With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point clouds as input. State-of-the-art image-based methods first learn a 3D edge point cloud then fit 3D edges to it. The edge point cloud is obtained by learning a 3D neural implicit edge field from which the 3D edge points are sampled on a specific level set (0 or 1). However, such methods present two important drawbacks: i) it is not realistic to sample points on exact level sets due to float imprecision and training inaccuracies. Instead, they are sampled within a range of levels so the points do not lie accurately on the 3D edges and require further processing. ii) Such implicit representations are computationally expensive and require long training times. In this paper, we address these two limitations and propose a 3D edge mapping that is simpler, more efficient, and preserves accuracy. Our method learns explicitly the 3D edge points and their edge direction hence bypassing the need for point sampling. It casts a 3D edge point as the center of a 3D Gaussian and the edge direction as the principal axis of the Gaussian. Such a representation has the advantage of being not only geometrically meaningful but also compatible with the efficient training optimization defined in Gaussian Splatting. Results show that the proposed method produces edges as accurate and complete as the state-of-the-art while being an order of magnitude faster. Code is released at this https URL.
边缘作为计算机视觉中有意义的几何元素，广泛存在于3D世界中，因而是极为有用的基础元素。3D边缘由直线和曲线构成，重建它们的方法通常使用多视角图像或点云作为输入。当前最先进的基于图像的方法首先学习3D边缘点云，然后拟合3D边缘。边缘点云是通过学习一个3D神经隐式边缘场获得的，从中在特定的水平集（0或1）上采样出3D边缘点。然而，这类方法存在两个重要缺陷：i) 由于浮点不精确和训练误差，精确在水平集上采样点是不现实的。相反，点是在一定的水平范围内采样，导致这些点不能准确位于3D边缘上，且需要进一步处理。ii) 这类隐式表示计算量大，训练时间长。在本文中，我们解决了这两个问题，提出了一种更简单、更高效且能保持准确性的3D边缘映射方法。我们的方法显式地学习3D边缘点及其方向，从而避免了点采样的需求。该方法将3D边缘点表示为3D高斯的中心，并将边缘方向表示为该高斯的主轴。这种表示不仅在几何上有意义，还与高斯散点中的高效训练优化相兼容。结果表明，该方法在边缘的准确性和完整性上与最先进方法相当，但速度快了一个数量级。