Convex Optimization for Parallel Energy Minimization

03/05/2015
by   K. S. Sesh Kumar, et al.
0

Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in particular, some efficient combinatorial algorithms, are difficult to par-allelize. By exploiting results from convex and submodular theory, we reformulate the quadratic energy minimization problem as a total variation denoising problem, which, when viewed geometrically, enables the use of projection and reflection based convex methods. The resulting min-cut algorithm (and code) is conceptually very simple, and solves a sequence of TV denoising problems. We perform an extensive empirical evaluation comparing state-of-the-art combinatorial algorithms and convex optimization techniques. On small problems the iterative convex methods match the combinatorial max-flow algorithms, while on larger problems they offer other flexibility and important gains: (a) their memory footprint is small; (b) their straightforward parallelizability fits multi-core platforms; (c) they can easily be warm-started; and (d) they quickly reach approximately good solutions, thereby enabling faster "inexact" solutions. A key consequence of our approach based on submodularity and convexity is that it is allows to combine any arbitrary combinatorial or convex methods as subroutines, which allows one to obtain hybrid combinatorial and convex optimization algorithms that benefit from the strengths of both.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/10/2014

Signal Reconstruction Framework Based On Projections Onto Epigraph Set Of A Convex Cost Function (PESC)

A new signal processing framework based on making orthogonal Projections...
research
02/01/2022

Review of Serial and Parallel Min-Cut/Max-Flow Algorithms for Computer Vision

Minimum cut / maximum flow (min-cut/max-flow) algorithms are used to sol...
research
10/13/2010

Combinatorial Continuous Maximal Flows

Maximum flow (and minimum cut) algorithms have had a strong impact on co...
research
06/26/2018

Quadratic Decomposable Submodular Function Minimization

We introduce a new convex optimization problem, termed quadratic decompo...
research
08/17/2019

Parametric Majorization for Data-Driven Energy Minimization Methods

Energy minimization methods are a classical tool in a multitude of compu...
research
02/21/2023

Learning Gradually Non-convex Image Priors Using Score Matching

In this paper, we propose a unified framework of denoising score-based m...
research
10/01/2020

PHASED: Phase-Aware Submodularity-Based Energy Disaggregation

Energy disaggregation is the task of discerning the energy consumption o...

Please sign up or login with your details

Forgot password? Click here to reset