# Examining User Perception of the Size of Multiple Objects in Virtual Reality
## 1 Introduction
### Background
#### 1.2.2 Virtual Reality Technologies  
Virtual Reality is the display technology employed in the study present in this article. Although this article is concerned with size estimations, distance estimations can provide insight into the size judgement ability of users in VR. [PERSON] and [PERSON] [18] found participants in their study slightly overestimated distance judgements by a similar amount in both their horizontal and vertical estimates in VR with an HMD. The section will start with a review of the literature concern users' size judgement in HMD versions of VR, and this is followed by a discussion of other display technologies employed to study size judgement of users' in VR. **Size Judgement HMD:** This section provides a description of some of the experiments to understand a user's ability to estimate the size of virtual objects in VR using a HMD. HMDs can be categorised into eight major categories, as shown by [PERSON] and [PERSON] [19]. HMDs have different optical parameters and characteristics [20] including method of augmentation, vergence and accommodation, ocularity, stereoscopy, focus, occlusion, resolution, refresh rate, depth of field, viewpoint offset, brightness, contrast, distortions and aberrations, latency, ergonomics and social acceptance (social weight [21]). When viewing in VR in HMDs, people frequently underestimate egocentric distances (the measured distance from themselves to a target). The range underestimates egocentric distances is from 50% to 90% of the displayed distance [22; 23; 24]. [PERSON] et al. conducted a series of tests to compare the influence of different factors on the perception of shapes displayed on stereoscopic displays. They found that head tracking has a more significant impact than other parameters [25]. [PERSON] et al. [26] investigated display attributes that affect a user's perception of the scale of virtual objects, and these are as follows, (1) stereoscopic, (2) tracking the user's viewpoint and (3) the field of view (FOV). Participants directly estimated the size of a gap by matching the distance between their hands to the gap width and judged their ability to pass unimpeded through the gap in one of five typical implementations of three display technologies: (1) wide-FOV HMD condition nVisor SX111 display, (2) nVisor SX60 display and (3) a back-projected display wall. The results showed gap width was similar for the HMD conditions and the back-projected display wall with stereo and tracking. Monocular viewing conditions showed an underestimation of size. It has been shown users employing a HMD perceived objects around them relative to the size of their body. [PERSON], [PERSON] and [PERSON] [27] examined how in VR a virtual avatar of the user would affect perceived graspable object sizes as the size of the user's avatar hand changes. They manipulated the realism to be high, medium or low, and they changed the size of the avatar's hand to smaller or enlarged. They measured the user's perceived size of a virtual cube they held. They found that the size of the cube was perceived to be reduced when the user's avatar hand was enlarged, and this was true for all conditions of realism of the hand. [PERSON] et al. [7] investigated the effects of six factors on size judgement in a HMD VR system: (1) binocular vs. stereoscopic viewing; (2) image resolution \(1280\times 1024\) vs. \(640\times 480\); (3) FOV \(60^{\circ}\times 60^{\circ}\) vs.  
\(100^{\circ}\times 60^{\circ}\); (4) scene contrast of single luminance level for every surface vs. multiple luminance level for every surface; (5) consistent contrast environment vs. inconsistent contrast environment; and (6) target distance of 10, 60, and 120 feet. The general findings from this study suggest more natural viewing conditions in VR differ from natural viewing conditions. [PERSON] et al. [28] investigated visual-haptic size estimation in HMD VR. They found participants demonstrated a central tendency effect where they overestimated for smaller haptic sizes but had an under-estimation for larger haptic sizes.