This paper proposes the use of an adaptive locally oriented coordinate frame when calculating an optical flow field. The coordinate frame is aligned with the least curvature direction in a local window about each pixel. This has advantages to both fitting the flow field to the image data and in imposing smoothness constraints between neighboring pixels. In terms of fitting, robustness is obtained to a wider variety of image motions due to the extra invariance provided by the coordinate frame. Smoothness constraints are naturally propagated along image boundaries which often correspond to motion boundaries. In addition, moving objects can be efficiently segmented in the least curvature direction. We show experimentally the benefits of the method and demonstrate robustness to fast rotational motion, such as what often occurs in human motion.