Closed-Form Convolution for physically-accurate defocus in Gaussian Splatting

Abstract

Recent advancements in 3D Gaussian Splatting (3DGS) have achieved impressive photorealism; however, its foundational assumption of perfectly sharp, all-in-focus imagery often breaks down in real-world scenarios. Lens-induced defocus blur, common in natural captures, can significantly degrade reconstruction quality. While prior work has attempted to address this, existing solutions either rely on implicit deblurring, restricting post-capture artistic flexibility, or employ physically inaccurate blur approximations, particularly under large apertures. We present a rendering pipeline that seamlessly integrates a physically accurate and differentiable depth-of-field model into the 3D Gaussian Splatting (3DGS) rasterization process. At its core, our method models defocus by convolving each projected 3D Gaussian with a kernel shaped by the camera’s Circle of Confusion (CoC). To maintain efficiency, we derive a closed-form analytical solution for this convolution using the error function (erf). Our approach further extends to anisotropic Gaussians and approximates arbitrary polygonal apertures by decomposing them into non-overlapping rectangles. As a result, our method enables high-fidelity 3D reconstruction from blurry, multi-focus image sets, while supporting realistic post-capture effects such as refocusing and aperture manipulation. Experiments on defocus-focused benchmarks show that our technique yields visibly sharper in-focus details and smoother defocus transitions, delivering results competitive with the current best-performing methods.