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Symbols are used in scatterplots to encode data in a way that is appropriate for perception through human visual channels. Color is believed to be the most dominant channel with lightness regarded as the most important one of three color dimensions. We study lightness perception in scatterplots in the context of analytic tasks requiring symbol discrimination. More specifically, we performed an experiment to measure human performance in three visual analytic tasks. Outlined circles and unframed spots, equally sized, with a uniform luminance that was varied at ten or eleven equispaced levels between black and white were used as symbols and displayed on a uniform white background. Sixteen subjects divided in two groups, participated in the experiment and their task performance times were recorded. We propose a model to describe the process. The perception of lightness is assumed to be an early step in the complex cognitive process to mediate discrimination, and psychophysical laws are used to describe this perceptual mapping. Different mapping schemes are compared by regression on the experimental data. The results show that approximate homogeneity of lightness perception exists in our complex tasks and can be closely described by a blended combination of two opposite power functions assuming either the light end or the dark end of the lightness scale as the starting point. The model further yields discriminability scales of lightness for sparse scatterplots with a white background.