In CT imaging, what is measured are projections of a 3D object, and the goal is to reconstruct the object from these projections.

Geometric algebra provides a mathematical framework that allows us to work with lines in computer vision, which is more complex than working with points.

By integrating a 3D representation into models, we can better align the model's capabilities with the tasks we want it to perform, enhancing user affordances. Spatial intelligence is crucial for creating technology that understands and interacts with the 3D world, enabling a wide range of applications.

Conformal geometric algebra, which extends to five-dimensional space, allows for the representation of points, lines, planes, and spheres as algebraic objects, simplifying many geometric operations.

Using geometric algebra provides a clear origin point for calculations, eliminating the confusion of multiple coordinate systems and making it easier to handle rotations and translations in computer vision.

Lidar measurements provide 3D models of trees, allowing for more detailed analysis compared to traditional planar images.

Geometric algebra allows for easy differentiation of geometric objects, making it simpler to derive solutions compared to traditional methods involving matrices or tensors.

Denoising is integrated into the image reconstruction process, addressing both the lack of data and the noise present in measurements.

In my postdoc, I shifted towards inverse imaging problems, where the observed data is not a direct image but a transform, such as in CT scans.