Enhancing cardiac image segmentation through persistent homology regularization

Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Sergio Escalera Guerrero, Carles Casacuberta i Rubén Ballester Bautista
[en] Cardiovascular diseases are a major cause of death and disability. Deep learning-based segmentation methods could help to reduce their severity by aiding in early diagnosing but high levels of accuracy are necessary. The vast majority of methods focus on correcting local errors and miss the global picture. To ad- dress this issue, researchers have developed techniques that incorporate global context and consider the relationships between pixels. Here, we apply persistent homology, a branch of topology that studies the topological structure of shapes, along with deep learning methods to improve the heart segmentation. We use multidimensional topological losses to avoid spurious components and holes and increase the total accuracy. We evaluate the performance of three different approaches: using the dice and pixel-wise losses with the sum of persistences of label diagrams as a regularizer, using the dice and pixel-wise losses with the bottleneck distance as a regularizer, and using both losses without any regularization. We find that, while more computationally demanding, the methods using topological regularizers outperform the other method in terms of accuracy.