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/

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