A phase-based approach to the estimation of the optical flow field using spatial filtering

Abstract

We introduce a new technique for estimating the optical flow field, starting from image sequences. As suggested by Fleet and Jepson (1990), we track contours of constant phase over time, since these are more robust to variations in lighting conditions and deviations from pure translation than contours of constant amplitude. Our phase-based approach proceeds in three stages. First, the image sequence is spatially filtered using a bank of quadrature pairs of Gabor filters, and the temporal phase gradient is computed, yielding estimates of the velocity component in directions orthogonal to the filter pairs' orientations. Second, a component velocity is rejected if the corresponding filter pair's phase information is not linear over a given time span. Third, the remaining component velocities at a single spatial location are combined and a recurrent neural network is used to derive the full velocity. We test our approach on several image sequences, both synthetic and realistic.

Local image structures and optic flow estimation

“…In this paper, we investigate these claims more closely for several optic flow algorithms [29,27,14]. We will show that the continuous formulation of intrinsic dimensionality allows for a better quantitative investigation and characterization of the quality of optic flow estimation (and hence the optic flow properties as stated in A0-A2) depending on the local signal structure.…”

Dynamic Magnetic Resonance Imaging

“…In this thesis, we will use a different method based on a phased-based algorithm by Gautama and Hulle [40]. Their results show low average error and very low standard deviation when the dynamic image includes a flowing structure, which we prefer because of the cardiovascular system.…”

“…Gautama and Hulle use 11 quadrature Gabor filters with bandwidths of β = 0.6 octaves shown in Figure 2.13 [40]. Each component velocity constrains the two-dimensional velocity v to lie on a constraint line L j orthogonal to the component velocity which is defined as…”

“…We also use a three-frame window to calculate the velocity vectors. Due to the rapid movement of the heart more time frames create nonlinearity errors as explained by Gautama and Hulle [40]. After calculating each velocity vector v n,i , we create the sparse motion matrix F i whose every element is zero except…”

“…Unless the number of measurement points is overwhelming or necessary to plot both low-resolution and high-resolution changes, identity matrix is not a good choice. Another approach is to use an optical flow algorithm [40] that calculates displacement of pixels between each time frame. The idea behind this approach is mathematically explained above.…”