@article {12740,
	title = {Fast two-frame multiscale dense optical flow estimation using discrete wavelet filters},
	journal = {Journal of the Optical Society of America AJ. Opt. Soc. Am. A},
	volume = {20},
	year = {2003},
	month = {2003///},
	pages = {1505 - 1515},
	abstract = {A multiscale algorithm with complexity O(N) (where N is the number of pixels in one image) using wavelet filters is proposed to estimate dense optical flow from two frames. Hierarchical image representation by wavelet decomposition is integrated with differential techniques in a new multiscale framework. It is shown that if a compactly supported wavelet basis with one vanishing moment is carefully selected, hierarchical image, first-order derivative, and corner representations can be obtained from the wavelet decomposition. On the basis of this result, three of the four components of the wavelet decomposition are employed to estimate dense optical flow with use of only two frames. This overcomes the {\textquotedblleft}flattening-out{\textquotedblright} problem in traditional pyramid methods, which produce large errors when low-texture regions become flat at coarse levels as a result of blurring. A two-dimensional affine motion model is used to formulate the optical flow problem as a linear system, with all resolutions simultaneously (i.e., coarse-and-fine) rather than the traditional coarse-to-fine approach, which unavoidably propagates errors from the coarse level. This not only helps to improve the accuracy but also makes the hardware implementation of our algorithm simple. Experiments on different types of image sequences, together with quantitative and qualitative comparisons with several other optical flow methods, are given to demonstrate the effectiveness and the robustness of our algorithm.},
	keywords = {digital image processing, Image analysis, optical flow},
	doi = {10.1364/JOSAA.20.001505},
	url = {http://josaa.osa.org/abstract.cfm?URI=josaa-20-8-1505},
	author = {Liu,Haiying and Chellapa, Rama and Rosenfeld,Azriel}
}
