Exploring differential geometry in neural implicits

We introduce a neural implicit framework that exploits the differentiable properties of networks and discrete geometry point-sampled surfaces to approximate them as level sets functions . To train function, we propose loss functional approximates signed distance allows terms with high-order derivatives, such alignment between principal directions curvature, learn more geometric details. During training, consider non-uniform sampling strategy based on curvatures surface prioritize points This implies faster learning while preserving accuracy when compared previous approaches. also use analytical derivatives function estimate differential measures underlying surface. • Introduction by smooth using geometry. Definition exploration tools from during training network. , dataset sample important regions. network