AffineGS: Unlocking Accurate Geometry in 3DGS via Spatially Varying Affine Rectification

3D Gaussian Splatting (3DGS) has become the leading approach for photorealistic novel view synthesis, yet its geometric accuracy lags behind its visual quality. Existing depth-guided methods attempt to resolve this by regularizing the optimization with monocular depth priors, typically using a single global scale-and-shift alignment. Crucially, we discover a fundamental flaw in this assumption: modern monocular depth networks systematically exhibit region-dependent, piecewise-linear distortions. This discovery invalidates standard global alignment strategies, which warp scene geometry by enforcing a single transform. To address this, we introduce a spatially varying affine rectification model that corrects monocular disparity into consistent metric depth using regionally smooth, edge-aware fields. We further derive a normal-aware regularizer that uses spatial gradients to couple the rectified disparity with 3DGS depth and normals. Across diverse experimental settings, our sensor-free method shows strong photometric quality of Gaussian Splatting while substantially improving geometric accuracy and outperforming state-of-the art geometry-focused methods.