# The Effects of Augmented Reality Interaction Techniques on Egocentric Distance Estimation Accuracy
## 1 Introduction
### Direct vs. Indirect Interaction Methods  
Since many applications in VEs require selecting a target object among other objects, prior studies have applied an acquisition task as their basis of study. To acquire the object (target), the user performs an action to position the selection tool (e.g., a finger, cursor) over the target. A tracking system also needs to acquire all the necessary information from the user through his/her actions or other movements [9; 10]. [PERSON] and [PERSON] [11] investigated the performance of a direct pointing technique, wherein participants directly moved a hand to reach for a real/virtual target shown continuously in a VE with projection display. Similar studies by [PERSON] et al. [12] and [PERSON] et al. [13] employed direct-reaching by hand as a reporting method. In [PERSON], [PERSON], and [PERSON] [12], a comparison of interaction techniques with direct 3D mid-air interaction and a direct-2D touch screen found no significant difference in error rates in a selection task performed in a stereoscopic multi-touch tabletop setup. In contrast, [PERSON], [PERSON], and [PERSON] [13] conducted a comparative study of direct-matching and blind reaching in estimating the position of real/virtual objects in the stereoscopic display, and they found that perceptual direct-matching was more accurate than blind reaching in estimating egocentric distance. Overall, distances have been underestimated by up to 4 cm in blind reaching, but the disparity was reduced to 2.6 cm in perceptual direct matching. In our study, these techniques (direct pointing, reaching, and direct matching) are considered direct interaction methods.  
Unlike direct interaction methods, which utilize the human body, including gestures and gaze direction, to complete a task [14], indirect interaction methods allow the user to observe representations in a display. The user controls the representation or an icon to perform a specific task. The icon can represent a virtual hand, a virtual cursor, or anything imaginable that can be used as a virtual control [14]. The user directly controls an intermediary, such as a mouse, gamepad, stylus or other physical controls, to manipulate the icons. Previous studies have applied virtual representations to perform a task in IVEs. [PERSON] and [PERSON] [15] presented the possibility of an interaction metaphor of a virtual pointer and a virtual hand for object selection and repositioning tasks in IVE. In their study, the participants interacted with objects by ray casting pointing technique, wherein when both the virtual pointer and the virtual hand intersected with an object, the object could be manipulated (selected or repositioned). The comparison showed that the virtual pointer provided more accuracy in a selection of objects within the user's reaching distance than did the virtual hand. [PERSON] and [PERSON] [16] evaluated manipulation (positioning, grasping) performance with 3D controllers (i.e., virtual hand control and 3D cursor control) in a stereoscopic environment. The virtual hand control was set such that a participant manipulated a virtual object by contacting a virtual hand created by wearing a DataGlove on the right hand. The position and orientation of the glove were tracked in real time while the participant was manipulating the object. In the 3D cursor control setting, the participant controlled a SpaceMouse to move the 3D cursor (i.e., a virtual arrow) in VE. The results showed that in positioning tasks, virtual hand control was more accurate than the 3D cursor. A recent study by [PERSON] et al. [17] asked participants to position a ball-shaped object in a spherical area in a virtual space using a handheld controller in a ray casting technique setup. This technique allows a virtual light ray emitted from the controller to move an object remotely in a VE. Based on our definition of how users interact with objects, we considered those settings in indirect interaction methods.