This is a classical computer vision problem, the 3D reconstruction problem, structure for motion, although Carl likes to take a mathematical spin on it. In fact, the main challenge of this work lays in the mathematics: to understand these functions, how they behave on the SO(3) manifold, the manifold of rotations. With this work, Carl is particularly proud of two things. One is the formulation that allows to approximate functions well; and the fact that they found out how to make it work in a global optimization framework. How did Carl handle the process of working on this problem? It was a long process. The initial inspiration simply came from a paper that was doing local optimization on similar things. He thought that this can easily be incorporated in certifiably optimal rotation averaging frameworks. But then it turned out that it wasn't that easy: “I had to spend a lot of time,” Carl explains, “digging into the equations here and then connecting it to some theory on optimization and convex envelopes, basically. It was a long process and lots of lots of lots of studying optimization.” In his regular work, Carl is in some sense more a mathematician than a computer vision scientist. But his application has always been structure from motion. Everything that he has done sort of relates to 11 DAILY ICCV Wednesday Carl Olsson
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