Path Matters: Unveiling Geometric Implicit Bias via Curvature-Aware Sparse View Optimization

3D Gaussian Splatting (3DGS) has recently emerged as a powerful approach for novel view synthesis by reconstructing scenes as sets of Gaussian ellipsoids. Despite its success in scenarios with dense input images, 3DGS faces critical challenges in sparse view settings, often resulting in geometric inaccuracies, inconsistencies across views, and degraded rendering quality. In this paper, we uncover and address two key implicit biases of 3DGS reconstruction algorithm in sparse-view: (1) the model has a stronger demand for supervision signal toward regions of high curvature, and (2) the model is sensitive to the smoothness of the trajectory of the input views. To tackle these issues, we propose a novel framework that optimizes camera trajectories to maximize curvature coverage while enforcing smooth motion, and we further enhance the informativeness of data through a synthetic view generation process. Extensive experiments on Mip-NeRF 360, DTU, Blender, Tanks & Temples, and LLFF datasets show that our method substantially outperforms state-of-the-art solutions in sparse-view scenarios, both in rendering quality and geometric fidelity. Beyond these empirical gains, our investigation uncovers the subtle ways in which data representation and trajectory planning interact to shape 3DGS performance, offering deeper theoretical insights into the algorithm’s inherent biases.