Synergies between optical and physical variables in intercepting parabolic targets

Abstract

Interception requires precise estimation of time-to-contact (TTC) information. A long-standing view posits that all relevant information for extracting TTC is available in the angular variables, which result from the projection of distal objects onto the retina. The different timing models rooted in this tradition have consequently relied on combining visual angle and its rate of expansion in different ways with tau being the most well-known solution for TTC. The generalization of these models to timing parabolic trajectories is not straightforward. For example, these different combinations rely on isotropic expansion and usually assume first-order information only, neglecting acceleration. As a consequence no optical formulations have been put forward so far to specify TTC of parabolic targets with enough accuracy. It is only recently that context-dependent physical variables have been shown to play an important role in TTC estimation. Known physical size and gravity can adequately explain observed data of linear and free-falling trajectories, respectively. Yet, a full timing model for specifying parabolic TTC has remained elusive. We here derive two formulations that specify TTC for parabolic ball trajectories. The first specification extends previous models in which known size is combined with thresholding visual angle or its rate of expansion to the case of fly balls. To efficiently use this model, observers need to recover the 3D radial velocity component of the trajectory which conveys the isotropic expansion. The second one uses knowledge of size and gravity combined with ball visual angle and elevation angle. Taking into account the noise due to sensory measurements, we simulate the expected performance of these models in terms of accuracy and precision. While the model that combines expansion information and size knowledge is more efficient during the late trajectory, the second one is shown to be efficient along all the flight.

Gravity as a Strong Prior: Implications for Perception and Action

“…While again Gómez and López-Moliner (2013) propose a way of integrating air resistance into their model of parabolic target interception, a relatively accurate and precise gravity prior (as brought forward by authors such as Lacquaniti and Zago) seems contradictory with effectively observed acceleration values of under 9.81 m/s 2 . And in fact, Flavell (2014) suggests that the gravity prior may actually not be set at 1g exactly, but rather at a value between 1g and just below 1g.…”

On-line and model-based approaches to the visual control of action

“…Sometimes specific knowledge of fixed parameters or constants, such as Earth's gravitational acceleration or a ball's diameter or elasticity, is also referred to as an internal model. We will reserve the term “internal model” for an inner surrogate that mimics an external physical process; constants do not meet this standard, although they can act as constraints on the calibration of optical variables or visual-motor control laws (Gómez & López-Moliner, 2013; Jacobs & Michaels, 2006). Further, the fidelity of an internal model, as well as its temporal duration, are rarely specified.…”

The Use of Visual Cues in Gravity Judgements on Parabolic Motion

“…The next step is an analysis on the subject level for the chosen cues. Then, we try out different combinations of and , which, according to a gravity-based TTC model ("GS model"; Gómez & López-Moliner, 2013), might be used as approximate heuristics to estimate gravity. Finally, we employ Generalized Linear Mixed Modelling (Moscatelli & Lacquaniti, 2012) to assess whether participants used homogeneous or rather idiosyncratic strategies, and finish with a short assessment of the role of purely temporal information.…”

“…While thus all information necessary for distance recovery is readily available to the subject, it has been observed that distance may be underestimated in virtual environments, especially when these are scarce (Loomis & Knapp, 2003;Messing & Durgin, 2005). While the visual angle itself can be estimated with accuracy (McKee & Welch, 1992), its rate of change over time is very noisy, with Weber fractions of 10 % and beyond (Gómez & López-Moliner, 2013;Regan & Hamstra, 1993). Nonetheless, as suggested by the important, though contested role of the visual angle and its rate of expansion (for the parameter τ) in the literature on TTC estimation for linearly approaching targets (Lee & Reddish, 1981), it may still deliver some information, e. g. about the physical horizontal velocity.…”

“…As (1981). ̇ is very small during the first half of the trajectory, which may further impact its estimation; in general, it has been shown to be extremely noisy until it gets very close to the observer (Gómez & López-Moliner, 2013). Estimating and is, in turn, not very noisy (McKee & Welch, 1992).…”