A one-dimensional Radon transform on SO(3) and its application to texture goniometry

TL;DR

This paper introduces a one-dimensional Radon transform on SO(3) motivated by texture goniometry, deriving inversion formulas and comparing them with spherical Radon transform inversions for even functions.

Contribution

It presents new inversion formulas for the Radon transform on SO(3) and compares them with existing spherical Radon transform methods.

Findings

Derived several inversion formulas for the Radon transform on SO(3)

Compared the SO(3) Radon transform inversion with spherical Radon transform inversion

Provided insights into texture goniometry applications

Abstract

We consider a one-dimensional Radon transform on the group SO(3) which is motivated by texture goniometry. In particular we will derive several inversion formulae and compare them with the inversion of the one-dimensional spherical Radon transform on the three dimensional unit sphere for even functions.