# SurfDist: Interpretable Three-Dimensional Instance Segmentation Using Curved Surface Patches

arXiv: https://arxiv.org/abs/2507.08223 · HTML: https://mlsanity.com/paper/2507.08223/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 11 Jul 2025.

## Builds on (most cited first, 6 of 6)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Cell Detection with Star-convex Polygons](https://mlsanity.com/paper/1806.03535/) (2018)
- [Star-convex Polyhedra for 3D Object Detection and Segmentation in Microscopy](https://mlsanity.com/paper/1908.03636/) (2019)
- [NucMM Dataset: 3D Neuronal Nuclei Instance Segmentation at Sub-Cubic Millimeter Scale](https://mlsanity.com/paper/2107.05840/) (2021)

## Abstract (arXiv)

We present SurfDist, a convolutional neural network architecture for three-dimensional volumetric instance segmentation. SurfDist enables prediction of instances represented as closed surfaces composed of smooth parametric surface patches, specifically bicubic B'ezier triangles. SurfDist is a modification of the popular model architecture StarDist-3D which breaks StarDist-3D's coupling of instance parameterization dimension and instance voxel resolution, and it produces predictions which may be upsampled to arbitrarily high resolutions without introduction of voxelization artifacts. For datasets with blob-shaped instances, common in biomedical imaging, SurfDist can outperform StarDist-3D with more compact instance parameterizations. We detail SurfDist's technical implementation and show one synthetic and one real-world dataset for which it outperforms StarDist-3D. These results demonstrate that interpretable instance surface models can be learned effectively alongside instance membership.