Geometric reconstruction of opaque surfaces from images is a longstanding challenge in computer vision, with renewed interest from volumetric view synthesis algorithms using radiance fields. We leverage the geometry field proposed in recent work for stochastic opaque surfaces, which can then be converted to volume densities. We adapt Gaussian kernels or surfels to splat the geometry field rather than the volume, enabling precise reconstruction of opaque solids. Our first contribution is to derive an efficient and almost exact differentiable rendering algorithm for geometry fields parameterized by Gaussian surfels, while removing current approximations involving Taylor series and no self-attenuation. Next, we address the discontinuous loss landscape when surfels cluster near geometry, showing how to guarantee that the rendered color is a continuous function of the colors of the kernels, irrespective of ordering. Finally, we use latent representations with spherical harmonics encoded reflection vectors rather than spherical harmonics encoded colors to better address specular surfaces. We demonstrate significant improvement in the quality of reconstructed 3D surfaces on widely-used datasets.
从图像中进行不透明表面的几何重建是计算机视觉中的一个长期挑战，近年来，基于辐射场的体视角合成算法重新激发了对这一问题的兴趣。我们利用最近研究中提出的用于随机不透明表面的几何场（geometry field），将其转换为体密度，并适配高斯核或表面元（surfels）对几何场进行投影（splatting），从而实现对不透明固体的精确重建。我们的主要贡献包括以下三点：1. 高效且近乎精确的可微渲染算法：针对使用高斯表面元参数化的几何场，我们推导出一种高效且近乎精确的可微渲染算法，避免了当前方法中涉及的泰勒级数近似以及自衰减问题。2. 解决不连续的损失梯度问题：在表面元聚集于几何附近时，损失函数可能表现出不连续性。我们提出了一种方法，保证渲染颜色是内核颜色的连续函数，无论其排序如何，从而确保优化的稳定性。3. 改进镜面反射的建模：我们使用包含球谐反射向量的潜在表示替代传统的球谐颜色编码，以更好地处理镜面表面。在广泛使用的数据集上的实验表明，我们的方法显著提高了重建 3D 表面的质量，为几何重建任务提供了重要进展。