Solving Partial Differential Equations using Compact Neuronal Volumetric Representations

Efficient object representation is a key objective in computer graphics. In thesis we apply the recently introduced Differential Indirection framework to object representation. With the methods we replace time consuming and memory inefficient parts of the Heat Method for object representation. This method was also introduced only recently and is based on leveraging mathematical facts from differential geometry and the representation of the object as the zero set of a Signed Distance Function. We demonstrate how Differential Indirection can advantageously be integrated into the Heat Method replacing the costly numerical solution of partial differential equations. When trained with the right choice of losses the result convincingly shows that the approach taken in this thesis can mitigate the problems arising in the original Heat Method. We present experimental evaluations of the method developed in this thesis. Through these evaluations we explain our choices and provide arguments why other choices lead to unsatisfying results.