Comparing Geodesic Filtering to State-of-the-Art Algorithms: A Comprehensive Study and CUDA Implementation
Bibliographic record
Abstract
This paper presents a comprehensive investigation into advanced image processing using geodesic filtering within a Riemannian manifold framework. We introduce a novel geodesic filtering formulation that uniquely integrates spatial and intensity relationships through minimal path computation, demonstrating significant improvements in edge preservation and noise reduction compared to conventional methods. Our quantitative analysis using peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) metrics across diverse image types reveals that our approach outperforms traditional techniques in preserving fine details while effectively suppressing both Gaussian and non-Gaussian noise. We developed an automatic parameter optimization methodology that eliminates manual tuning by identifying optimal filtering parameters based on image characteristics. Additionally, we present a highly optimized GPU implementation featuring innovative wave-propagation algorithms and memory access optimization techniques that achieve a 200× speedup, making geodesic filtering practical for real-time applications. Our work bridges the gap between theoretical elegance and computational practicality, establishing geodesic filtering as a superior solution for challenging image processing tasks in fields ranging from medical imaging to remote sensing.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".