From Curves to Trees: A Tree-like Shapes Distance Using the Elastic Shape Analysis Framework.

Area of Science:

• Biomedical Imaging
• Computational Biology
• Graph Theory

Background:

• Tree-like structures like neurons are crucial in biomedical imaging.
• Analyzing their morphology aids in understanding function and disease.
• Quantifying shape differences is essential for accurate characterization.

Purpose of the Study:

• To develop a novel method for comparing tree-like shapes using both topological and geometrical information.
• To apply this method to analyze and differentiate axon morphology.
• To compute the mean shape of tree populations.

Main Methods:

• Employed the Elastic Shape Analysis Framework for shape comparison.
• Integrated topological and geometrical information.
• Evaluated on two datasets of neuronal and axonal trees from open databases and microscopy images.

Main Results:

• The proposed method demonstrated superior performance in distinguishing between different neuronal and axonal populations compared to state-of-the-art algorithms.
• Inter and intra-class distances were calculated and used in a classification scheme.
• Mean shapes for each population were computed, offering a comprehensive view of morphological characteristics.

Conclusions:

• The developed Elastic Shape Analysis method effectively compares tree-like structures in biomedical imaging.
• It provides a robust tool for classifying and understanding morphological variations in biological populations.
• The mean shape representation offers richer insights than traditional feature-based analyses.