Comparative Evaluation of 2D and 3D Gaussian Splatting for Full-Parallax Holographic Stereogram Printing

Holographic stereograms record large sets of multi-view projection images into elementary hologram units (hogels), and their visual quality is governed primarily by the quality and inter-view consistency of the input multi-view imagery. Conventional photogrammetry-based pipelines for generating such imagery rely on surface meshes and require burdensome post-processing, which limits the fidelity of thin structures and view-dependent reflections. This paper proposes an integrated workflow that replaces the photogrammetric stage with Gaussian splatting and presents a controlled comparison of volumetric 3D Gaussian splatting (3DGS) and surface-aligned 2D Gaussian splatting (2DGS) for hogel-based digital hologram production. Using 397 drone-captured images of a 3 m bronze Pegasus statue, both representations were trained under identical input data, camera poses, and hyperparameters, and 119,808 full-parallax multi-view images (768 × 156 grid; 120° × 52° field of view) were rendered from each model, converted into hogel arrays by an identical ray-tracing transform, and printed onto Ultimate U04 silver halide plates under identical optical conditions. In the digital domain, 3DGS outperformed 2DGS on all three standard novel-view-synthesis metrics (PSNR 32.68 vs. 31.03 dB; SSIM 0.9281 vs. 0.9139; and LPIPS 0.1150 vs. 0.1406) while using approximately 1.67 times more Gaussians. Conversely, 2DGS produced superior results at viewpoints outside the training distribution, on thin structures such as wings and mane, and at the extremes (±60°) of the virtual camera array, and these differences propagated consistently to the printed holograms, whose edge sharpness was higher for 2DGS at every measured viewpoint (mean 39.6 vs. 23.8). Notably, 2DGS achieved this superior printed-output quality while using approximately 40% fewer Gaussians than 3DGS, combining model efficiency with the multi-view consistency that proved decisive for hogel-based printing. The results demonstrate that single-view metrics such as PSNR do not capture the multi-view consistency that dominates hogel-based output quality and provide practical guidance for representation selection in holographic-printing workflows.