A QUBO Formulation of the Stereo Matching Problem for D-Wave Quantum Annealers.

William Cruz-Santos,Salvador Venegas-Andraca,Marco Lanzagorta

doi:10.3390/e20100786

William Cruz-Santos, Salvador Venegas-Andraca + Show 1 more

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https://doi.org/10.3390/e20100786

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Abstract

In this paper, we propose a methodology to solve the stereo matching problem through quantum annealing optimization. Our proposal takes advantage of the existing Min-Cut/Max-Flow network formulation of computer vision problems. Based on this network formulation, we construct a quadratic pseudo-Boolean function and then optimize it through the use of the D-Wave quantum annealing technology. Experimental validation using two kinds of stereo pair of images, random dot stereograms and gray-scale, shows that our methodology is effective.

Highlights

Computer vision is an interdisciplinary field of research with almost six decades of theoretical and algorithmic developments [1,2] that focuses on developing mathematical techniques and algorithms that aim at enabling computers to identify, analyze, and understand information from elements of imagery [3]
We focus on the stereo matching problem using a basic stereo system
To validate our methodology for the solution to the stereo matching problem, we present the results of the minimization of the QUBO expression using the classic solver qbsolv developed by D-Wave

Summary

Introduction

Computer vision is an interdisciplinary field of research with almost six decades of theoretical and algorithmic developments [1,2] that focuses on developing mathematical techniques and algorithms that aim at enabling computers to identify, analyze, and understand information from elements of imagery [3]. The most basic stereo system consists of two cameras (left and right) and any stereo system must solve two problems: The stereo matching problem [4]: Which parts of the left and right images are projections of the same scene element?. The reconstruction problem, which is stated as follows: given a number of corresponding parts of the left and right images, what can we say about the 3-D locations and structures of the observed objects?. We focus on the stereo matching problem using a basic stereo system This problem is difficult to solve because some parts of the scene are visible only by either the left or right camera but not by both; a stereo system must be able to select the image parts to be matched [5]. Stereo vision has many applications, such as in photogrammetry [6], stereo-based head tracking [7], volumetric and 3-D surface reconstruction [8], video-based walkthroughs [9], and stereo-based autonomous navigation [10], among others

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