Fast Decomposable Submodular Function Minimization using Constrained Total Variation
This work addresses computational efficiency in submodular function minimization, which is incremental for applications like graph cuts in 2D and 3D graphs.
The paper tackles the problem of minimizing the sum of submodular set functions by developing a modified convex formulation that uses constrained total variation oracles, reducing the number of calls to simpler minimization oracles compared to existing methods.
We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding Lovász extensions and the squared Euclidean norm, leading to algorithms requiring total variation oracles of the summand functions; without further assumptions, these more complex oracles require many calls to the simpler minimization oracles often available in practice. In this paper, we consider a modified convex problem requiring constrained version of the total variation oracles that can be solved with significantly fewer calls to the simple minimization oracles. We support our claims by showing results on graph cuts for 2D and 3D graphs