3-D Motion Estimation in Passive Navigation by Acoustic Imaging Hassan Assalih Ocean Systems Lab - School of EPS Heriot Watt University Edinburgh, UK EH14 4AS Email: ha92@hw.ac.uk Shahriar Negahdaripour ECE Department University of Miami Coral Gables, Florida – USA Email: shahriar@miami.edu Yvan Petillot Ocean Systems Lab - School of EPS Heriot Watt University Edinburgh, UK EH14 4AS Email: Y.R.Petillot@hw.ac.uk Abstract-In this paper, we introduce a new method to tackle Motion Estimation, Correspondence Problem and 3D Reconstruction in underwater environments using an acoustic camera, such as, a DIDSON camera. Here, we mainly focus on motion estimation. We introduce the background on the new concepts of sampling a DIDSON arc and the Modified District Uniform Distribution (MDUD). The motion estimation methodology utilizes weighted-Hough array in choosing a solution from among many potential candidates. Index Terms – Motion Estimation, acoustic imaging, underwater imaging. I. INTRODUCTION 2-D Imaging systems, e.g., optical or acoustic, encode rich visual cues about the geometry of the work that is imaged and the position of the sensor relative to the world. In motion vision applications dealing with robotics platforms, one of the objectives is to determine the trajectory of a mobile system from the variations in the 2-D scene imagery. While this problem has been addressed extensively for numerous terrestrial applications [1, 2, 3] and to some extend in underwater by optical imaging [4, 5], less than a handful of earlier studies have explored application to 2-D sonar imaging systems [6, 7, 8]. Recently, 2-D sonar imaging systems, e.g., DIDSON video cameras [9], are installed on Remotely Operated Vehicles (ROVs) and Autonomous Underwater Vehicles (AUVs) for the inspection of ship hulls and other subsea structures in turbid coastal and harbour waters. The control systems of these platforms and (or) their designs are to eliminate the pitch and roll motions, namely the rotations around the X and Y axes of the platform [12, 13]. Therefore, they typically undergo movements with 4 degrees of freedom, which means no/negligible pitch and roll. Alternatively, these two rotation components (around the X and Y axes) can be measured by external sensor, e.g., gyros, while sensors for measuring rotations about the Z axis use magnets. Thus, while the former can be measured with relatively good accuracy, the performance of the latter may be affected by metal structures such as the ship hull, pipelines, etc. Thus, it is important to devise a robust and accurate method for the estimation of rotations around the Z axis, namely heading motions. In this paper, a new framework for the analysis of 2-D sonar video image is explored, comprising the principles of Modified District Uniform Distribution (MDUD), sonar projection function (SPF) and sonar arc sampling. It can be applied to address the problems of motion estimation, correspondence problem and 3D reconstruction. This will facilitate various routine tasks of ROVs/AUVs, including the inspection of ship hulls and other subsea structures, autonomous navigation, and target localization and classification. The immediate application of interest is the estimation of sonar motion with 4 degrees of freedom. We present an algorithm that applies the proposed framework along with a weighted-Hough transform formulation to select a solution from among many potential candidates. This paper is organized as follows: section II presents background concepts including Sampling DIDSON arc, Modified District Uniform Distribution, and probability adjustment based on shadow, section III describes using the framework in the motion estimation algorithm and presents a new technique to infer the rotation angle about the Z axis, section IV explains briefly how to use the framework to tackle the correspondence problem in stereo acoustic system, section V presents real results of the motion estimation algorithm using data gathered from DIDSON camera. II. BACKGROUND CONCEPTS A. Sampling DIDSON Arc The sonar measurements !"# $% comprise two components of the spherical coordinate !"# $# &% of a 3-D point of interest (POI). These define an arc in 3-D space as the locus of the POI, corresponding to an arbitrary elevation angle &. We can sample this arc with N discrete points, each point being a candidate 3-D point which can be assigned a pre-estimated probability; more precisely, these 3D Points ( ) * !+ ) #, ) #- ) % are associated with the probability . ) /. ) )01 )02 *3 !3% In terms of the sonar measurements, the N sampled points are given by the following equations: 978-1-4244-4333-8/10/$25.00 ©2010 IEEE