# Exploring the Cost Function in Color Perception and Memory: An Information-Theoretic Model of Categorical Effects in Color Matching

- Chris R. Sims,
*Drexel University*
- Zheng Ma,
*Johns Hopkins University*
- Sarah R. Allred,
*Rutgers University*
- Rachel A. Lerch,
*Drexel University*
- Jonathan I. Flombaum,
*Johns Hopkins University*

## Abstract

Recent evidence indicates that color categories can exert a strong
influence over color matching in both perception and memory. We explore this
phenomenon by analyzing the cost function for perceptual error. Our analysis is
developed within the mathematical framework of rate–distortion theory.
According to our approach, the goal of perception is to minimize the expected
cost of error while subject to a constraint on the capacity of perceptual
processing. We propose that the cost function in color perception is defined by
the sum of two components: a metric cost associated with the magnitude of error
in color space, and a cost associated with perceptual errors that cross color
category boundaries. A computational model embodying this assumption is shown to
produce an excellent fit to empirical data. The results generally suggest that
what appear as 'errors' in working memory performance may reflect reasonable and
systematic behaviors in the context of costs.

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