In this paper, we put forward a new method for surface reconstruction from image-based point clouds. In particular, we introduce a new visibility model for each line of sight to preserve scene details without decreasing the noise filtering ability. To make the proposed method suitable for point clouds with heavy noise, we introduce a new likelihood energy term to the total energy of the binary labeling problem of Delaunay tetrahedra, and we give its s-t graph implementation. Besides, we further improve the performance of the proposed method with the dense visibility technique, which helps to keep the object edge sharp. The experimental result shows that the proposed method rivalled the state-of-the-art methods in terms of accuracy and completeness, and performed better with reference to detail preservation.