Implicit surface representations such as the signed distance function (SDF) have emerged as a promising approach for image-based surface reconstruction. However, existing optimization methods assume solid surfaces and are therefore unable to properly reconstruct semi-transparent surfaces and thin structures, which also exhibit low opacity due to the blending effect with the background. While neural radiance field (NeRF) based methods can model semi-transparency and achieve photo-realistic quality in synthesized novel views, their volumetric geometry representation tightly couples geometry and opacity, and therefore cannot be easily converted into surfaces without introducing artifacts. We present $\alpha$Surf, a novel surface representation with decoupled geometry and opacity for the reconstruction of semi-transparent and thin surfaces where the colors mix. Ray-surface intersections on our representation can be found in closed-form via analytical solutions of cubic polynomials, avoiding Monte-Carlo sampling and is fully differentiable by construction. Our qualitative and quantitative evaluations show that our approach can accurately reconstruct surfaces with semi-transparent and thin parts with fewer artifacts, achieving better reconstruction quality than state-of-the-art SDF and NeRF methods. Website: https://alphasurf.netlify.app/

翻译：隐式曲面表示（如符号距离函数，SDF）已成为基于图像的表面重建的一种有前景的方法。然而，现有的优化方法假设表面为实体，因此无法正确重建半透明表面与薄壁结构——这些结构由于与背景的混合效应也表现出较低的不透明度。尽管基于神经辐射场（NeRF）的方法能够建模半透明效果，并在合成新视角时实现照片级真实感，但其体素几何表示将几何与不透明度紧密耦合，因此在转换为表面时难以避免引入伪影。本文提出αSurf，一种新颖的曲面表示方法，其几何与不透明度相互解耦，专门用于重建颜色混合的半透明与薄壁表面。在我们的表示中，光线-曲面交点可通过三次多项式的解析解以闭式形式求得，避免了蒙特卡洛采样，且整个构建过程完全可微。我们的定性与定量评估表明，本方法能够精确重建具有半透明与薄壁部分的表面，伪影更少，在重建质量上优于当前最先进的SDF与NeRF方法。项目网站：https://alphasurf.netlify.app/