Measurement of Individual Color Space using Luminous Vector Field

International audienceA luminous vector field is a set of couples (x,v) where x is a point in the computer display color space and v the direction of observer’s dependent achromatic luminosity change from x. That vector field is the set of orthogonal vectors to iso-luminous surfaces considering each vector v locally orthogonal to one surface passing through x. If the set of surfaces covering individual color space by stacking are considered quadratic and proportional, iso-luminous surfaces can be reconstructed from vector field.Hypothesis: If, like luminance in colorimetry, luminosity vectors are parallels for the whole color space, iso-luminous surfaces were planes. Otherwise, iso-luminous surface can be ellipsoid or hyperboloid depending on the vector field divergence or convergence. Method: We embedded computer display color space into a Euclidean space for enabling orthogonality. We choose two orthogonal planes passing through x where we measure luminous vector by heterochromatic photometry using minimum motion stimulus contrasts around x. Two sessions of minimum motion in either plane determines the three coordinates of luminous vector v attached to x. We repeat the measurement for several points placed on spheres of different radii. Fifteen points on five different radii for the two authors and six points for three different radii for twenty naïve observers. We estimate an affine model v = Ax+a0 for each observer. From observer’s data A and a0 we deduced the quadratic form of the surface (x-x0)tH(x-x0) = k2. Where x0 is the origin for the visual system, k is the level of the surface passing through x and H the surface metric for the observer’s color space. Results: All the iso-luminous surfaces we estimated were hyperboloids with a metric tensor H having one or two negative eigenvalues. This suggests that observer’s color space is a stack of iso-luminous hyperboloid sheets. All hyperboloids are included into a cone, the spectral cone for the observer of equation (x-x0)tH(x-x0)=0. From the spectral cone three vectors LMS are extracted, composing with the visual origin x0 and the metric H, a frame for the observer hyperbolic color space