# Deep Learning Parametrization for B-Spline Curve Approximation

arXiv: https://arxiv.org/abs/1807.08304 · HTML: https://mlsanity.com/paper/1807.08304/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2018.

## Built on by (most cited first, 5 of 5)

- [Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty](https://mlsanity.com/paper/2210.08095/) (2022)
- [Binary segmentation of medical images using implicit spline representations and deep learning](https://mlsanity.com/paper/2102.12759/) (2021)
- [Fast spline detection in high density microscopy data](https://mlsanity.com/paper/2301.04460/) (2023)
- [B-Spine: Learning B-Spline Curve Representation for Robust and Interpretable Spinal Curvature Estimation](https://mlsanity.com/paper/2310.09603/) (2023)
- [Spline refinement with differentiable rendering](https://mlsanity.com/paper/2503.14525/) (2025)

## Abstract (arXiv)

In this paper we present a method using deep learning to compute parametrizations for B-spline curve approximation. Existing methods consider the computation of parametric values and a knot vector as separate problems. We propose to train interdependent deep neural networks to predict parametric values and knots. We show that it is possible to include B-spline curve approximation directly into the neural network architecture. The resulting parametrizations yield tight approximations and are able to outperform state-of-the-art methods.