages correspond roughly to the different visual areas along the ventral visual pathway in the hierarchical visual cortex. Marr suggested that visual computation proceeds in a bottom-up, feedforward fashion, employing a series of loosely coupled, decomposable computational modules, each of which can be studied mathematically and computationally in isolation. Recent research, however, has begun to emphasize the functional roles of recurrent interaction among [Page 279]the different computational processes during perceptual inference.

Varieties of Computational Approaches

There are three major computational approaches in the study of perception: the inverse optics approach, the dynamical system/neural network approach, and the statistical inference approach. All three approaches consider perception fundamentally as a problem of inference, as proposed by Hermann von Helmholtz, for filling in the missing logical gap between the retinal images and the perceptual knowledge to be derived from them. Current research formulates perceptual inference in the Bayesian framework, which emphasizes the integration of prior knowledge in the inference process. To illustrate Bayesian inference, let us consider the following example. Suppose I saw a woman wandering around in my yard wearing a hat one evening when I got home. Normally, I would have concluded that it was my wife because she was the only woman in the house. On the other hand, grandma told me she would be visiting either that day or the next day. Thus, it could also be granny. In Bayesian terms, the prior probability of the woman being my wife was p(wife) = 2/3, and that of granny was p(granny) = 1/3. Now, from experience, I also knew granny loved wearing hats but my wife was not fond of it. Thus, the likelihood of observing granny in a hat was p(hat|granny) = 0.2, but that of observing my wife in a hat was much lower at p(hat|wife) = 0.05. The probability of a certain interpretation after combining the likelihood of a certain observation and the prior probability of that interpretation, called the posterior probability (i.e., p(granny|hat), p(wife|hat)), can be obtained by the Bayes'

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