用可微分的多视角草图点云重建3D边缘，让结果更准更完整。

Edges are one of the most basic parametric primitives to describe structural information in 3D. In this paper, we study parametric 3D edge reconstruction from calibrated multi-view images. Previous methods usually reconstruct a 3D edge point set from multi-view 2D edge images, and then fit 3D edges to the point set. However, noise in the point set may cause gaps among fitted edges, and the recovered edges may not align with input multi-view images since the edge fitting depends only on the reconstructed 3D point set. To mitigate these problems, we propose SketchSplat, a method to reconstruct accurate, complete, and compact 3D edges via differentiable multi-view sketch splatting. We represent 3D edges as sketches, which are parametric lines and curves defined by attributes including control points, scales, and opacity. During reconstruction, we iteratively sample Gaussian points from a set of sketches and rasterize the Gaussians onto 2D edge images. Then the gradient of the image loss can be back-propagated to optimize the sketch attributes. Our method bridges 2D edge images and 3D edges in a differentiable manner, which ensures that 3D edges align well with 2D images and leads to accurate and complete results. We also propose a series of adaptive topological operations to reduce redundant edges and apply them along with the sketch optimization, yielding a more compact reconstruction. Finally, we contribute an accurate 2D edge detector that improves the performance of both ours and existing methods. Experiments show that our method achieves state-of-the-art accuracy, completeness, and compactness on a benchmark CAD dataset.