Advancements in 2D/3D Image Registration Methods
Fawaz Hjouj, Mohamed Soufiane Jouini, Mohammad Al-Khaleel
Abstract
In this paper, we present methods for identifying an image from a given set of Radon projections. Given a suitably regular 2-D or 3-D function, we form a new function <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> using a linear transformation. We show how the Radon projections of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</i> can be used to determine the transformation. The proposed algorithms introduce three major contributions, (1) Improvements on the 2-D setting using the moments of the Radon projections with only two orthogonal projections. (2) A natural extension of the 2-D setting to work with the 3-D setting. In particular, reducing the 3-D problem to a 2-D problem so that we can recover a translation, a scaling, or a rotation transformation of a 3-D object in the Radon domain. (3) An efficient method of recovering a rotation of a 3-D image around an arbitrary axis and an angle of rotation.