Optical flow techniques are often used to estimate velocity fields to represent motion in successive video images. Usually the method is mathematically ill-posed, because the single scalar equation representing the conservation of local intensity contains more than one unknown velocity component. Instead of regularizing the problem using optimization techniques, we formulate a well-posed problem for the gerbil hemicochlea preparation by introducing an in-plane incompressibility constraint, and then show that local brightness is also conserved. We solve the resulting system using a Lagrangian description of the conservation equations. With this approach, the displacement of isointensity contours on sequential images determines the normal component of velocity of an area element, while the tangential component is computed from the local constant area constraint. We have validated our method using pairs of images generated from our calculations of the vibrational deformation in a cross section of the organ of Corti and tectorial membrane in the mammalian cochlea, and quantified the superior performance of our method when complex artificial motion is applied to a noisy image obtained from the hemicochlea preparation. The micromechanics of the organ of Corti and the tectorial membrane is then analyzed by our new method.