Hierarchical Properties of Multi-resolution Optical Flow Computation

Most of the methods to compute optical flows are variational-technique-based methods, which assume that image functions have spatiotemporal continuities and appearance motions are small. In the viewpoint of the discrete errors of spatial-and time-differentials, the appropriate resolution for optical flow depends on both the resolution and the frame rate of images since there is a problem with the accuracy of the discrete approximations of derivatives. Therefore, for low frame-rate images, the appropriate resolution for optical flow should be lower than the resolution of the images. However, many traditional methods estimate optical flow with the same resolution as the images. Therefore, if the resolution of images is too high, down-sampling the images is effective for the variational-technique-based methods. In this paper, we analyze the appropriate resolutions for optical flows estimated by variational optical-flow computations from the viewpoint of the error analysis of optical flows. To analyze the appropriate resolutions, we use hierarchical structures constructed from the multi-resolutions of images. Numerical results show that decreasing image resolutions is effective for computing optical flows by variational optical-flow computations in low frame-rate sequences.