# BezierSeg: Parametric Shape Representation for Fast Object Segmentation in Medical Images

arXiv: https://arxiv.org/abs/2108.00760 · HTML: https://mlsanity.com/paper/2108.00760/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 2 Aug 2021.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [BiSeNet: Bilateral Segmentation Network for Real-time Semantic Segmentation](https://mlsanity.com/paper/1808.00897/) (2018)
- [PANet: Few-Shot Image Semantic Segmentation with Prototype Alignment](https://mlsanity.com/paper/1908.06391/) (2019)
- [YOLACT: Real-time Instance Segmentation](https://mlsanity.com/paper/1904.02689/) (2019)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [PolarMask: Single Shot Instance Segmentation with Polar Representation](https://mlsanity.com/paper/1909.13226/) (2019)
- [Deep Snake for Real-Time Instance Segmentation](https://mlsanity.com/paper/2001.01629/) (2020)
- [Fast Interactive Object Annotation with Curve-GCN](https://mlsanity.com/paper/1903.06874/) (2019)
- [Deep Watershed Transform for Instance Segmentation](https://mlsanity.com/paper/1611.08303/) (2016)
- [Explicit Shape Encoding for Real-Time Instance Segmentation](https://mlsanity.com/paper/1908.04067/) (2019)
- [Volumetric Attention for 3D Medical Image Segmentation and Detection](https://mlsanity.com/paper/2004.01997/) (2020)
- [Joint Liver Lesion Segmentation and Classification via Transfer Learning](https://mlsanity.com/paper/2004.12352/) (2020)
- [FourierNet: Compact mask representation for instance segmentation using differentiable shape decoders](https://mlsanity.com/paper/2002.02709/) (2020)
- [MixNet: Multi-modality Mix Network for Brain Segmentation](https://mlsanity.com/paper/2004.09832/) (2020)

## Built on by (most cited first, 4 of 4)

- [FCSN: Global Context Aware Segmentation by Learning the Fourier Coefficients of Objects in Medical Images](https://mlsanity.com/paper/2207.14477/) (2022)
- [FourierLoss: Shape-Aware Loss Function with Fourier Descriptors](https://mlsanity.com/paper/2309.12106/) (2023)
- [Bridging Vision, Language, and Mathematics: Pictographic Character Reconstruction with B'ezier Curves](https://mlsanity.com/paper/2511.00076/) (2025)
- [PRISM-DR: Per-lesion Retinal Inference with Specialist Models for Diabetic Retinopathy](https://mlsanity.com/paper/2607.19864/) (2026)

## Abstract (arXiv)

Delineating the lesion area is an important task in image-based diagnosis. Pixel-wise classification is a popular approach to segmenting the region of interest. However, at fuzzy boundaries such methods usually result in glitches, discontinuity, or disconnection, inconsistent with the fact that lesions are solid and smooth. To overcome these undesirable artifacts, we propose the BezierSeg model which outputs bezier curves encompassing the region of interest. Directly modelling the contour with analytic equations ensures that the segmentation is connected, continuous, and the boundary is smooth. In addition, it offers sub-pixel accuracy. Without loss of accuracy, the bezier contour can be resampled and overlaid with images of any resolution. Moreover, a doctor can conveniently adjust the curve's control points to refine the result. Our experiments show that the proposed method runs in real time and achieves accuracy competitive with pixel-wise segmentation models.