Advancements in 2D/3D Image Registration Methods

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 $g$ from $f$ using a linear transformation. We show how the Radon projections of $f$ and $g$ 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.

Keywords

• Digital watermarking
• affine transformation
• radon transform
• linear transformation