Distributed Non-Convex ADMM-inference in Large-scale Random Fields

We propose a parallel and distributed algorithm for solving discrete labeling problems in large scale random fields. Our approach is motivated by the following observations: i) very large scale image and video processing problems, such as labeling dozens of million pixels with thousands of labels, are routinely faced in many application domains; ii) the computational complexity of the current state-of-the-art inference algorithms makes them impractical to solve such large scale problems; iii) modern parallel and distributed systems provide high computation power at low cost. At the core of our algorithm is a tree-based decomposition of the original optimization problem which is solved using a non convex form of the method of alternating direction method of multipliers (ADMM). This allows efficient parallel solving of resulting sub-problems. We evaluate the efficiency and accuracy offered by our algorithm on several benchmark low-level vision problems, on both CPU and Nvidia GPU. We consistently achieve a factor of speed-up compared to dual decomposition (DD) approach and other ADMM-based approaches. Probabilistic graphical models such as the Markov Random Fields (MRF) and Conditional Random Fields (CRF), and related energy minimization based techniques have become ubiquitous in computer vision and image processing. They have been proven especially useful to solve a variety of important, high-dimensional, discrete inference problems. Examples include per-pixel object labelling, image denoising, image inpainting, disparity and optical flow estimation, etc. [2]. Their use nonetheless implies computational costs that are often not compatible with very large scale problems met today in many applications. This concern is at the heart of present work. We first define a discrete random field Y = {y1,y2, ...,yN} attached to the N nodes of a graph G = (V,E) with vertex set V and edge set E . Each random variable takes a label from a discrete space L of size L. We define Y = LN the set of all possible label assignments. This random field is a pairwise Markov Random Field (MRF) if there exists an energy function of the form E(Y) := ∑ i∈V θi(yi)+ ∑ (i, j)∈E θi j(yi,y j), (1)