Paper:
Variational Laws of Visual Attention for Dynamic Scenes
Computational models of visual attention are at the crossroad of disciplines like cognitive science, computational neuroscience, and computer vision. This paper proposes a model of attentional scanpath that is based on the principle that there are foundational laws that drive the emergence of visual attention. We devise variational laws of the eye-movement that rely on a generalized view of the Least Action Principle in physics. The potential energy captures details as well as peripheral visual features, while the kinetic energy corresponds with the classic interpretation in analytic mechanics. In addition, the Lagrangian contains a brightness invariance term, which characterizes significantly the scanpath trajectories. We obtain differential equations of visual attention as the stationary point of the generalized action, and we propose an algorithm to estimate the model parameters. Finally, we report experimental results to validate the model in tasks of saliency detection.

Review:
Variational Laws of Visual Attention for Dynamic Scenes
The authors investigate what locations in static and dynamic images tend to be attended to by humans. They derive a model by first defining three basic principles for visual attention (defined as an energy function to be minimized by the movements of the eye): (1) Eye movements are constrained by a harmonic oscillator at the borders of the image within a limited-sized retina. (2) a “curiosity driven principle” highlighting the regions with large changes in brightness in both a fine and blurred version of the image, and (3) brightness invariance, which increases as a function of changes in brightness. Using a cost function derived from these three functions, the authors derive differential equations for predicting the eye movements across static or dynamic images (depending on the starting location and initial velocity). The authors evaluate their technique quantitatively on data sets of static and dynamic scenes coupled with human eye movements. They demonstrate that their method performs comparable to the state-of-the-art. 
Formal definitions of saliency and modeling eye movements are critical issues in computational vision and cognitive science. Psychologists have long been plagued by vague definitions of saliency, and the authors propose a novel and innovative model (as far as I am aware) that could aid the development of better understanding how what makes something salient and a formal model for eye movements (within the bottom-up tradition). Although it is not necessarily state-of-the-art on every metric for every data set, it performs well and provides a refreshingly different perspective on the problem. 
Unfortunately, some of what I wrote above is based on conjecture as the paper is poorly written and hard to follow. I recommend the authors have others proofread the paper and expand on abbreviations (both within the equations and also those used in Section 3). I would recommend they move the 2 page Appendix to supplementary material and use those extra pages to define each variable and function used (even if it is a convention within your own field – the NIPS audience comes from many different disciplines and some will have trouble following the mathematics otherwise). 
As a psychologist, I would have liked the authors to connect their work to some of the psychological literature on eye movements as optimal steps for gathering information. See for example, Najemnik, J., & Geisler, W. S. (2008). Eye movement statistics in humans are consistent with an optimal search strategy. Journal of Vision, 8(3), 1-14. There are other relevant articles (particularly from Geisler’s lab, but that should give the authors a pointer to follow into that literature). I would be interested to see a discussion of how their approach compares to their findings (e.g., are they restatements of similar models or provide independent information that could be integrated to produce a better model?)