Surface reconstruction from point clouds is a crucial task in the fields of computer vision and computer graphics. SDF-based methods excel at reconstructing smooth meshes with minimal error and artefacts but struggle with representing open surfaces. On the other hand, UDF-based methods can effectively represent open surfaces but often introduce noise, leading to artefacts in the mesh. In this work, we propose a novel approach that directly predicts the intersection points between line segment of point pairs and implicit surfaces. To achieve it, we propose two modules named Relative Intersection Module and Sign Module respectively with the feature of point pair as input. To preserve the continuity of the surface, we also integrate symmetry into the two modules, which means the position of predicted intersection will not change even if the input order of the point pair changes. This method not only preserves the ability to represent open surfaces but also eliminates most artefacts on the mesh. Our approach demonstrates state-of-the-art performance on three datasets: ShapeNet, MGN, and ScanNet. The code will be made available upon acceptance.
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