Push-Forward Signed Distance Functions enable interpretable and robust continuous shape quantification

• URL: http://arxiv.org/abs/2410.21004v1
• Date: Mon, 28 Oct 2024 13:28:21 GMT
• Title: Push-Forward Signed Distance Functions enable interpretable and robust continuous shape quantification
• Authors: Roua Rouatbi, Juan Esteban Suarez, Ivo F. Sbalzarini,
• Abstract summary: Push-Forward Signed Morphometric (PF-SDM) is a novel method for shape quantification in biomedical imaging. PF-SDM effectively captures the geometric properties of shapes, including their topological skeletons and symmetries.
• Score: 1.433758865948252
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We introduce the Push-Forward Signed Distance Morphometric (PF-SDM), a novel method for shape quantification in biomedical imaging that is continuous, interpretable, and invariant to shape-preserving transformations. PF-SDM effectively captures the geometric properties of shapes, including their topological skeletons and radial symmetries. This results in a robust and interpretable shape descriptor that generalizes to capture temporal shape dynamics. Importantly, PF-SDM avoids certain issues of previous geometric morphometrics, like Elliptical Fourier Analysis and Generalized Procrustes Analysis, such as coefficient correlations and landmark choices. We present the PF-SDM theory, provide a practically computable algorithm, and benchmark it on synthetic data.

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