Bachelor Project
June, 2023
The present work is concerned with rotations of three-dimensional digital signals, sampled evenly on Cartesian grids. Such settings are ubiquitous across the field of sensing, in particular imaging. Arbitrary rotation of 3D scalar fields represents a cornerstone of multi-modal imaging, where multiple signals are aligned under rigid body transformations. In this work we use them to compute light attenuation within large-scale volumetric dataset. We revise the foundations laid by Unser in 1995 [9] on how to accurately carry out 2D rotations on 2D images, and extend it to 3D rotations on volumetric images. Relying on classical digital filter design, we devise novel computational schemes that are algorithmically efficient while allowing the underlying computational workload to be effectively mapped onto contemporary computer microarchitectures. Achieving close-to-ideal performance on such applications remains nonetheless a challenge. Considerations about the careful software implementation of such schemes are therefore included in the present document.