3D image analysis

From a theoretical point of view, increasing the number of dimensions in image analysis does not necessarily pose new mathematical difficulties. For example, one of the most commonly used theoretical frameworks in image analysis, that of linear algebra, poses no formal difficulty when the number of dimensions of the starting space increases.

The topological framework, on the other hand, is closely linked to the number of dimensions. In three-dimensional Euclidean space, there are unknown topological structures in two dimensions. Characterizing the shape of an object therefore becomes more complex as the number of dimensions increases.

From a practical point of view, the increase in the number of dimensions has important consequences. The volume of data tends to be significantly greater, posing problems of data storage and transport, as well...