High dynamic range (HDR) tone mapping is formulated as an optimization problem of maximizing perceivable spatial details given the limited dynamic range of display devices. This objective can be attained, as supported by our results, by a novel image display methodology called locally adaptive rank-constrained optimal tone mapping (LARCOTM). The scientific basis for LARCOTM is that the maximum discrimination power of human vision system can only be achieved in a relatively small locality of an image. LARCOTM is fundamentally different from existing HDR tone mapping techniques in that the former can preserve pixel value order statistics within localities in which human foveal vision retains maximum sensitivity, while the latter cannot. As a result, images enhanced by LARCOTM are free of artifacts such as halos and double edges that plague other HDR methods.