image registration algorithms based on gradient methods provide quantitative motion measurements from sequences of video images. Although such measurements can be degraded by image noise, larger degradations typically result from systematic bias in the algorithms that is present even if the images are noise-free. To improve the accuracy of motion measurements, we develop a new class of multi-image algorithms based on multidimensional digital filters. The new algorithms provide better estimates of spatial and temporal gradients and also compensate for motion blur caused by the nonzero acquisition time of the imager. We optimize filters to measure arbitrary motions, and we illustrate the results when those filters are used to estimate constant velocity movements. We also show results for filters that are optimized for harmonic analysis of periodic motions. Using these algorithms, systematic bias in the amplitude of sinusoidal motion is less than 0.001 pixels for motions smaller than 1 pixel in amplitude. This represents a hundredfold decrease in bias compared to existing methods.