Comparing Geodesic Filtering to State-of-the-Art Algorithms: A Comprehensive Study and CUDA Implementation

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.