A Topological Loss Function for Deep-Learning Based Image Segmentation Using Persistent Homology.

Area of Science:

• Medical image analysis
• Topological data analysis
• Machine learning

Background:

• Image segmentation is crucial for medical analysis but often requires extensive labeled data.
• Incorporating prior knowledge can improve segmentation accuracy, especially for complex structures.
• Topological data analysis provides tools to quantify shape and structure properties.

Purpose of the Study:

• To introduce a method for training neural networks for image segmentation using explicit topological prior knowledge.
• To leverage persistent homology for guiding segmentation without ground-truth labels.
• To demonstrate the efficacy of this method across diverse imaging datasets.

Main Methods:

• Utilized differentiable persistent homology to encode desired topological features (Betti numbers) into the neural network training process.
• Developed a method to incorporate this topological prior knowledge as a training gradient.
• Applied the method to image denoising, digit recognition, cardiac MRI segmentation, and 3D ultrasound placenta segmentation.

Main Results:

• The method successfully guided neural network segmentation by embedding explicit topological priors.
• Performance gains were most significant in challenging segmentation tasks.
• The approach proved effective in semi-supervised and post-processing contexts, extracting gradients from unlabeled data.

Conclusions:

• Explicit topological prior knowledge can significantly enhance neural network-based image segmentation.
• This method offers a powerful alternative to traditional supervised learning, reducing reliance on pixel-wise labels.
• The approach demonstrates broad applicability across various medical imaging and computer vision tasks.