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GilesStrong / tomopt

TomOpt: Differential Muon Tomography Optimisation
GNU Affero General Public License v3.0
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PoCA 3D Gaussian distribution should be tilted given the incoming and outgoing tracks #140

Open GilesStrong opened 2 years ago

GilesStrong commented 2 years ago

Currently 3 uncorrelated Gaussians in x,y,z are used to model the probabilities of the PoCA being located in each of the voxels in the passive volume. Really, thought, the PDF should account for the incoming tracks and be slightly tilted. Potentially this could be achieved by defining a 3D Gaussian with a correlation matrix.

GilesStrong commented 1 year ago

Thinking about this: Likely we'll need the use of MultiVariateNormal which lacks a CDF function, so integrating the distribution over voxels becomes non-trivial. Potentially, rsample could be used to differentiable sample points, which then seed univariate Gaussians in XYZ of a given bandwidth, which can form a 3D KDE over volume and be integrated over voxels, but this might be expensive to compute.