Representing Topological Self-Similarity Using Fractal Feature Maps for Accurate Segmentation of Tubular Structures

TL;DR

This paper introduces fractal feature maps derived from pixel-level fractal dimension to improve the segmentation of tubular structures, enhancing boundary accuracy and skeletal continuity in deep learning models.

Contribution

It extends fractal dimension to pixel-level using sliding windows and integrates these features into a modified U-Net architecture with additional decoders.

Findings

Improved segmentation accuracy on five datasets

Enhanced boundary and skeletal continuity

FFM can be integrated with various models as a plug-in

Abstract

Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical challenges. A fundamental property of such structures is their topological self-similarity, which can be quantified by fractal features such as fractal dimension (FD). In this study, we incorporate fractal features into a deep learning model by extending FD to the pixel-level using a sliding window technique. The resulting fractal feature maps (FFMs) are then incorporated as additional input to the model and additional weight in the loss function to enhance segmentation performance by utilizing the topological self-similarity. Moreover, we extend the U-Net architecture by incorporating an edge decoder and a skeleton decoder to improve boundary accuracy and skeletal continuity of segmentation, respectively. Extensive experiments on five tubular structure datasets validate the effectiveness and robustness of our approach. Furthermore, the integration of FFMs with other popular segmentation models such as HR-Net also yields performance enhancement, suggesting FFM can be incorporated as a plug-in module with different model architectures. Code and data are openly accessible at https://github.com/cbmi-group/FFM-Multi-Decoder-Network.