This research provides a general theoretical framework for the description and analysis of representations for variables in connectionist networks. The space in which all representations lie is defined, and existing representation schemes are described in terms of this space. In addition, the space is used to suggest new representations. A mathematical analysis of the representations is used to compare different representations in terms of various properties. This analysis has lead to theories about visual processing, and has been used to determine which types of information are best encoded by a particular representation, and is thus useful for choosing an optimal encoding for a given computational task. This research shows that in the early stages of visual processing the choice of representation for a visual feature variable depends not only on the type of information about the variable that is desired, but also on the measurement process used to extract the feature from an image. A tuning-curve technique has been developed for analyzing the measurment process, and thus determining the constraints placed on the choice of representation that are a function of the measurement process. The focus of this project is to study a special representation techniques, call Rho-space representation. It has been developed along with simple parallel connectionist computations for edge analysis. Rho-space has many advantages over other edge representations including: no thresholding of local edge elements is required; a natural representation of connectivity is created which agrees with human perception; both coarse and fine representation of orientation information is possible; and, illusory contours, of the type produced by the human visual system occur.
