Elliptical Tube Analysis

Elliptical tubes are a special case of generalized cylinders, formed by sweeping a sequence of ellipses along a central curve.

A variety of biological structures and organs, such as the hippocampus, mandible, and colon, can be represented as elliptical tubes.

Elliptical tube transformation, deformation, and interpolation are important for industrial applications—such as robotic arm kinematics—as well as for shape analysis, where they help define shape distances and dissimilarities.

Dealing with self-intersections during object transformations is a challenging problem.

The Relative Curvature Condition (RCC) is an important criterion for ensuring that tubular deformations avoid self-intersections.

The RCC defines a local curvature tolerance, restricting the amount of bending permitted based on the curvature of the central curve.

Based on the Relative Curvature Condition (RCC), the space of elliptical tubes can be viewed as a trumpet-like region bounded by a hyperbolic surface.

The statistical analysis of elliptical tubes respects this geometric structure, aligning with the constraints imposed by the space.

Statistical shape analysis of elliptical tubes, grounded in the defined geometric space, is important for cross-sectional studies aimed at uncovering group differences, such as those between the subcortical brain structures of patients with neurological disorders and healthy controls.

The ETRep R-package provides tools for representing, transforming, and analyzing elliptical tubes. 

The ETRep ensures geometrically valid deformations that avoid self-intersections by incorporating the Relative Curvature Condition.

The package supports shape interpolation, deformation, and statistical shape analysis based on the intrinsic geometry of the elliptical tube space. 

The package can be easily installed via RStudio and is available on the CRAN repository.

CRAN: ETRep R Package