Technological advances in measuring instruments have revolutionized our ability to digitize the world in 3D. This revolution has enabled new applications such as the automatic interpretation of scenes, the simulation of physical phenomena on the scale of cities, and the digital documentation of architectural heritage.
A key topic at the heart of this revolution is surface reconstruction, which involves converting measurements into a geometric representation that can be interpreted by the computer. The aim is to construct a surface solely from what are usually point measurements, such that the topology and geometry of the reconstructed surface approximate the physical surface measured. In essence, this is an ill-posed problem (with non-unique solutions), and the diversity of existing methods reflects the diversity of a priori knowledge about physical surfaces and the properties sought for the reconstructed surface.
This seminar will provide an introduction to the main families of surface reconstruction methods, from the point of view of the assumptions used to make the problem better posed.
We will then address the enduring problems posed by imperfect data, i.e. imprecise, sparse, incomplete or even aberrant. The quest for robustness to such imperfect data has motivated variational methods and more recent approaches inspired by optimal transport theory.
Finally, we will discuss the emerging scientific challenges associated with new data acquisition paradigms (sensor networks, continuous digitization, community data) and the societal impacts of the democratization of 3D digitization methods.
