Editing Visual acuity (section)

=== Subtended angular velocity detection threshold (SAVT) ===
There is a specific acuity limit in detecting an approaching object's looming motion.<ref name="Weinberger-1971">{{Cite journal |last=Weinberger |first=Hershel |name-list-style=vanc |date=19 February 1971 |title=Conjecture on the Visual Estimation of Relative Radial Motion |journal=[[Nature (journal)|Nature]] |volume=229 |issue=5286 |page=562 |bibcode=1971Natur.229..562W |doi=10.1038/229562a0 |pmid=4925353 |s2cid=4290244 |doi-access=free}}</ref><ref name="Schrater-2001">{{Cite journal |last1=Schrater |first1=Paul R. |last2=Knill |first2=David C. |last3=Simoncelli |first3=Eero P. |name-list-style=vanc |date=12 April 2001 |title=Perceiving visual expansion without optic flow |journal=[[Nature (journal)|Nature]] |volume=410 |issue=6830 |pages=816–819 |bibcode=2001Natur.410..816S |doi=10.1038/35071075 |pmid=11298449 |s2cid=4406675 |quote=When an observer moves forward in the environment, the image on his or her retina expands. The rate of this expansion conveys information about the observer's speed and the time to collision... this rate might also be estimated from changes in the size (or scale) of image features... we show, ... observers can estimate expansion rates from scale-change information alone, and that pure scale changes can produce motion after-effects. These two findings suggest that the visual system contains mechanisms that are explicitly sensitive to changes in scale.}}</ref> This is regarded as the [[subtended]] angular velocity detection threshold (SAVT) limit of visual acuity.<ref>{{Cite journal |last1=Hoffmann |first1=Errol R. |last2=Mortimer |first2=Rudolf G. |name-list-style=vanc |date=July 1996 |title=Scaling of relative velocity between vehicles |journal=Accident Analysis & Prevention |volume=28 |issue=4 |pages=415–421 |doi=10.1016/0001-4575(96)00005-X |issn=0001-4575 |pmid=8870768 |quote=Only when the subtended angular velocity of the lead vehicle exceeded about 0.003 rad/s were the subjects able to scale the relative velocity}}</ref> It has a practical value of 0.0275 rad/s.<ref>{{Cite journal |last1=Maddox |first1=Michael E. |last2=Kiefer |first2=Aaron |name-list-style=vanc |date=September 2012 |title=Looming Threshold Limits and Their Use in Forensic Practice |journal=Proceedings of the Human Factors and Ergonomics Society Annual Meeting |volume=50 |pages=700–704 |doi=10.1177/1071181312561146 |s2cid=109898296 |quote=A number of laboratory researchers have reported values of the looming threshold to be in the range of 0.003 radian/sec. Forensic practitioners routinely use elevated values of the looming threshold, e.g., 0.005–0.008, to account for the complexity of real-world driving tasks. However, only one source has used data from actual vehicle accidents to arrive at a looming threshold – and that value, 0.0275 rad/sec, is an order of magnitude larger than that derived from laboratory studies. In this study, we examine a much broader range of real-world accident data to obtain an estimate of the reasonable upper end of the looming threshold. The results show a range of 0.0397 to 0.0117 rad/sec... |number=1}}</ref> For a person with SAVT limit of <math>\dot\theta_t</math>, the looming motion of a directly approaching object of size {{mvar|S}}, moving at velocity {{mvar|v}}, is not detectable until its distance {{mvar|D}} is<ref name="Weinberger-1971" />

<math display="block">D \lessapprox \sqrt{\frac{S \cdot v}{\dot{\theta_{t}}}-\frac{S^2}{4}},</math>

where the {{math|S<sup>2</sup>/4}} term is omitted for small objects relative to great distances by [[small-angle approximation]].

To exceed the SAVT, an object of size {{mvar|S}} moving as velocity {{mvar|v}} must be closer than {{mvar|D}}; beyond that distance, [[subjective constancy]] is experienced. The SAVT <math>\dot\theta_t</math> can be measured from the distance at which a looming object is first detected:

<math display="block"> \dot\theta_t \approx \frac{4S \cdot v}{S^2 + 4D^2}, </math>

where the {{math|S<sup>2</sup>}} term is omitted for small objects relative to great distances by [[small-angle approximation]].

The SAVT has the same kind of importance to driving safety and sports as the static limit. The formula is derived from taking the [[derivative]] of the [[visual angle]] with respect to distance, and then multiplying by velocity to obtain the time rate of visual expansion ({{math|d<var>θ</var>/d<var>t</var> {{=}} d<var>θ</var>/d<var>x</var> · d<var>x</var>/d<var>t</var>}}).