Moving from rigid to non-rigid domains reveals new fundamental challenges. Simple tasks, such as matching, alignment, and recognition become extremely hard to solve due to the high number of unknowns and non-linearity that pops out of the equations. Trying to linearize such tasks led to a successful framework known as functional maps that was later used in many applications. In this lecture, I will present a different approach where we contain a non-linear solution in the kernel of a matrix turning a complex geometric problem into a diagonalization procedure. Specifically, I will show how to rebuild non-rigid structures from multiple local observations.
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