# The iterative convolution-thresholding method (ICTM) for image segmentation

arXiv: https://arxiv.org/abs/1904.10917 · HTML: https://mlsanity.com/paper/1904.10917/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2019.

## Built on by (most cited first, 9 of 9)

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- [Learning Restoration is Not Enough: Transfering Identical Mapping for Single-Image Shadow Removal](https://mlsanity.com/paper/2305.10640/) (2023)
- [Computer-aided Recognition and Assessment of a Porous Bioelastomer on Ultrasound Images for Regenerative Medicine Applications](https://mlsanity.com/paper/2201.11987/) (2022)
- [An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multi-phase Image Segmentation](https://mlsanity.com/paper/2203.09036/) (2022)
- [DEFN: Dual-Encoder Fourier Group Harmonics Network for Three-Dimensional Indistinct-Boundary Object Segmentation](https://mlsanity.com/paper/2311.00483/) (2023)
- [Topology preserving Image segmentation using the iterative convolution-thresholding method](https://mlsanity.com/paper/2503.17792/) (2025)
- [Fracture interactive geodesic active contours for bone segmentation](https://mlsanity.com/paper/2509.14817/) (2025)
- [RefLSM: Linearized Structural-Prior Reflectance Model for Medical Image Segmentation and Bias-Field Correction](https://mlsanity.com/paper/2512.07191/) (2025)

## Abstract (arXiv)

In this paper, we propose a novel iterative convolution-thresholding method (ICTM) that is applicable to a range of variational models for image segmentation. A variational model usually minimizes an energy functional consisting of a fidelity term and a regularization term. In the ICTM, the interface between two different segment domains is implicitly represented by their characteristic functions. The fidelity term is then usually written as a linear functional of the characteristic functions and the regularized term is approximated by a functional of characteristic functions in terms of heat kernel convolution. This allows us to design an iterative convolution-thresholding method to minimize the approximate energy. The method is simple, efficient and enjoys the energy-decaying property. Numerical experiments show that the method is easy to implement, robust and applicable to various image segmentation models.