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Three-Dimensional Shape Modeling and Analysis of Brain Structures
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Alpha shapes: determining 3D shape complexity across morphologically diverse structures.

James D Gardiner1, Julia Behnsen2, Charlotte A Brassey3

  • 1Institute of Ageing and Chronic Disease, University of Liverpool, Liverpool, L7 8TX, UK.

BMC Evolutionary Biology
|December 7, 2018
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Summary
This summary is machine-generated.

A new alpha-shapes method quantifies 3D shape complexity in irregular biological structures without landmarks. This technique is sensitive to surface topology and shows promise for evolutionary and ecological studies.

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Area of Science:

  • Evolutionary biology
  • Geometric morphometrics
  • Bioimaging

Background:

  • Advances in bioimaging enable rapid, low-cost generation of high-resolution 3D biological models.
  • Existing tools for shape analysis and topographic complexity quantification are limited for irregular structures lacking homologous landmarks.
  • The alpha-shapes method is proposed for quantifying 3D shape complexity in such challenging datasets.

Purpose of the Study:

  • To introduce and validate the alpha-shapes method for quantifying 3D shape complexity.
  • To apply alpha-shapes to analyze the complex morphology of mammalian bacula.
  • To assess the sensitivity and utility of alpha-shapes compared to other complexity metrics.

Main Methods:

  • Alpha-shapes were applied to micro-computed tomography (μCT) scans of mammalian bacula.
  • Bacula data were converted into point clouds after binarization and scaling.
  • Optimal alpha refinement was determined when alpha-shape volume matched CT voxel volume, serving as a complexity metric.

Main Results:

  • Alpha-shapes successfully quantified interspecific variation in shape complexity for disparate biological structures.
  • The method revealed distinct complexity patterns in bacula, identifying ursid bacula as low complexity and mustelid bacula as high complexity.
  • Alpha-shapes demonstrated sensitivity to surface concavities, differentiating it from other metrics like 3D fractal dimension.

Conclusions:

  • The alpha-shapes method provides a robust, automated approach for quantifying 3D shape complexity without landmark identification.
  • Its sensitivity to surface topology and straightforward implementation make it suitable for large datasets.
  • Alpha-shapes offer significant potential for applications in evolutionary, ecological, and palaeoecological research beyond genital morphology.