# The Effect of Depth Information on Visual Complexity Perception in Three-Dimensional Textures
## 1 Introduction  
Visual complexity is one of the subjective impressions associated with visual information of stimuli and plays an important role in human perception and recognition of patterns and images. The study of visual complexity is significant for visual understanding and aesthetic evaluation. It is useful in many applications, such as image segmentation, content-based image retrieval, and user interface design. It has been shown that visual complexity also affects human emotions, memory, and active movement [1]. However, it is challenging to describe human sensitivity to perception of visual complexity quantitatively. The definition of visual complexity also varies according to the research field and application [2; 3; 4].  
In the field of computer science, researchers have attempted to describe, measure, and model image complexity based on mathematical and computational approaches, such as information theory [5], spatial information [6], visual attention [7], independent component analysis [8], and machine learning [9; 10; 11]. Computer scientists are usually interested in the objective description of image complexity rather than the subjective perception of visual complexity. In the field of psychology, researchers are more interested in exploring attentional models and identifying factors that affectvisual complexity perception [12; 13; 14; 15]. Previously, several studies have attempted to correlate the computational measures and the perception of visual complexity [16; 17; 18]. Quantitative analyses have been conducted to investigate the relationship between the perception of visual complexity and the factors influencing it [19; 20].  
The stimuli and target images used in previous studies of visual complexity perception include abstract patterns [14; 21], outline images and hieroglyphs [22], texture images [23; 24; 25], grayscale images [26], paintings [16; 19; 20], webpages [27; 28], and real-world images [8; 13; 18]. Thus, in conventional studies of visual complexity perception, the research objects have been limited to two-dimensional (2D) images. Due to the rapid development of technologies such as three-dimensional (3D) measurement, range imaging, and stereoscopic display, users now have more opportunities to appreciate 3D or RGB-depth (RGB-D) images that convey depth information. In this study, we aimed to explore how depth information affects visual complexity perception. It should be noted that the depth information we introduced in this study refers to spatial changes in depth on the continuous image surface. Structural complexity in 3D modeling lies outside the scope of this study.  
Virtual reality (VR) technology has been widely used as a research tool in psychological studies of visual perception over the last few decades [29; 30]. One of the advantages of VR in psychological experiments is that it can display visual stimuli with controlled parameters in 3D. The impression of depth can be reproduced by presenting binocular vision cues using a head-mounted display (HMD) [31]. VR technology also provides an immersive environment for studies on multimodal sensory interactions [32; 33; 34].  
In this study, we constructed a VR system and applied it to investigate the visual complexity perceptions of texture images in 2D and 3D conditions. One of the reasons we chose textures as the stimuli in this study is that the properties of textures are more accessible and easier to manipulate than natural images [35]. Moreover, the visual perception of textures can be represented in a lower feature space. Three to five textural features have been commonly used to describe perceptual dimensions of textures [24; 25; 36; 37]. We scanned three textures with different visual complexities from physical objects using photogrammetry. We investigated the relationship between visual complexity perception and depth information, and found that depth information is essential in the visual complexity perception of 3D textures.