We have developed direct methods for recovering the motion of an observer in a static environment in th e case of pure rotation, pure translation, and arbitrary motion when the rotation is known. Some of these methods are based on the minimization of the difference between the observed time derivative of brightness and that predicted from the spatial brightness gradient, given the estimated motion. We minimize the square of the integral of this difference taken over the image region of interest. Other methods presented here exploit the fact that surfaces have to be in front of the observer in order to be seen. We do not establish point correspondences, nor do we estimate the optical flow. We use only first-orde r derivatives of the image brightness, and we do not assume an analytic form for the surface. We show tha t the field of view should be large to accurately recover the components of motion in the direction towar d the image region. We also demonstrate the importance of points where the time derivative of brightness is small and discuss difficulties resulting from very large depth ranges. We emphasize the need for adequat e filtering of the image data before sampling to avoid aliasing, in both the spatial and tempora l dimensions. 1 .3 Comments on Sampling. Filtering. and Aliasing Work with real image data has demonstrated th e need to take care in filtering and sampling. Th e estimates of spatial gradient and time derivative s are sensitive to aliasing effects resulting from inadequate low-pass filtering before sampling. This 'We do not discuss here related methods using optical flow , such as those of Bross and Horn (l] .

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Wave forced impacts of the head with the ocean bottom typically occurred at moderate to severe shorebreaks, and involved inexperienced, large-build males in their 40s. Spinal stenosis and degenerative spondylosis may increase the risk of cervical spine injury associated with WFI due to the increased risk of neck hyperextension and hyperflexion impacts inherent to this activity.