## 1 Introduction  
In recent years, thanks to the remarkable development of VR technology, it has become possible to provide VR experiences with visual and auditory qualities comparable to reality. However, although tactile sensation is an important perception for reproducing a realistic environment, an established method of expressing it has not yet been proposed. Even now, many researchers have proposed various tactile expression methods. Currently proposed methods can be roughly divided into two types. One is a method that simulates tactile sensation by stimulating the tactile receptive field using electrical stimulation [1] or vibration [2], and controlling the force sensation on a pen-shaped device or fingertip like PHANToM [3] or SPIDAR [4]. The other is a method that uses the real object. Specifically, \"encounter-type tactile presentation\" [5,6] is one of the main methods that provides a tactile sensation that matches the user's experience by moving the object by machine or human power, or arranging a real object at the same coordinates as the object seen in the visual environment. Here, we focus on the latter type of haptic display. A method that uses a real object for haptic presentation can present haptics comparable to reality. Furthermore, users do not need to wear the devices, which is otherwise a burden to the user. In contrast, in current studies on tactile presentation using real objects, it is necessary to prepare one tactile object for each type of materials to be visually represented. In other words, the types of materials that can be used for the VR experience are limited by the types of haptic objects that can be prepared. One way to solve this issue is to express materials with similar tactile sensations using one real tactile texture. For example, if there are some materials that have a texture similar to a \"grainy textured wood\", a standard \"grained wood\" is used in the tactile expression and a variety of visual images are presented. In this way, there is no need to prepare a large number of physical objects. To implement this technique, we need to determine the permissible range of consistency between visual and tactile presentations. There are several published studies on the sensory characteristics of human senses such as sight and touch, and the characteristics of texture discrimination by vision or touch have been studied at least since the 1960s. For example, [PERSON] et al. [7] and [PERSON] et al. [8] showed that the shape and size of an object are mainly perceived visually. [PERSON] [9], in contrast, showed that tactile sensation rather than vision is used for recognition in texture perception. [PERSON] et al. [10] exposed participants to 96 textures, by either vision or touch only, and asked them to order the textures according to roughness. As a result, [PERSON] et al. concluded that tactile sensation is accurate for the perception of textures with a spatial period of less than 0.1 mm, and visual sensation is accurate for the perception for textures with a spatial period of 1 mm. [PERSON] et al. [11] conducted a discrimination experiment with similar settings, and suggested that texture discrimination may be modulated by skin vibration. [PERSON] et al. [12] concluded in another experiment that tactile texture discrimination was based on surface roughness and friction. In contrast, in [PERSON] et al. 's research [13], they printed a texture sample with a 3D printer based on images of natural objects and performed a discrimination experiment by touch alone, but subjects could not discriminate most of the textures. In light of this result, they pointed out that the tactile discrimination ability of complex spatial structures may be insensitive. As mentioned above, there have been many studies on whether the visual or tactile sense is better at texture discrimination, but most of these are examples comparing visual-only experiences with tactile-only experiences. These differ from the scenario in which the visual and tactile senses are presented simultaneously.