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），已成为基于图像的曲面重建的一种有前景的方法。然而，现有的优化方法假设实体表面，因此无法正确重建半透明表面和薄结构，这些结构由于与背景的混合效应而表现出低不透明度。虽然基于神经辐射场（NeRF）的方法可以建模半透明性并在合成的新视角中实现照片级真实感质量，但其体积几何表示将几何与不透明度紧密耦合，因此无法在不引入伪影的情况下轻松转换为曲面。我们提出$\alpha$Surf，一种新颖的曲面表示，其解耦了几何与不透明度，用于重建颜色混合的半透明和薄表面。我们的表示上的射线-曲面交点可以通过三次多项式的解析解以闭式形式找到，避免了蒙特卡洛采样，并且通过构造完全可微。我们的定性和定量评估表明，我们的方法能够准确重建具有半透明和薄部分的曲面且伪影更少，比现有最先进的SDF和NeRF方法实现了更好的重建质量。网站：https://alphasurf.netlify.app/