Derivative-Based Optical Flow Estimation: Controlled Comparison of First- and Second- Order Methods

11 geiicralizat~ion of' t.hc first-orclcr, 1oca.l least-squares opt,ical flow cst.imatiol\ a.lgorit,hm provides a, hasis for controlleel coml~a.rison brt.wecn t,hc first,anel sccoiiil-orilcr order opt,ical flow cst,imatioii mcthoils. 'I'lic g('11craliza.tion rcsult,~ from t,he fact that. t,hc first,orcler iiiet.liod performs a compi~tat.ion t.1ia.t is ccll~ivalciit, .o t1ia.t of t8hc sccond-orclcr mc.t.liocl when t lic inp11t is prcproccsscc-1 to cstract the sl)at.ial gradient, ficlcl ancl t,hc local nc~iglil~orhood is reilncecl to a. single point. [lsing t,lic I ~ P I I ~ gc~iicralizccl framcmorlr, tlit. rclativc. performance of the two mctliorls is coml,a.red through a scrics of csprrimcnts. 'I'hc rspcriments rcvea.1 t,liat hot,Ii mctliods are syst,cmat.ically biased ancl t,hat this hias can I,c recll~cecl hy low-pass filtering. 'I'lic cspcrimc1it.s also rcvcal that t,hc scconil-or(-lcrhascil 01'tical flow est,imatcs arc gcuc?rally much less accurat,c than t.he first,-order-I)asecl cstimat.cs, ancl that, t,liis ina.ccurxcy is clue primarily t,o t.he fact, t1ia.t t,he seconrl-orcler mct.liocl cmploys significa.nt.ly fewer mot.ion consttra.intjs per cstimatc than the first-orclcr rncthoc-I.