A low beta would decrease the variance and thus would learn the given examples better. This will help us
learn the given surface better with the given training examples.
The algorithm begins with the points at the origin. These are the origins of the rays
that will be cast. Then for each iteration until we have reached the max number of iterations,
we calculate the circle such that it computes the nearest surface point from the current set of points.
We then move along the ray by the radius of the circle. This will move us dynamically along the array
until we are either at our max iterations or we hit a surface.
We update points by
points = circle radius * ray directions + points
I ended up not needing to tune the parameters to get a good result
and my network was of the shape n_harmonic_functions_xyz was of size 4
Harmonic Embedding 3 --> n_harmonic_functions_xyz
Linear n_harmonic_functions_xyz --> 128
relu
Linear 128 --> 128
relu
Linear 128 --> 128
relu
Linear 128 --> 128
relu
Linear 128 --> 128
relu
Linear 128 --> 128
relu
Linear 128 --> 3
My
The eikonal loss was computed by following a similar equation to
the paper. I took the mean of the norm of the gradient along the points - 1
squared.
Alpha: Alpha is a scaling factor of our densities.
Beta: Beta is the L1 version of the standard deviation. It gives the scale for the CDF of the Laplace distribution.
How does high beta bias your learned SDF? What about low beta?
A high beta would allow us to have a higher variance which in turn would allow for better generalization. This
generalization causes the image to be blurrier as seen in the images below
A low beta would decrease the variance and thus would learn the given examples better. This will help us
learn the given surface better with the given training examples.
Would an SDF be easier to train with volume rendering and low beta or high beta? Why? It would be easier to train with a higher beta because it would be less prone to overfitting. Since the beta would encourage learning further away from the surface it could get stuck at a local minima and not learn as well. <
Would you be more likely to learn an accurate surface with high beta or low beta? Why? We are more likely to get more accurate surface with a low beta. This is because we are giving the system less variance on the boundary which will keep generalization low but make it harder to train but learn a more accurate surfae
Comment on the settings you chose, and why they seem to work well. The result above is using the original parameters. I decided to lower beta to be 0.003. This allowed me to get a more accurate feature.
The next thing I tried was lowering the number of epochs to 50. I noticed an overfitting problem
so lowering the number of epochs
