# A Novel Method Using 3D Interest Points to Place Markers on a Large Object in Augmented Reality
## 1 Introduction  
Augmented reality (AR) is a computer graphics technology that (1) combines a virtual image with a real environment, (2) enables real-time interaction, and (3) registers a virtual object in a three-dimensional space [1]. The technology to register an augmented virtual object to an object in the real environment (hereafter real object) is not only a core technology of AR but also an index for ensuring performance [2]. Registration is conducted by using markers to combine the real world and the virtual world (hereafter marker-based AR), or by using features between the real and virtual world through sensors (hereafter markerless AR). A marker generally refers to an object that can be identified and tracked through digital devices, such as camera sensors. There are various types of markers, such as simple flat images [3; 4; 5; 6], infrared markers [7; 8], and optical markers [9; 10]. Markers are used as reference points for registration not only in marker-based AR but also in markerless AR. For AR applications where accurate registration is essential, such as in medical and industrial fields, marker-based registration is still required [11; 12]. If the target is a large object for registration in AR using markers (e.g., vehicles, robots, and factory machines), the registration error of the marker can be increased according to the scale of the object. This error can be complemented by using more than one marker (hereafter multiple markers). This is because other markers can correct errors that may arise in a certain marker, thereby providing more accurate registration [13; 14; 15]. In AR using these markers, there are two inevitable problems: (1) geometric shape discrepancies between a real object and a virtual object (hereafter geometric discrepancyproblem), and (2) the relative positions of markers placed on the virtual object and markers placed on the real object are not consistent (hereafter relative position consistency problem). The geometric discrepancy problem arises from the issue that the virtual objects designed by 3D/CAD/CAM engineers are not 1:1 identical to the real objects printed out into the real world. This is because errors inevitably occur during the production process due to the state of the machinery, environment, materials, costs, etc. As it is impossible to solve these errors, acceptable errors known as tolerance are generally applied. Registration errors owing to this problem can be reduced by placing multiple markers evenly on the surface of the object. The relative position consistency problem arises from the issue that, when the marker (A) is placed on the real object based on the position of marker (B) that is placed on the virtual object, there is no guarantee that A and B have relatively consistent positions. This is because the process of referencing A (e.g., subjective interpretation by human or image processing result by machine) may be inaccurate, and errors may occur in the process of placing markers. Registration errors owing to this problem can be reduced by placing multiple markers in clearly identifiable positions. However, studies on applying multiple markers to a large object are still insufficient [5; 14; 15]. [PERSON] et al. (2020) proposed a method to reliably augment a large object using multiple markers for remote collaboration [5]. In the proposed method, five markers were used to augment a large object, but the registration aspect was not considered because it was augmented in an actual box that was not related to the actual object to be registered. [PERSON] et al. (2020) developed and proposed an AR system based on multiple markers. In the proposed method, multiple markers were placed 1.5 m apart around the perimeter of a large object. However, in this study, the registration was performed again each time a marker was tracked, so it was considered a single marker-based registration [14]. [PERSON] et al. (2023) proposed a method for 3D scanning actual a large object using AR head-mounted display.