Angular Declination and Perceived Distance

In two experiments involving a total of 83 participants, the effect of a vertical angular optical compression on the perceived distance and size of a target on the ground was investigated. Replicating an earlier report (Wallach & O’Leary, 1982), reducing the apparent angular declination below the horizon produced apparent object width increases (by 33%) consistent with the perception of a greater ground distance to the object. A throwing task confirmed that perceived distance was indeed altered by about 33%. The results are discussed in relation to cue recruitment and recent evidence of systematic bias in the perception of angular declination. ANGULAR DECLINATION AND PERCEIVED DISTANCE 3 Direct manipulation of perceived angular declination affects perceived size and distance: A replication and extension of Wallach and O’Leary (1982) The rules of pictorial perspective include the implication that the higher the base of a terrestrial object appears in a picture, the farther away it is along the ground (Gibson, 1950), and thus “height in the field” is a pictorial cue to distance representing proximity to the horizon (see Sedgwick, 1980). When an observer is situated within a 3D environment, the precise angular direction to the point where an object contacts a horizontal ground plane can provide a direct measure of the distance to the object along the ground, provided one can (implicitly) take one’s eye-height into account. The first to document angular direction as a source of ground distance information were Wallach and O’Leary (1982; henceforth WOL). WOL developed a novel optical instrument to distort the apparent angular direction to an object on the ground (i.e., “slope of regard”) without altering the perceived direction of the horizon, and showed that the apparent size of the object was appropriately altered by this manipulation. That is, compressing the apparent vertical angular deviation from straight ahead increased the perceived width of the object consistent with the notion that it was perceived as being farther away. As we will explain below, WOL’s decision to measure perceived size led to an ambiguity about whether perceived distance was actually affected by their optical manipulation. Here we report a replication in which we reconstructed their optical device and measured both perceived size (replicating the main conditions of their experiments) and perceived distance (extending their work). Although there are now independent reasons to believe that angular declination is an important distance cue that controls walking behavior and explicit distance perception (Li et al., 2013; Messing & Durgin, 2005; Ooi, Wu & He, 2001), no one apart from WOL have previously directly manipulated perceived angular declination without altering the perceived horizon itself. ANGULAR DECLINATION AND PERCEIVED DISTANCE 4 For example, Ooi, Wu and He (2001) showed that adaptation to base-up prism goggles changed perceived distance (measured by walking behavior) in a manner consistent with a resetting of the perceived height of the (implicit) visual horizon. But using prisms to alter the apparent horizon also alters the apparent orientation of the ground plane (see Harris, 1974). Messing and Durgin (2005) showed that a subtle direct manipulation of the explicit visual horizon in a virtual environment (i.e., lowering it by 1.5°) also shifted perceived distance as predicted – both for explicit estimation and for a blindfolded walking task. But these manipulations both involve shifting the perceived horizon rather than rescaling perceived angles relative to the true horizon as WOL did. WOL’s rescaling of perceived angular declination is of particular current interest because of recent evidence that people may generally underestimate egocentric ground distance because their perceptual scaling of angular declination is already distorted (Durgin & Li, 2011; Li & Durgin, 2012; Li, Phillips & Durgin, 2011). The device employed by WOL is a sort of embodiment of angular expansion/compression.