Fractional-order variational optical flow model for motion estimation

Abstract

A new class of fractional-order variational optical flow models, which generalizes the differential of optical flow from integer order to fractional order, is proposed for motion estimation in this paper. The corresponding Euler-Lagrange equations are derived by solving a typical fractional variational problem, and the numerical implementation based on the Grünwald-Letnikov fractional derivative definition is proposed to solve these complicated fractional partial differential equations. Theoretical analysis reveals that the proposed fractional-order variational optical flow model is the generalization of the typical Horn and Schunck (first-order) variational optical flow model and the second-order variational optical flow model, which provides a new idea for us to study the optical flow model and has an important theoretical implication in optical flow model research. The experiments demonstrate the validity of the generalization of differential order.

An Improved Fractional-Order Optical Flow Model for Motion Estimation

“…For convenient description, we call the HS optical flow model the HS model, the model in [12] the FOVOF model, and our proposed model the DFOVOF model. The mask window size is .…”

“…Combined with (2.19) and (2.20) in [12], we can get the fractional-order optical flow model in this paper:…”

“…In [12,13], the fractionalorder smoothing constraint equation was used in the HS optical flow model to preserve the discontinuity of motion estimation, but it does not consider the correlation of the pixel intensity. Although the edge discontinuity of the image can be preserved to a certain extent, the accuracy of the optical flow field estimation is not high.…”

“…Because of its ability to preserve the texture details of the smooth region while highlighting the image edge feature and its spatiotemporal memory of the target point neighborhood, a fractional differential is applied to many image processing fields [9], such as image denoising [10], image enhancement [11], and motion estimation [12][13][14][15][16]. In [12,13], the fractionalorder smoothing constraint equation was used in the HS optical flow model to preserve the discontinuity of motion estimation, but it does not consider the correlation of the pixel intensity.…”

Fractional calculus and its applications

“…The rest of the papers can be roughly grouped into three parts: three papers for fundamental theories of fractional calculus [7][8][9], five papers for fractional modelling with applications [10][11][12][13][14] and four papers for numerical approaches [15][16][17][18].…”