Image registration algorithms based on piecewise linear interpolators (spatiotemporal gradients or block matching) are analyzed to determine subpixel registration accuracy. Results reveal not only random errors due to image noise but also systematic bias present even if the images are noise free. If the displacement between the images is small, bias is small. However, if the displacement between the images is larger than about 1/25 pixel, the bias component of the registration error exceeds the random component for most imaging conditions. Bias also depends on image content: it is generally larger for images with higher spatial frequency content than for images with lower spatial frequency content. We have developed a reduced-bias registration algorithm that takes advantage of the nearly linear relation between image displacement and bias that results for small displacements. The new algorithm is direct (noniterative), increases computational costs by approximately a factor of 4, and reduces the bias by approximately a factor of 4. This improvement is large compared to improvement obtained with averaging. For our applications, in which imaging noise is typically 50 dB smaller than the signal, registration errors using the new algorithm are smaller than 1/50 pixel.