Fig. 2.

Geodesics (shortest paths computed with the shooting method) between the corners of the sRGB cube in CIE LAB with its non-Euclidean metric $\mathrm{\Delta }{E}_{2000}^{*}$ (79) illustrate what has long been known for perceptual color spaces in general, namely that in contrast to a Euclidean setting (e.g., $\mathrm{\Delta }{E}_{1976}^{*}$), the geodesics do not form straight lines. In this paper, we go one step further and show what CIE LAB does not capture: that in contrast to a Riemannian setting, their lengths do not even coincide with the distances between their endpoints.