Simulations data for symmetry-3748042

File Contents & Naming Conventions  `fig1.m`: Generates 3D isosurfaces for Euclidean/TLD/TED/TID metrics                 `fig2.m`: Implements teapot denoising visualization (Algorithm 1)                    `fig3.m`: Compares loss functions of Euclidean/TLD/TED/TID means                     `fig4.m`: Validates TLD superiority over Log-Euclidean Metric                       | `Table1_Euclid.m`:Computes TPR/FPR/SNRG for Euclidean metric at SNR=10/2/1                  `Table1_TLD.m`: Computes TPR/FPR/SNRG for TLD at SNR=10/2/1 `Table1_TED.m`: Computes TPR/FPR/SNRG for TED at SNR=10/2/1 `Table1_TID.m`: Computes TPR/FPR/SNRG for TID at SNR=10/2/1   4.

Key Parameters & Output Metrics SNR Configuration (critical for Table 1): % In Table1_*.m files:num_data = 4148;    % Signal points (fixed) num_noise = 415;    % SNR=10 (num_noise = num_data/10) num_noise = 2074;   % SNR=2 (num_noise = num_data/2) num_noise = 4148;   % SNR=1 (num_noise = num_data)``` Output Metrics Definition: TPR=TP / (TP + FN): True Positive Rate | FPR= FP / (FP + TN): False Positive Rate | SNRG = (TP/FP)×(TN/FN) - 1 : Signal-to-Noise Ratio Growth |  5.

Data Value & Reusability Reproducibility: Executing scripts in order regenerates all manuscript figures/table exactly Benchmarking: Enables direct performance comparison of new denoising algorithms against TBD metrics Parameter Studies: Easily modify:  - `dist_num` (neighborhood size in Algorithm 1)  - `dim` (SPD matrix dimension in Table1_*.m)  - Noise models (currently Gaussian) - Educational Utility: Demonstrates practical implementation of:  - Total Bregman Divergences on matrix manifolds  - Influence function analysis (Section 4.2)  - Anisotropy indices (Section 4.1)   6.

Recommended Workflow 1. Run `fig1.m → fig2.m → fig3.m → fig4.m` for visual results 2. For Table 1:   ```matlab  % In each Table1_*.m file:  num_noise = 415;  % Set SNR=10  % Run and record TPR/FPR/SNRG  num_noise = 2074; % Set SNR=2  % Run and record...  num_noise = 4148; % Set SNR=1  ``` 3.

Compare outputs across scripts to replicate Table 1  7. Technical Specifications - Software: MATLAB R2023a (min R2021b) - Toolboxes Required: Statistics and Machine Learning, Computer Vision - Dataset Dependency: `teapot.ply` from MATLAB's `teapotGeometry` ---  Key Improvements Over Initial Submission1. Explicit SNR Control: Documented exact parameter locations for SNR configuration 2.

Metric Formulae: Provided mathematical definitions of TPR/FPR/SNRG 3. Reproducibility Pathway: Clear step-by-step execution sequence 4. Extension Guidance: Highlighted modifiable parameters for new studies 5.

Technical Context: Added computation requirements and dependencies