# Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1904.10030 · HTML: https://mlsanity.com/paper/1904.10030/

## Key facts

- Cited by 116 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2019.

## Built on by (most cited first, 30 of 116)

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- [PocketNet: A Smaller Neural Network for Medical Image Analysis](https://mlsanity.com/paper/2104.10745/) (2021)
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- [Binary segmentation of medical images using implicit spline representations and deep learning](https://mlsanity.com/paper/2102.12759/) (2021)
- [Region-wise Loss for Biomedical Image Segmentation](https://mlsanity.com/paper/2108.01405/) (2021)
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## Abstract (arXiv)

The Hausdorff Distance (HD) is widely used in evaluating medical image segmentation methods. However, existing segmentation methods do not attempt to reduce HD directly. In this paper, we present novel loss functions for training convolutional neural network (CNN)-based segmentation methods with the goal of reducing HD directly. We propose three methods to estimate HD from the segmentation probability map produced by a CNN. One method makes use of the distance transform of the segmentation boundary. Another method is based on applying morphological erosion on the difference between the true and estimated segmentation maps. The third method works by applying circular/spherical convolution kernels of different radii on the segmentation probability maps. Based on these three methods for estimating HD, we suggest three loss functions that can be used for training to reduce HD. We use these loss functions to train CNNs for segmentation of the prostate, liver, and pancreas in ultrasound, magnetic resonance, and computed tomography images and compare the results with commonly-used loss functions. Our results show that the proposed loss functions can lead to approximately 18-45 % reduction in HD without degrading other segmentation performance criteria such as the Dice similarity coefficient. The proposed loss functions can be used for training medical image segmentation methods in order to reduce the large segmentation errors.