Efficient calculations of NSS-based gaze similarity for time-dependent stimuli

The degree of spatial similarity between the gaze of participants viewing dynamic stimuli such as videos has been previously measured using metrics which are based on the NSS (Normalized Scanpath Saliency). Methods currently used to calculate this metric rely upon a numerical grid, which can be computationally prohibitive for a variety of otherwise useful applications such as Monte Carlo analyses. In the present work we derive a new analytical calculation method for the same metric that yields equal or more accurate results, but with speeds than can be orders of magnitude faster (depending on parameters). Our analytical method scales well with dimensionality, and could also be of use for other applications. The drawback is that it can become very slow if the number of participants in the study is very large or if the gaze sampling rate is high. We provide performance benchmarks for a Fortran implementation of our method, and make available the source code developed.