NeRF Differentiable Forward Maps
source link: https://jyzhu.top/NeRF-Differentiable-Forward-Maps/
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This is part of my journey of learning NeRF.
2.3. Differentiable Forward Maps
image-20221208175453557
Differentiable rendering
image-20221208181457315
Volume rendering can render fogs. Sphere rendering only render the solid surface, and needs ground truth supervision.? Neural renderer combines the two.
Differentiability of the rendering function itself
- BRDF Shading? details later.
Differentiation itself
Design a neural network with higher order derivatives constraints and therefore directly use its derivative.
image-20221208182302568
For example the Eikonal equation forces the neural network has a derivative as 1. Adding the eikonal loss then promises the neural network valid.
Generally, this kind of problems are: the solutions are constrained by its partial derivatives.
Special: Identity Operator
Reconstruction→1^()→Sensor domainReconstruction==Sensor domain
- Can we obtain a neural network in just one forward, without optimization?
- Can we design special forward maps for specific downstream tasks, eg., classification? Absolutely yes. We can design it to represent a compact representation as the sensor domain. The key idea is to get a differentiable function to map your specific recon and sensor domain.
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