A Skeletonization Algorithm for Gradient-Based Optimization

MCML Authors

Martin Menten

Dr.

JRG Leader AI for Vision

Artificial Intelligence in Healthcare and Medicine

Julia Schnabel

Prof. Dr.

Principal Investigator

Computational Imaging and AI in Medicine

Daniel Rückert

Prof. Dr.

Director

Artificial Intelligence in Healthcare and Medicine

Abstract

The skeleton of a digital image is a compact representation of its topology, geometry, and scale. It has utility in many computer vision applications, such as image description, segmentation, and registration. However, skeletonization has only seen limited use in contemporary deep learning solutions. Most existing skeletonization algorithms are not differentiable, making it impossible to integrate them with gradient-based optimization. Compatible algorithms based on morphological operations and neural networks have been proposed, but their results often deviate from the geometry and topology of the true medial axis. This work introduces the first three-dimensional skeletonization algorithm that is both compatible with gradient-based optimization and preserves an object's topology. Our method is exclusively based on matrix additions and multiplications, convolutional operations, basic non-linear functions, and sampling from a uniform probability distribution, allowing it to be easily implemented in any major deep learning library. In benchmarking experiments, we prove the advantages of our skeletonization algorithm compared to non-differentiable, morphological, and neural-network-based baselines. Finally, we demonstrate the utility of our algorithm by integrating it with two medical image processing applications that use gradient-based optimization: deep-learning-based blood vessel segmentation, and multimodal registration of the mandible in computed tomography and magnetic resonance images.

inproceedings

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ICCV 2023

IEEE/CVF International Conference on Computer Vision. Paris, France, Oct 02-06, 2023.

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Authors

M. J. Menten • J. C. Paetzold • V. A. Zimmer • S. Shit • I. Ezhov • R. Holland • M. Probst • J. A. Schnabel • D. Rückert

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Links

DOI

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Research Area

 C1 | Medicine