EUROGRAPHICS 2018/ E. Jain and J. Kosinka Poster From spectra to perceptual color: Visualization tools for the dimensional reduction achieved by the human color sense Joshua S. Harvey 1,2 , Clive R. Siviour 1 and Hannah E. Smithson 2 Departments of 1 Engineering Science and 2 Experimental Psychology, University of Oxford, UK Abstract Physical colors, defined as unique combinations of photon populations whose wavelengths lie in the visible range, occupy an infinite-dimensional real Hilbert space. Any number of photon populations from the continuous spectrum of monochromatic wavelengths may be present to any positive amount. For normal vision, this space collapses to three dimensions at the retina, with any physical color eliciting just three sensor values corresponding to the excitations of the three classes of cone pho- toreceptor cells. While there are many mappings and visualizations of three-dimensional perceptual color space, attempts to visualize the relationship between infinite-dimensional physical color space and perceptual space are lacking. We present a visualization framework to illustrate this mathematical relation, using animation and transparency to map multiple physical colors to locations in perceptual space, revealing how the perceptual color solid can be understood as intersecting surfaces and volumes. This framework provides a clear and intuitive illustration of color metamerism. 1. Introduction Physical colors occupy an infinite-dimensional real Hilbert space, H color , and may be represented by countable infinite column vec- tors s. At the retina, this space collapses to three dimensions of sen- sor values, that is, the photon catches and resultant excitations of the three classes of photosensitive cones [Koe10]. The cone spec- tral responses, L, M and S, of cones with response function row vectors r are then given by:    L M S    =    r L r M r S    s While the three-dimensionality of perceptual color space is a fa- miliar and intuitive concept, the same cannot be said for H color . We are accustomed to conceptualizing spaces of three dimensions or fewer, living in a spatially three-dimensional world. Perceptual color space is, by nature, relatable to the perceptual experience of color, which may be used to navigate the space such as when se- lecting colors with a hue-saturation-value (HSV) or red-green-blue (RGB) color-picker. Any projection of physical color space must violate our intuitions of either space or color: namely that objects should not occupy the same space, or that colors should be sep- arated according to their perceptual dissimilarity. The visualiza- tion framework proposed here maintains the distance relations of color dissimilarity, using transparency and animation to illustrate the intersecting surfaces and volumes of physical colors projected throughout the perceptual color solid. 2. Two-wavelength color set surfaces We begin by considering physical color sets comprising just two wavelength populations, w 1 and w 2 . Each color set, C, is defined by the intensities of each population, C{w 1 , w 2 }, giving rise to a sur- face extended between the monochromatic axes C{w 1 } and C{w 2 }. Figure 1 shows two color sets, C{610, 540} and C{460, 540}. Figure 1: Projection of the C{610, 540} and C{460, 540} two- wavelength physical color sets onto the [w 1 , w 2 ] plane. Projection to a fully three-dimensional color space will re- sult in continuous C{w 1 , w 2 } surfaces. These spaces may be geared towards intuition (HSV), practical considerations (RGB), or representing perceptual space (La*b*). Figure 2 shows sev- eral C{w 1 , w 2 } color sets projected to a HSV space, using the spherical coordinate system (r,θ,φ) such that r=value, θ=hue, and φ=saturation. The summation of primaries rather than proportional mixing makes surfaces and primaries more readily identifiable. c  2018 The Author(s) Eurographics Proceedings c  2018 The Eurographics Association. DOI: 10.2312/egp.20181025