@article{d19ff95598f74556821c3c24a845bec4,
title = "A Frequency Domain Performance Analysis of Horn and Schunck's Optical Flow Algorithm for Deformable Motion",
abstract = "A frequency domain performance analysis of Horn and Schanck's optical flow (HSOF) algorithm for estimation of deformable motion is presented. Noise sources in the algorithm are modeled using the discrete Fourier transform of the brightness pattern. This noise model along with the estimation error covariance function derived in previous work is used to derive an expression for the expected performance of the optical flow estimate that is valid for an arbitrary discrete brightness pattern. Simulation results are presented that demonstrate the validity of our methods and show that HSOF is more accurate that the optical flow estimate of Anandan for certain low-frequency patterns.",
author = "Denney, {Thomas S.} and Prince, {Jerry L.}",
note = "Funding Information: In the case of two-frame motion estimation in the presence of noise, differential methods such as Horn and Schunck{\textquoteleft}s optical flow algorithm (HSOF) [2] are thought to perform poorly relative to other methods because of the difficulty of approximating spatial and temporal derivatives of a discrete image sequence [3J. Region-matching techniques such as Anandan{\textquoteright}s optical flow algorithm (AOF) [4] are generally considered to perform better in this case because no derivatives are required [3]. Recent research, however, has shown that for deformable motion with no occlusion, the performance of HSOF is highly dependent on the brightness pattern of the object undergoing motion [5], [6], and in applications such as MR tagging [l] where the brightness pattern of the object can be controlled, use of the optimal brightness pattern can result in accurate HSOF estimates of motion. Denney and Prince proposed a brightness pattern optimization procedure in [6] for a parametric class of patterns that was based on the estimation error covariance function Manuscript received November 4, 1993; revised December 5, 1994. This work was supported by Whitaker Foundation Biomedical Engineering Research Grant 91-0108 and National Science Foundation Presidential Faculty Fellow Award MIP-9350336. The associate editor coordinating the review of this paper and approving it for publication was Dr. Homer H. Chen.",
year = "1995",
month = sep,
doi = "10.1109/83.413178",
language = "English (US)",
volume = "4",
pages = "1324--1327",
journal = "IEEE Transactions on Image Processing",
issn = "1057-7149",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "9",
}