Introduction

An object's perceived stability affects our interactions with it and our expectations about its behaviour [1], [2]. In order to know whether an object will fall over or right itself, the brain must accurately represent the physical laws governing object stability. When an object is in a uniform gravitational field, all forces acting on the object can be represented by a single resultant force and the point at which this resultant force acts is called the centre of mass. In accordance with Newton's first and second laws of motion [3] when the gravity-projected centre-of-mass (COM) of an object lies directly above the point or area of support, there is no net torque and the object remains in static equilibrium. We will call the critical angle (CA) the angle through which the object must be rotated so that it corresponds to the situation when the centre of mass is vertically above the point of support (see red gravity projection and red shaded area in Figure 1A). When the COM lies outside the support area (> CA), the object falls over. When the COM lies inside the support area (< CA), the object rights itself. Thus an object at the edge of a table whose COM is high (i.e., top-heavy) will sooner fall off the table than an object whose COM is lower in the presence of a perturbation.

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Figure 1. Influence of body tilt on perceived object stability.

(A) Stimuli. Critical angle (CA) predictions (shaded areas) relative to physical (red) and perceived (blue) gravity. (B) Results. Mean CA when upright (▾), left (•) and right side down (▪) for objects with a different COM relative to physical (black) and perceived (coloured solid lines) gravity. Linear regression slopes are shown as coloured dashed lines. Error bars are ±1 S.E. Cartoon inserts indicate the extent to which the SVV shifts towards the body. (C) Correlation (dashed line) between the SVV and the perceived CA averaged across all objects. Here the perceived gravity prediction is based on the average SVV setting and the physical gravity prediction is based on the ground truth CA averaged across the five objects. (D) Correlations between the CA and the SVV for each participant ordered according to the CA-SVV slope. Underlined initials identify control experiment participants.

https://doi.org/10.1371/journal.pone.0019289.g001

The force of gravity is not sensed directly. It is the indirect effects of gravity that are detected. To estimate an object's stability visually, the brain must integrate information across the shape to estimate the COM position relative to the support point and compare its orientation to gravity [4]. While it has been shown that observers typically underestimate the CA, suggestive of a conservative bias to not allow objects to fall [4], whether the brain relies solely on visual heuristics to estimate object stability has not previously been investigated. When observers lie on their sides, gravity is perceived as tilted towards the orientation of the body [5]–[12], consistent with a representation of gravity derived from multisensory information [11]–[15]. We exploited this to determine whether CA estimates are consistent with gravity's true direction or the direction in which gravity is perceived.

The perceived direction of gravity can be measured using the subjective visual vertical (SVV) [5]–[10]. If objects are perceived to topple over when the perceived gravity-projected COM lies outside the support area then when a participant lays right side down (RSD) the CA of a rightward leaning object should increase compared to when they are upright (Figure 1A, blue line and shaded area). Likewise the CA should decrease when lying left side down (LSD). The extent to which the CA changes with body posture, compared to how the SVV changes, provides a metric for assessing the contribution of multisensory estimates versus purely visual estimates of gravity in determining the perceived stability of objects.

By dissociating biased from veridical estimates of gravity we show that the perceived critical angle is significantly biased in the same direction as the subjective visual vertical, indicating that a multisensory estimate of gravity is used when judging whether objects will fall or not.

Results

Participants either sat upright or lay on their left or right side and viewed stimuli presented on a laptop computer through a circular tube and responded with button presses. In one task, participants viewed computer rendered images of objects with different mass distributions depicted close to the precipitous right edge of a table (see Figure 1B and Materials and Methods). The vertical direction in the depicted scene was aligned with the direction of gravity in the participant's physical environment and the table was always upright in the real world and therefore provided a visual reference to earth-horizontal. In a second task the perceived direction of gravity was measured using the SVV where participants indicated whether a visual line was oriented clockwise or counterclockwise relative to gravitational vertical.

The SVV results show that gravity is perceived veridically when upright (0.6°, SE: 0.4) but is perceived as tilted towards the body (Figure 1B) when left (−15.2°, SE: 1.8) and right side down (14.8°, SE: 2.1; F(1.2,16.7) = 70.3, p<.001). The perceived CA is influenced by body orientation (F(2,28) = 22.5, p<.001) such that left tilted participants underestimate – and right tilted participants overestimate – the stability of rightward falling objects in the same direction as the SVV.

This close relation between the perceived CA and the average SVV is highly significant (slope  = .24, r = .40, p = .007; Figure 1C) confirming that participants do not judge the stability of falling objects relative to a veridical estimate of gravity. Rather, the perceived stability of objects is affected by multisensory estimates of gravity's direction. This effect is also found for leftward falling objects and with different background images (see below). Note that while the slope of the relation between the CA and the SVV varies across individuals (Figure 1D), the perceived CA changes in the same direction as perceived gravity in all but one participant - who does estimate object stability relative to an unbiased estimate of gravity's direction.

Body orientation also affects the extent to which object shape influences the perceived stability of objects (F(8,112) = 3.3, p = .002) such that the effect of object shape is most pronounced in the RSD condition. It is not readily apparent what can account for the significant interaction between body orientation and object shape. Given that different frames of reference can influence the perceptual organization of shapes [16]–[21], it seems plausible that participants attend to different aspects of the geometry depending on the object's orientation relative to their body, leading to different response criteria.

Slopes of linear regression fits to the CA of the five objects are significantly shallower than the slope of the ground truth prediction when LSD (t(14) = 3.2, p = .007), upright (t(14) = 2.6, p = .020) and RSD (t(14) = 5.2, p<.001), indicating that top heavy objects are perceived as more stable than they are. In addition, no significant downward shift of CA estimates was found when upright (t(14) = 1.5, p = .15) relative to the ground truth prediction, which would have indicated being conservative in estimating object stability. While CA estimates are significantly down shifted in the LSD condition (t(14) = 4.4, p = .001) and in the RSD condition (t(14) = 1.6, p = .14), these results are difficult to interpret in terms of being conservative given the interaction of the CA with body orientation.

Leftward Falling Objects

An additional perceived CA experiment using 7 of the same participants from the initial experiment was run in order to further study the effect of body posture on the CA. The methods are the same as in the perceived CA experiment above, but here objects are placed close to the precipitous left edge of a table. When comparing estimates for leftward versus rightward falling objects we do not find a significant effect of the direction in which objects fall (F(1,6) = .04, p = .85). Otherwise the results agree completely with those from the original experiment such that body orientation (F(2,12) = 5.3, p = .022) and object shape (F(4,24) = 4.8, p = .005) significantly affect the perceived CA (Figure 2A). Here, however, we find that left tilted participants overestimate – and right tilted participants underestimate – the stability of leftward falling objects in the same direction as the SVV.

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Figure 2. Control experiment results.

(A) Mean CA for leftward falling objects relative to physical (black) and perceived (coloured lines) gravity as measured with the upright table visual background. (B) Correlations between the SVV with the grey background (filled symbols, dashed line), and the SVV with the table image (empty symbols, dotted line) paired with the perceived CA averaged across all objects. Data in A and B are from the same group of 7 participants from the original group of 15 for two different control experiments. Note that the prediction line for perceived gravity is a negative slope for leftward falling objects and a positive slope for rightward falling objects as shown in Figure 1C. All other conventions as in Figure 1.

https://doi.org/10.1371/journal.pone.0019289.g002

Discussion

Humans spend most of their time engaging in the world with an upright posture. Here sensory information about self-orientation is usually redundant and the perceived stability of objects [2] and the body [5]–[10] are generally veridical. Knowing an object's physical stability is important as it affects our interactions with it and our expectations about its behaviour [1], [2]. Equally important is knowing about the orientation and stability of the body, which affects our ability to coordinate our actions [12]–[15], [22], [23], maintain our balance [24] and correctly identify objects [8]–[10]. The vestibular system, which detects tilt of the head relative to gravity, provides a more reliable signal for small tilts of the head relative to an upright posture than for large tilts of the head [5]. Our results are in accord with previous studies showing that the perceived direction of gravity is influenced by visual, body sense and prior information because of compensation for poor vestibular sensitivity when tilted which helps maintain optimal perception and action [5]–[12], [25]–[27].

It has been suggested that multisensory information is integrated by the brain to generate separate but related frames of reference tailored for different task demands [8]–[12]. The present study extends and qualifies these previous results by showing that the stability of objects is not perceived relative to a veridical estimate of gravity's true direction. Rather, a potentially biased internal representation of gravity derived from multisensory information is used as a frame of reference when estimating the critical angle and the SVV. This is surprising given that the table in the scene provides a strong, purely visual frame of reference that the visual system could use for estimating the gravity direction and computing stability. As both the SVV and CA tasks require comparing a visual object with an unseen line representing gravity's orientation relative to the body, and both tasks relate to stability – of the self and of objects, respectively – we propose that a common internal representation of gravity is used as a frame of reference for both tasks. In agreement with previous studies [25]–[27], we suggest that use of this frame of reference is optimized for when the body is upright at the cost of introducing systematic errors in visual estimates of physical stability when tilted; objects appear more stable than they are when the head is tilted in the same direction in which they fall.

Humans tend to adopt a reasonable strategy of using the perceived centre of an object's shape, which is close to the centre of mass, to determine an object's centre of mass [4], [28]–[30]. This strategy is reasonable in so far as the object is of uniform density. It is important to note that although we explicitly instructed our participants to treat the objects that we used as being of uniform density, biases from this assumption could explain the fact that the effect of object shape on the critical angle did not always follow the physical predictions. Further, it has been shown previously that centre of mass estimates can be inconsistent with stability estimates [4]. Finally, upright observers tend to underestimate the critical angle suggesting a conservative bias to not allow the object to fall [4]. While this hypothesis has strong ecological appeal, it is clear that this conservative tendency was not consistent across all conditions and object shapes used here.

An optimal estimate of gravity's direction is internally represented by the brain to disambiguate [13] or supplement sensory information [15]. Our findings indicate that although the physical laws governing object stability are reasonably accurately represented by the brain, they are in turn biased by multisensory estimates of gravity. This result has important implications for existing theories of how humans perceive the stability of objects. For example, since the work of Piaget [1] it has been shown that children [1], [31] and adults [2] have difficulty in solving problems involving the physical laws which govern equilibrium, even when these laws are explicitly taught to them [32]. We suggest that having to integrate multisensory information, which has been shown to change during development [33], [34], with sex of the participant [9], [34]–[37], and in patients with neuropsychiatric disorders [10], [38]–[40], may contribute to the errors associated with solving these problems.

Materials and Methods

Acknowledgments

We gratefully thank Marc Ernst and Massimiliano Di Luca for comments on an earlier version of the manuscript as well as Thomas Tanner and Martin Breidt for technical assistance.