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We assume an underlying characteristic function that represents the object

By convoluting with a smoothing kernel , we obtained a blurred version

of which the gradient coincides with the normals of the object we want to reconstruct.

Given points with estimated normals , we can thus state that



In order to solve for , we turn the problem into a Poisson equation:


Which can be discretized into a linear system by taking finite differences.

Non-oriented normals
If we only have normal directions without consistent orientations, we can state that should be parallel to the normal directions:




With the additonal smoothness constraint: