Several approaches for optical flow estimation use partial differentia
l equations to model changes in image brightness throughout time. A co
mmonly used equation is the so-called optical flow constraint (OFC), w
hich assumes that the image brightness is stationary with respect to t
ime. More recently, a different constraint referred to as the extended
optical flow constraint (EOFC) has been introduced, which also contai
ns the divergence of the how field of image brightness. There is no ag
reement in the literature about which of these constraints provides th
e best estimation of the velocity held. In this paper, two new solutio
ns for optical how computation are proposed, which are based on an app
roximation of the constraint equations. The two techniques have been u
sed with both EOFC and OFC constraint equations. Results achieved by u
sing these solutions have been compared with several well-known comput
ational methods for optical flow estimation in different motion condit
ions. Estimation errors have also been measured and compared for diffe
rent types of motion.