# Virtual Marker Technique to Enhance User Interactions in a Marker-Based AR System
## 1 Introduction  
The evolution of augmented reality (AR) technology has created different types of AR for various purposes [1]. AR can be combined with other new technologies, thus it has been widely used in various fields such as education [2; 3; 4], medicine [5; 6; 7], robotics [8; 9; 10], and manufacturing [11; 12]. Previous research has investigated the state of the art technology in this area by reviewing some recent applications of AR technology as well as some known limitations regarding human factors in the use of AR systems [13; 14; 15]. Some studies have mentioned some technical challenges faced in future AR applications--for example, binocular (stereo) view, high resolution, colour depth, luminance, contrast, field of view (FOV), and focus depth [16; 17; 18]. Aside from the technical challenges, the user interface must also follow some guidelines [19]. Interaction is an important aspect that has been widely discussed [18; 20]. Early AR interfaces used input techniques inspired from desktop interfaces or virtual reality, but over time more innovative methods have been used, such as tangible AR [21; 22] and natural gesture interaction [23; 24]. ser issues encompass such things as ease of use, whether the hardware necessary for AR will reach an acceptable design that people will want to wear and use, and whether the technology will be accepted as part of daily life [25]. For example, if the cost of using an AR system is too high, this may affect the social acceptance of the system. Therefore, one of the most important aspects of AR is to create appropriate techniques for intuitive interaction between the user and the virtual content of AR applications [19]. There are three different types of AR, which are marker-based AR, markerless AR, and location-based AR [26; 27; 28]. Marker-based AR is used when what the user is looking at is known [29]. It has been proven to be sufficiently robust and accurate, and so far almost all AR software development kits support marker-based tracking methods [30]. Marker-based AR gives the position of the marker in the camera coordinate system [31]. Therefore, the sequence of markers can be determined by obtaining the coordinate information ofmultiple markers. Coordinate information can be used to combine multiple markers to complete some control functions [32]. In fact, although many AR sdks support the simultaneous recognition of multiple markers, there have been few in-depth studies on the cooperation of multiple markers [33]. In the work of [PERSON] et al. [34], the authors implemented a prototype system which was capable of drawing and moving shapes with multiple physical markers and created loops and branch executions. It was possible to edit the program by writing on the paper cards. Users can carry out some creative activities and perform simple operations on 2D images. Although the research attempts to establish the connection of multiple markers, the use of multiple markers is mainly intended to provide learners with simple and intuitive basic programming learning. More often, multiple AR markers are just used for more accurate detection and tracking [35; 36; 37]. The question of how to use multiple markers to build an AR system framework is our main research purpose. There are some problems in marker-based AR systems. In marker-based AR systems, markers are usually relatively independent. Moreover, the markers are predefined by the system creator in advance, and users can only use these predefined markers to complete the construction of certain specified content [38]. Therefore, such systems usually lack flexibility and do not allow users to create content freely. In our research, we propose a virtual marker technique to build a marker-based AR system framework where multiple AR markers, including virtual and physical markers, work together. Virtual markers are generated from physical template markers or existing virtual markers. Virtual markers mainly consist of function markers, variable markers, and number markers.