  Dozens of new models on fixation prediction are published every year and
compared on open benchmarks such as MIT300 and LSUN. However, progress in the
field can be difficult to judge because models are compared using a variety of
inconsistent metrics. Here we show that no single saliency map can perform well
under all metrics. Instead, we propose a principled approach to solve the
benchmarking problem by separating the notions of saliency models, maps and
metrics. Inspired by Bayesian decision theory, we define a saliency model to be
a probabilistic model of fixation density prediction and a saliency map to be a
metric-specific prediction derived from the model density which maximizes the
expected performance on that metric given the model density. We derive these
optimal saliency maps for the most commonly used saliency metrics (AUC, sAUC,
NSS, CC, SIM, KL-Div) and show that they can be computed analytically or
approximated with high precision. We show that this leads to consistent
rankings in all metrics and avoids the penalties of using one saliency map for
all metrics. Our method allows researchers to have their model compete on many
different metrics with state-of-the-art in those metrics: "good" models will
perform well in all metrics.
