Crease surfaces: from theory to extraction and application to diffusion tensor MRI.

Area of Science:

• Computer Vision
• Image Processing
• Scientific Visualization

Background:

• Crease surfaces capture extremal structures (ridges/valleys) in data, unlike isosurfaces.
• Traditional crease extraction methods overlooked Hessian degeneracies, impacting topological accuracy.

Purpose of the Study:

• To develop an efficient algorithm for crease surface extraction that accounts for Hessian degeneracies.
• To address the topological implications of Hessian degeneracies on crease surfaces.
• To provide a more accurate alternative to existing methods, including diffusion tensor magnetic resonance imaging (DT-MRI) stream surfaces.

Main Methods:

• Developed an algorithm for crease surface extraction incorporating Hessian degeneracies.
• Analyzed the topological consequences of Hessian degeneracies, including boundary conditions and orientability.
• Applied the method to analyze planarity in DT-MRI data.

Main Results:

• Hessian degeneracies act as boundaries for crease surfaces and affect their orientability.
• The new algorithm yields more accurate crease surface extraction compared to previous methods.
• Demonstrated the mathematical ill-definition of DT-MRI stream surfaces.

Conclusions:

• Crease surface extraction must consider Hessian degeneracies for topological accuracy.
• The proposed algorithm offers a robust and accurate method for crease surface extraction.
• Creases in planarity measures are a valid substitute for DT-MRI stream surfaces in data analysis.