HotSpot: Screened Poisson Equation for Signed Distance Function Optimization

Existing losses such as the eikonal loss is to ensure that the implicit function indeed outputs cannot guarantee the recovered implicit function to be a the signed distance. A standard regularization loss used is distance function, even when the implicit function satisfies the eikonal equation: it constrains the norm of the gradient the eikonal equation almost everywhere. Furthermore, the of an implicit function to be 1 almost everywhere. If eikonal loss suffers from stability issues in optimization and the implicit function is a signed distance function, then it the remedies that introduce area or divergence minimization satisfies the eikonal equation. However, the converse is not can lead to oversmoothing. We address these challenges true. Figure 1 shows an example: on the left, we optimize by designing a loss function that when minimized can an implicit function to satisfy the eikonal equation, while converge to the true distance function, is stable, and naturally it successfully does so, it converges to a solution that is far penalize large surface area. We provide theoretical from the actual distance [5, 6].