# A Texture-Based Simulation Framework for Pose Estimation
## 3 Simulations and Design Criterion
### Results, Discussion, and Design Criterion  
In the performance test of the test set, the MAE, RMSE, and Std of each texture corresponding to the test set are recorded, and the texture characteristics and performance on the validation set are summarized, as shown in Table 2 below.  
The experimental results demonstrate a strong positive correlation between texture complexity and pose estimation accuracy. The validation set performance progressively improves with increasing complexity, and the high-complexity color textures (Texture_3_color) achieve the optimal results (MAE: 0.416\({}^{\circ}\), RMSE: 0.543\({}^{\circ}\), and per-axis Std \(\leq\) 0.549\({}^{\circ}\)). Notably, the grayscale and color variants exhibit parallel trends, with MAE reductions of 58.2% and 57.3%, respectively, from Texture_1 to Texture_3, underscoring complexity's universal benefit across the color modalities.  
However, the test set analyses reveal critical nuances in the model generalization. While color enhances the validation accuracy universally, its real-world impact proves complexity-dependent: low-complexity color textures (Texture_1_color) suffer a 35.5% test error increase, accompanied by a 9.4% RMSE degradation (1.411\({}^{\circ}\)to 1.543\({}^{\circ}\)), over their grayscale counterparts, suggesting that chromatic noise dominates when structural features are sparse. Conversely, high-complexity color textures (Texture_3_color) maintain superior test performance (MAE: 0.731\({}^{\circ}\), RMSE: 0.876\({}^{\circ}\)), with the color-to-grayscale RMSE advantage persisting (0.876\({}^{\circ}\) and 0.911\({}^{\circ}\)), despite the domain shift. This duality establishes texture complexity as a prerequisite for effective color utilization in pose estimation systems.  
Based on the analysis results of the above experimental data and the previous theories, a design criterion for the surface texture of spherical particles for attitude estimation is finally established:  
(1) Orientation uniqueness: it should be ensured that each view corresponds to a unique orientation, so that the model can distinguish between different poses;  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Texture** & **Description** & **Val\_** & **Val\_** & **Test\_Mae** & **Test\_** & **Test\_Std** \\ \hline Texture\_1\_bw & Black and white; low complexity & 1.178 & 1.469 & 1.052 & 1.411 & 0.997, 0.625, 0.916 \\ Texture\_1\_color & Color; low complexity & 0.974 & 1.189 & 1.32 & 1.543 & 0.649, 0.48, 0.632 \\ Texture\_2\_bw & Black and white; medium complexity & 0.842 & 1.078 & 1.039 & 1.335 & 0.6, 0.639, 1.059 \\ Texture\_2\_color & Color; medium complexity & 0.791 & 1.037 & 1.008 & 1.237 & 0.659, 0.737, 0.762 \\ Texture\_3\_bw & Black and white; high complexity & 0.492 & 0.661 & 0.758 & 0.911 & 0.327, 0.665, 0.483 \\ Texture\_3\_color & Color; high complexity & 0.416 & 0.543 & 0.731 & 0.876 & 0.421, 0.422, 0.549 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of test data for different textures.  
(2) Proper proportion distribution: the proportions of the texture areas and blank areas should be appropriate, and the pixel ratio should be close to 1:1;  
(3) Stripe spacing control: the stripe spacing should be moderate, and the annular ratio of the stripe spacing should be greater than or equal to 5%;  
(4) Complex texture design: the texture design should include complex texture parts with obvious features to strengthen the features;  
(5) Color complementarity: a CIE-Lab color difference \(\Delta E>30\) color texture combination of black, white, green, and blue should be used to enhance the color information.  
Finally, the color texture with a high texture complexity is chosen as the surface texture of the spherical particles.