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Optical flow or translational flow can be used to describe the change from one image to another. This concept was also presented in class. The second assignment was one on the Robust Estimation of Image Features (well, it isn't a surprise that this also pops up). In it we attempt to estimate image motion with lines of constraint. However, it turns out that the least squares fitting we learned in class is identical to linear regression. In one, we fit lines to a point and in the other we fit points to a line. The following examples are dicussed in terms of .
Optical flow is initially discussed in terms of ``Affine Fit'' and ``Affine Flow''. It seems that the main difference between affine fit and affine flow is that 1) results in a problem that models the optical flow at every point and then trying to fit this with an affine model and 2) models the optical flow in terms of the affine motion model itself. It seems that although these technicques are different depending on the choice of weights then can be made to give the same results.
The idea is extended to ``Projective Fit'' and ``Projective Flow''. The equation for the projective model is describing a hyperbola. So the linear regression becomes hyperbolic regression. The solution to this in both and is presented in [1].
The rest of this paper will focus on a few lines from [1]:
As is well known, the optical flow field in two dimensions is underconstrained. The model of pure translation at every point has two parameters, but there is only one to solve, thus it is common practice to computer the optical flow over some neighbourhood, which must be at least two pixels, but is generally taken over a small block, 3x3, 5x5, or sometimes larger (e.g., the entire image, as in this paper).