SSD Recon with Dirichelet boundary condition

[markloyman]

When I use SSD recon with Neumann boundary condition on a point cloud that is sparse near the floor: --width 0.0035 --valueWeight 0.4 --gradientWeight 0.14 --biLapWeight 0.3 --bType 3 --scale 1.2 --samplesPerNode 15 --colors

So based on my experience with Poisson Recon, I tried to use the "watertight" Dirichlet boundary condition: --width 0.0035 --valueWeight 0.4 --gradientWeight 0.14 --biLapWeight 0.3 --bType 2 --scale 1.2 --samplesPerNode 15 --colors

The Dirichlet result was surprising. But if I ask myslef what should happen if you set to 0 the SDF at the bounding box, than a surface on the bounding box actually makes sense and seem trivial. So it seems that the SDF formulation is actually incompatible with dirichlet boundary conditions.

According to the original paper:

• This case of "hole" in the point cloud is excplicitly not coverted in the paper.

  Usually we are only interested in reconstructing the surface S within a bounded volume V, such as a cube containing all the data points, which may result in an open surface at the boundaries of the volume V, particularly when the points only sample one side of the object, there are holes in the data, or more generally if the points are not uniformly distributed along the surface of the solid object. Point clouds produced by 3D scanning systems are viewpoint dependent, and to cover the whole surface of the object several scans need tobe registered and merged. We are not covering these topics here. Instead, we assume that point multiple scans have already been registered, and we seek a method that works well on regularly sampled as well as unevenly sampled data.

• Apperently does not require boundary conditions

  The formulation allows for a number of different efficient discretizations, reduces to a finite least squares problem for all linearly parameterized families of functions, and does not require boundary conditions.

So I am confused as to how / why boundary conditions were introduced in this implementation? In particular the option for dirichlet boundary condition.

Would really appriciate clarification on this.

Thank you!

[mkazhdan]

You are correct. SDF reconstruction with Dirichlet boundary conditions doesn't make sense. The SDF wants to grow larger as you move towards the boundary. The Dirichlet boundary conditions do the opposite. The two are incompatible.

The reason the flag for Dirichlet is there for SDF is simply that we kept it from Poisson Reconstruction. Our goal was to show that the FEM solver we designed for PR was more general than just for indicator function reconstruction. We didn't mean to suggest that the different variants of the FEM system were necessarily appropriate for other systems.

[markloyman]

Thank you for the swift reply!