Equivalence of subpixel motion estimators based on optical flow and block matching

We compare two classes of algorithms for estimating subpixel, rigid-body translation between two images. One class is based on optical flow. Optical flow algorithms determine translations between images from estimates of spatial and temporal derivatives of brightness. The other class is based on block matching. Block matching algorithms determine translations between images by minimizing the difference between shifted (warped) versions of the original images. We show that these two classes of algorithms are equivalent for subpixel displacements. Specifically, we show that all block matching algorithms that use bilinear interpolation can be recast into equivalent optical flow formulations, and that all algorithms based on optical flow using first-order derivative estimators can be recast into equivalent block matching formulations