# Examining User Perception of the Size of Multiple Objects in Virtual Reality
## 1 Introduction  
The IVE: Australian Research Centre for Interactive and Virtual Environments at the University of South Australia has been working with CADwalk Global ([PERSON] and [PERSON], Project Managers for CADwalk Global--[[https://www.cadwalk.global/](https://www.cadwalk.global/)]([https://www.cadwalk.global/](https://www.cadwalk.global/))) in the development of visualisation tools for large scale designs [1]. Manufactured high-end instrumented facilities, such as command centres and control panels (as depicted in Figure 1), are almost entirely designed virtually [2]. Understanding the size and shape of the virtual controls is important for the understanding of the final design by the stakeholders [2]. Figure 2 depicts an example of a 3D virtual push button. Understanding the height of these buttons off the control panel is critical for understanding the design as a whole. The faithful representation of the size of a button, switch, dial or lever is critical for stakeholder understanding of control system designs [3]. Immersive Virtual Reality (VR) with a Head Mounted Display (HMD) and large stereo displays are the most common methods of presenting designs [4]. This study is motivated by the use of HMDs in the design process and understanding an HMD's ability to correctly represent the size of a virtual control when compared to the additional virtual controls in the user's view. This article presents the results of a user study to determine a user's perception of the size of a cylinder shaped object when presented in VR. The cylinder shape was chosen as an abstract representation of a button or dial, such as is shown in the Figure 2 depiction of a 3D virtual pushbutton control. The button has an apparent scale in \(\mathbb{R}^{3}\). This article explores how users perceive the size of these virtual objects in all three dimensions when viewed in a VR HMD. There have been numerous studies [5, 6] comparing the size of a virtual object in VR with a physical object. In other words, how do users judge the size of the virtual object in terms of real-world dimensions? In a study by [PERSON] and [PERSON] [7], their findings suggest that there may be a difference between VR and the natural environment in the way they affect the perception of size changes. This article investigates whether virtual objects of different colours appear to be different sizes to the user in a VR HMD. Measuring the amount of difference perceived by the users is critical for understanding the user's perception of various virtual objects in a virtual scene. In the design domain, we are investigating solutions; these virtual objects would be the individual controls on a control panel. Still, this insight extends to other VR applications that require users to interact with virtual objects, such as picking up or touching the objects. The study presented in this article employs concepts of Point of Subjective Equality and Just-Noticeable Distance as a means to understand the participants' ability to understand the sizes of the virtual objects. These concepts were first purposed in 1910 by [PERSON] [8]. The _\"Point of Subjective Equality\"_ (PSE) is when the two stimuli, the _standard_ and _comparison_ appear subjectively the same. The point of subjective equality is the 50% probability point of the user of choosing a measure for the comparison stimuli greater or less than the standard stimuli. Point of subjective equality has been used to detect sizes of objects for redirect haptics in VR [9], system latency [10] and rotational gain for redirected walking [11]. The method employed in this study presents to the participant (in VR wearing an HMD) a _standard_ virtual object and a second _comparison_ virtual object. The experiment employs _method of adjustment_ for the participants to interact with the stimulus. This is a psychophysical technique in which the participant manipulates a variable stimulus to match a fixed stimulus or standard [12]. In this experiment, the participant is shown a standard visual stimulus  
Figure 1: Control room example.