# DOPE: Distributed Optimization for Pairwise Energies

## TL;DR

This paper introduces a distributed optimization method using ADMM for pairwise energy functions in vision, enabling parallel computation and handling non-submodular potentials effectively.

## Contribution

It presents a novel distributed ADMM framework that decomposes pairwise energy optimization into parallel sub-problems with a new consistency constraint, applicable to non-submodular functions.

## Key findings

- Improves efficiency of pairwise energy optimization in vision tasks.
- Effectively handles non-submodular potentials.
- Demonstrates benefits over serial algorithms like BK in experiments.

## Abstract

We formulate an Alternating Direction Method of Mul-tipliers (ADMM) that systematically distributes the computations of any technique for optimizing pairwise functions, including non-submodular potentials. Such discrete functions are very useful in segmentation and a breadth of other vision problems. Our method decomposes the problem into a large set of small sub-problems, each involving a sub-region of the image domain, which can be solved in parallel. We achieve consistency between the sub-problems through a novel constraint that can be used for a large class of pair-wise functions. We give an iterative numerical solution that alternates between solving the sub-problems and updating consistency variables, until convergence. We report comprehensive experiments, which demonstrate the benefit of our general distributed solution in the case of the popular serial algorithm of Boykov and Kolmogorov (BK algorithm) and, also, in the context of non-submodular functions.