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Building a Mesh Using Spherical Embedding
Created: December 31, 2024 Modified: January 14, 2025 When trying to build a 3D model of an object in the real world, the goal is most often to construct a connected mesh of triangles or quadrilaterals that represents that object's surface. When we're using lidar or a stereo camera to collect 3D information, however, we can't create this mesh directly.
It's worth noting that although the stated goal in the paper is to perturb until the Laplace-Beltrami operators reach \mathbf{0}, the authors admit that in practice, we simply have to choose the number of iterations that gives us the quality that we're looking for. Limitations notwithstanding, we can take a look at what happens when running against the cropped bunny point cloud to see that we do still retain the advantage of forcing a hole-free output. What might be helpful would be to use the oriented points from the original Poisson surface reconstruction paper to have more of a "ballooning" strategy which pushes outward toward a spherical embedding.
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