Domain Decomposition

The vision system simulation of a single camera is computationally less expensive than the simulation of a system with multiple cameras, the visibility analysis of a single camera is less complex, and the size of the optimal camera placement problem of a single camera is smaller. Thus, greedily positioning the first camera with parameters x_1, then the second with parameters x_2, then the third, and so on, promises to be an efficient way to solve the problem types for vision systems with multiple cameras. However, the following video shows an example where the acquired solution of the problem is neither globally nor locally optimal.

In terms of optimization, we speak of a Subspace Decomposition: The parameters of a single camera x_i\in\mathbb{X}_i,\ i=1,\hdots,N are a block of parameters in the variable vector of the vision system x=(x_1,\hdots,x_N). The domain is decomposed into subspaces \Omega=\mathbb{X}_1\times\hdots\times \mathbb{X}_N. Instead of optimizing the objective function on the whole domain, the function is consecutively optimized on the subspaces. The challenge of this project is optimizing a piecewise differentiable, non-separable function on a decomposed domain.

This is a collaboration with C.-B. Schönlieb.