# A Texture-Based Simulation Framework for Pose Estimation
## 1 Introduction  
A three-dimensional pose of spherical objects is pivotal for industrial inspection [1], remote sensing applications [2], particle tracking [3], and Robotic Machining Systems [4]. While the traditional methods of pose estimation rely on geometric feature matching [5] or point cloud registration [6], they struggle under dynamic lighting and occlusion [7]. Recent research advances have combined pose estimation with deep learning to perform end-to-end pose estimation by training convolutional neural networks with datasets [8, 9, 10, 11]. Although this method is very convenient, there are still two key challenges in practical applications: (1) the cost of obtaining the real-world gesture data with intensive annotation [12] is too high, and human errors easily occur in the annotation process; (2) the lack of discriminability of features leads to a limited generalization ability of the model. When applied to unknown targets or when there are drastic lighting changes, the performance of the model decreases significantly [13, 14]. Moreover, if the observed object is regularly symmetric, such as a sphere, the problem of rotation ambiguity inherent in symmetry cannot be solved [14, 15].  
In recent years, the method of printing characteristic texture patterns on the surface of a sphere has been used to solve the problem of obtaining particle attitude information in particle rotation dynamics. [PERSON] et al. [16] matched experimental particle textures with synthetic templates using stereo vision, while [PERSON] et al. [17] optimized binary surface patterns via cost function minimization. Though effective in controlled settings, these methods exhibit limited generalization due to texture sensitivity. [PERSON] et al.'s stereolithography-based rendering [18] further highlights the trade-off between pattern complexity and computational feasibility.  
Recent advances in texture-driven pose estimation include the work of [PERSON] et al., who discussed in detail the importance of color and texture characteristics in using neural networks to estimate coal ash content and showed through experimental results and visualizations that the importance of color in a CNN was as high as 64.77%, while the texture characteristics contributed 35.23% [19]. [PERSON] et al. constructed a texture optimization network that combined contextual aggregate information and used the network for texture restoration to enhance low-light images [20]. These studies show that texture features play a crucial role in deep learning and image processing.  
To address these limitations, this work introduces a simulation-driven framework combining VTK-based synthetic data generation with Tamura texture theory. The specific research objectives and contents are as follows:  
* Objective: bridge the simulation-reality gap in attitude estimation for symmetrical objects using synthetic data and texture theory.
* Texture design: direction-sensitive surface textures governed by Tamura texture principles (coarseness, contrast, and directionality) with six variants (three complexity levels \(\times\) grayscale/color).
* Data generation: VTK-based synthetic data with automated pose space sampling (3\({}^{\circ}\) intervals) and implicit Euler angle encoding.
* Validation: experimental evaluation using 3D-printed textured spheres and real-world attitude measurements.  
This study establishes and experimentally validates a set of texture design criteria for spherical objects. Using 3D-printed textured spheres and actual attitude measurements, we bridge the simulation-reality gap in the positioning of symmetrical objects. This provides a robust attitude estimation for robotics and industrial metrology while offering a scalable synthetic data paradigm.