# A Texture-Based Simulation Framework for Pose Estimation
## 2 Materials and Methods
### Texture Design  
Texture, as a visual attribute of the surface of an object, reflects the statistical characteristics of the microstructure of the surface of an object and contains a wealth of structural information, which plays a crucial role in image recognition and object attitude estimation. In the field of computer vision, texture is usually defined as the spatial distribution pattern of gray pixel values within an image area. Early research shows that the key to texture perception is to extract the basic features of texture. [PERSON] et al. proposed six basic texture features, including coarseness, contrast, directionality, line-likeness, regularity, and roughness [21]. These features can effectively describe the statistical characteristics of texture and provide a theoretical basis for texture analysis and recognition. Recent studies have further quantified the relationship between texture features and research accuracy. [PERSON] et al. demonstrated that an optimized feature selection from 290 texture descriptors (including gray-level statistics and wavelet transforms) significantly improves osteoporosis detection in CT scans, with the k-nearest neighbors algorithm achieving 96.75% accuracy using 50 prioritized features [22]. [PERSON] et al. proposed a method to quantify surface roughness through multi-scale texture analysis and constructed a scalable roughness index. These indexes can reveal terrain texture characteristics at different spatial scales, provide a new dimension for terrain analysis, and improve the accuracy of geomorphic analysis [23]. [PERSON] et al. further studied the impact of texture distribution on visual perception and proposed rules for how texture distribution affects visual perception [24]. Their research showed that specific texture distribution patterns can enhance the visual system's perception, thereby improving the accuracy of object recognition. The stripe spacing annular ratio usually refers to the ratio of the spacing (d) between the adjacent stripes in a ring or periodic texture pattern to the characteristic size of the ring structure, such as the circumference L or radius r. Its mathematical expression is as follows:  
\[\eta=d/2\pi r\times 100\% \tag{1}\]  
This ratio reflects the distribution density of the fringes in the ring structure and is a key parameter of texture design. In optical measurement or machine vision, if the fringe spacing is too small (the ring ratio is too low), the imaging system may have aliasing effects due to insufficient sampling, resulting in the fringe not being able to be accurately resolved. According to [PERSON]'s sampling theorem, the sampling frequency needs to be at least twice the resolution of the system [25]. In display technology, if the spatial frequency corresponding to the pixel spacing is \(f_{p}\), the frequency of the moire fringe needs to meet the following:  
\[f_{Moir^{\prime}}\leq\frac{f_{p}}{2}\rightarrow\frac{d}{2\pi r}\geq 5\% \tag{2}\]  
In the fringe projection system, the ring ratio should be \(\geq\)5% to avoid the phenomenon of a moire fringe on the display screen, resulting in phase unwrapping errors [26]. We considered this in the process of designing the texture patterns, so the fringe spacing ratio is controlled above 5%. Based on the above theoretical basis, three textures with similar proportion distribution and fringe spacing but different complexities are designed. Texture1 is a low-complexity texture composed only of a horizontal stripe texture. Texture2 is a medium-complexity texture, adding a columnar stripe texture, and the texture differentiation is higher. Texture3 adds more columnar stripes and short horizontal stripes for a more complex texture area. CIE-Lab color difference (\(\Delta E\)) is an internationally used quantitative index of color difference. The minimum color difference perceptible to the human eye is \(\Delta E\approx 1\), but \(\Delta E\geq 5\) is needed to be reliably distinguished.