Comparative analysis of quasi-conformal deformations in shape space

Area of Science:

• Computational geometry
• Medical image analysis
• Differential geometry

Background:

• Classifying complex deformations in 3D models is challenging.
• Existing methods may not adequately capture subtle changes in shape during deformation.
• Analyzing cardiac function requires robust deformation classification techniques.

Purpose of the Study:

• To propose a novel shape space-based approach for classifying quasi-conformal deformations of 3D models.
• To introduce a new metric for quantifying curvature changes in deforming meshes.
• To evaluate the method's effectiveness in classifying cardiac deformations.

Main Methods:

• Utilizing the shape space concept and a new metric on the quotient space of meshes.
• Calculating geodesic curves to represent deformation trajectories in the shape space manifold.
• Employing Multi-Dimensional Scaling for dimensionality reduction and comparison of deformation curves.

Main Results:

• The proposed algorithm effectively classifies normal and abnormal left heart ventricle deformations.
• Experiments on synthetic and real cardiac datasets demonstrate the method's efficacy.
• The approach accurately captures curvature changes during deformation.

Conclusions:

• The shape space approach provides a robust framework for analyzing and classifying 3D model deformations.
• This method holds potential for applications in medical imaging, particularly in cardiac function analysis.
• The introduced metric and comparison techniques enhance the understanding of complex shape transformations.