Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis

Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical explanations that do consider both phenomena simultaneously follow parametric formulations based on empirical models. Therefore, it may be argued that the behavior does not come directly from the color statistics but from the convenient functional form adopted. In addition, many times the whole statistical analysis is based on simplified databases that disregard relevant physical effects in the input signal, as, for instance, by assuming flat Lambertian surfaces. In this work, we address the simultaneous statistical explanation of the nonlinear behavior of achromatic and chromatic mechanisms in a fixed adaptation state and the change of such behavior (i.e., adaptation) under the change of observation conditions. Both phenomena emerge directly from the samples through a single data-driven method: the sequential principal curves analysis (SPCA) with local metric. SPCA is a new manifold learning technique to derive a set of sensors adapted to the manifold using different optimality criteria. Here sequential refers to the fact that sensors (curvilinear dimensions) are designed one after the other, and not to the particular (eventually iterative) method to draw a single principal curve. Moreover, in order to reproduce the empirical adaptation reported under D65 and A illuminations, a new database of colorimetrically calibrated images of natural objects under these illuminants was gathered, thus overcoming the limitations of available databases. The results obtained by applying SPCA show that the psychophysical behavior on color discrimination thresholds, discount of the illuminant, and corresponding pairs in asymmetric color matching emerge directly from realistic data regularities, assuming no a priori functional form. These results provide stronger evidence for the hypothesis of a statistically driven organization of color sensors. Moreover, the obtained results suggest that the nonuniform resolution of color sensors at this low abstraction level may be guided by an error-minimization strategy rather than by an information-maximization goal.