Continuous colormaps are widely used to visualize scalar fields, and their quality is typically evaluated using measures such as discriminative power and uniformity. Existing measures primarily characterize the intrinsic perceptual properties of the colormap itself, largely independent of the underlying data distribution. In practice, however, user perception arises not from the colormap alone but from the visualization generated by mapping data values through the colormap. The perceptual differences that users actually experience depend jointly on the colormap and the underlying data. We propose a data-aware formulation that complements existing data-independent colormap assessment approaches. Rather than analyzing the colormap in isolation, we model the color-encoded visualization as a composite mapping from the spatial domain of the data to perceptual color space. This approach yields data-aware counterparts of established measures, including discriminative power, uniformity, and smoothness, as well as additional measures such as perceptual anisotropy and degeneracy. We validate the proposed measures against both the existing data-independent framework and empirical results from perceptual studies, extend the formulation to 2D colormaps, and demonstrate its integration into colormap optimization. An interactive system is provided for exploring colormap assessment under varying data distributions. Results demonstrate that our formulation offers a principled foundation for data-aware colormap assessment and design.

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