3D Velocity from 3D Doppler Radial Velocity

ABSTRACT: We present local least squares and regularizationframeworks for computing 3D velocity (3D optical flow) from 3D radialvelocity measured by a Doppler radar. We demonstrate the perfor-mance of our algorithms quantitatively on synthetic radial velocitydata and qualitatively on real radial velocity data, obtained from theDoppler radar at Kurnell Radar station, Botany Bay, New SouthWales, Australia. Radial velocity can be used to predict the futurepositions of storms in sequences of Doppler radar datasets. VV C 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 189–198, 2005;Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20048 Key words: 3D optical flow; 3D Doppler full/radial velocity; localleast squares; regularization I. INTRODUCTIONWe present an extension of our 2D Doppler storm tracking work(Cheng etal., 1998; Barron etal., 1999) to3D by using local 3D radialvelocity neighborhoods to compute local 3D velocity (local 3D opticalflow). Radial velocity (measured by the Doppler effect) is the compo-nent of 3D velocity along the radial ray from the radar station to somemoving 3D atmospheric point. Our computation of full velocity fromatmospheric radial velocities uses a combination of a 3D local leastsquares framework, much like Lucas and Kanade’s 2D least squarescomputation (Lucasand Kanade,1981) and aniterative 3D regulariza-tion framework, much like Horn and Schunck’s 2D regularization(Hornand Schunck, 1981). Preliminary resultswere initially presentedby Chen (2001, and Chen and colleagues (2001a,b). In addition tocomputing 3D velocity from Doppler radial velocities, it is also possi-ble to use densely sampled range sequences (Yamamoto et al., 1993)to compute range flow in a similar manner. Range flow, the 3D veloc-ity of points on a deformable surface relative to a moving range sen-sor, can be computed in a similar manner (Spies et al., 2000a,b; Spieset al., 2002). Note that range flow is computed with respect to moving3D surfacedata rather than with respect to moving 3D volumetric data(and is therefore not 3D optical flow) as it involves using a slightlydifferent constraint equation (Spies et al., 2002).2D optical flow methods have recently been generalized into the3D domain. Chaudhury et al. (1994) formulated a 3D optical flowconstraint, using I