# Binary segmentation of medical images using implicit spline representations and deep learning

arXiv: https://arxiv.org/abs/2102.12759 · HTML: https://mlsanity.com/paper/2102.12759/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 14 of 14)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Efficient Interactive Annotation of Segmentation Datasets with Polygon-RNN++](https://mlsanity.com/paper/1803.09693/) (2018)
- [Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.10030/) (2019)
- [Fast Interactive Object Annotation with Curve-GCN](https://mlsanity.com/paper/1903.06874/) (2019)
- [Annotating Object Instances with a Polygon-RNN](https://mlsanity.com/paper/1704.05548/) (2017)
- [CFUN: Combining Faster R-CNN and U-net Network for Efficient Whole Heart Segmentation](https://mlsanity.com/paper/1812.04914/) (2018)
- [Deep Learning Parametrization for B-Spline Curve Approximation](https://mlsanity.com/paper/1807.08304/) (2018)
- [SplineNets: Continuous Neural Decision Graphs](https://mlsanity.com/paper/1810.13118/) (2018)

## Built on by (most cited first, 7 of 7)

- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Estimating Neural Orientation Distribution Fields on High Resolution Diffusion MRI Scans](https://mlsanity.com/paper/2409.09387/) (2024)
- [A topology-preserving three-stage framework for fully-connected coronary artery extraction](https://mlsanity.com/paper/2504.01597/) (2025)
- [B-Spine: Learning B-Spline Curve Representation for Robust and Interpretable Spinal Curvature Estimation](https://mlsanity.com/paper/2310.09603/) (2023)
- [Three-dimensional visualization of X-ray micro-CT with large-scale datasets: Efficiency and accuracy for real-time interaction](https://mlsanity.com/paper/2601.15098/) (2026)
- [Dynamic PET Image Reconstruction via Non-negative INR Factorization](https://mlsanity.com/paper/2503.08025/) (2025)
- [NUDF: Neural Unsigned Distance Fields for high resolution 3D medical image segmentation](https://mlsanity.com/paper/2504.18344/) (2025)

## Abstract (arXiv)

We propose a novel approach to image segmentation based on combining implicit spline representations with deep convolutional neural networks. This is done by predicting the control points of a bivariate spline function whose zero-set represents the segmentation boundary. We adapt several existing neural network architectures and design novel loss functions that are tailored towards providing implicit spline curve approximations. The method is evaluated on a congenital heart disease computed tomography medical imaging dataset. Experiments are carried out by measuring performance in various standard metrics for different networks and loss functions. We determine that splines of bidegree (1,1) with 128×128 coefficient resolution performed optimally for 512× 512 resolution CT images. For our best network, we achieve an average volumetric test Dice score of almost 92%, which reaches the state of the art for this congenital heart disease dataset.