A Fractional-Order SSIM-Based Gaussian Loss with Long-Range Memory for Dense VSLAM

In dense visual simultaneous localization and mapping VSLAM (VSLAM), a fundamental challenge lies in the inability of existing loss functions to dynamically balance luminance, contrast, and structural fidelity under photometric variations, while their underlying mechanisms, particularly the conventional Gaussian kernel in SSIM, suffer from limited receptive fields due to rapid exponential decay, preventing the capture of long-range dependencies essential for global consistency. To address this, we propose a fractional Gaussian field (FGF) that synergizes Caputo derivatives with Gaussian weighting, creating a hybrid kernel that couples power-law decay for long-range memory with local smoothness. This foundational kernel serves as the core component of FGF-SSIM, a novel loss function that adaptively recalibrates luminance, contrast, and structure using fractional-order statistics. The proposed FGF-SSIM is further integrated into a complete 3D Gaussian Splatting (3DGS)-based SLAM system, named FGF-SLAM, where it is employed across both tracking and mapping modules to enhance performance. Extensive evaluations demonstrate state-of-the-art performance across multiple benchmarks. Comprehensive analysis confirms the superior long-range dependency of the fractional kernel, dedicated illumination robustness tests validate the enhanced invariance of FGF-SSIM, and quantitative results on TUM and Replica datasets show significant improvements in reconstruction quality and trajectory estimation. Ablation studies further substantiate the contribution of each proposed component.