# QIS : Interactive Segmentation via Quasi-Conformal Mappings

arXiv: https://arxiv.org/abs/2402.14695 · HTML: https://mlsanity.com/paper/2402.14695/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 22 Feb 2024.

## Builds on (most cited first, 16 of 16)

- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [Reviving Iterative Training with Mask Guidance for Interactive Segmentation](https://mlsanity.com/paper/2102.06583/) (2021)
- [Deep Interactive Object Selection](https://mlsanity.com/paper/1603.04042/) (2016)
- [f-BRS: Rethinking Backpropagating Refinement for Interactive Segmentation](https://mlsanity.com/paper/2001.10331/) (2020)
- [FocalClick: Towards Practical Interactive Image Segmentation](https://mlsanity.com/paper/2204.02574/) (2022)
- [Landmark and Intensity Based Registration with Large Deformations via Quasi-conformal Maps](https://mlsanity.com/paper/1310.1710/) (2013)
- [Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization](https://mlsanity.com/paper/2103.16768/) (2021)
- [Fast Disk Conformal Parameterization of Simply-connected Open Surfaces](https://mlsanity.com/paper/1408.6974/) (2014)
- [Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing](https://mlsanity.com/paper/1508.07569/) (2015)
- [A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings](https://mlsanity.com/paper/2210.03299/) (2022)
- [Free-boundary conformal parameterization of point clouds](https://mlsanity.com/paper/2010.15399/) (2020)
- [A unifying framework for n-dimensional quasi-conformal mappings](https://mlsanity.com/paper/2110.10437/) (2021)
- [A Generalized Asymmetric Dual-front Model for Active Contours and Image Segmentation](https://mlsanity.com/paper/2006.07839/) (2020)
- [Topology-Preserving Segmentation Network: A Deep Learning Segmentation Framework for Connected Component](https://mlsanity.com/paper/2202.13331/) (2022)
- [A novel variational model for image registration using Gaussian curvature](https://mlsanity.com/paper/1504.07643/) (2015)

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

- [Quasi-Conformal Convolution : A Learnable Convolution for Deep Learning on Simply Connected Open Surfaces](https://mlsanity.com/paper/2502.01356/) (2025)
- [Circular Quasiconformal Deturbulence: Geometry-Based Restoration from Multiple Turbulent Frames](https://mlsanity.com/paper/2504.13432/) (2025)
- [Learning Task-Aware Sampling with Shared Saliency through Density-Equalizing Mappings](https://mlsanity.com/paper/2606.12869/) (2026)
- [A Smooth Phase-Separation Model for Weak-Boundary Segmentation of Homogeneous Structures](https://mlsanity.com/paper/2607.22053/) (2026)

## Abstract (arXiv)

Image segmentation plays a crucial role in extracting important objects of interest from images, enabling various applications. While existing methods have shown success in segmenting clean images, they often struggle to produce accurate segmentation results when dealing with degraded images, such as those containing noise or occlusions. To address this challenge, interactive segmentation has emerged as a promising approach, allowing users to provide meaningful input to guide the segmentation process. However, an important problem in interactive segmentation lies in determining how to incorporate minimal yet meaningful user guidance into the segmentation model. In this paper, we propose the quasi-conformal interactive segmentation (QIS) model, which incorporates user input in the form of positive and negative clicks. Users mark a few pixels belonging to the object region as positive clicks, indicating that the segmentation model should include a region around these clicks. Conversely, negative clicks are provided on pixels belonging to the background, instructing the model to exclude the region near these clicks from the segmentation mask. Additionally, the segmentation mask is obtained by deforming a template mask with the same topology as the object of interest using an orientation-preserving quasiconformal mapping. This approach helps to avoid topological errors in the segmentation results. We provide a thorough analysis of the proposed model, including theoretical support for the ability of QIS to include or exclude regions of interest or disinterest based on the user's indication. To evaluate the performance of QIS, we conduct experiments on synthesized images, medical images, natural images and noisy natural images. The results demonstrate the efficacy of our proposed method.