In previous work we found that Korte's law and other characterizations of apparent motion are special cases of a simple new law (Gepshtein & Kubovy, 2003; Gepshtein, Kubovy, & Tyukin, under review), which is consistent with what is known about human sensitivity to continuous motion, summarized by Kelly's (1979) spatiotemporal threshold surface. Our goal is to explain Kelly's surface and our results.

We propose that visual sensitivities are allocated in accordance with a Pareto criterion of optimality, first proposed in economics in 1906. According to the Pareto criterion, uncertainties due to different sources are balanced such that no improvement can be achieved by decreasing losses due one source of uncertainty without increasing losses due to another. To satisfy the criterion, the parameters of the most sensitive motion detectors must tradeoff: detectors tuned to high speeds must be tuned to low spatial frequencies and high temporal frequencies, whereas detectors tuned to low speeds must be tuned to high spatial frequencies and low temporal frequencies, just as they are in human vision (Burr & Ross, 1982; van Doorn & Koenderink, 1982; Nakayama, 1985). To achieve a constant error of speed estimation across speeds (Weber's law), the sensitivities of those detectors must be scaled logarithmically (Nover, Anderson, & DeAngelis, 2005). This induces an order across the space of prameters, such that the conditions of isosensitivity must be distributed as described by Kelly's surface and our results on apparent motion.