The estimator developed in the last section can compute motion
parameters even in the presence of large motions provided
the initialising displacement field 
aligns the 
and 
frame to within the
width of the smoothed 
operator. This initial motion
field could be recovered from block matching or corner
matching. Block matching allows large motion estimates to be
recovered but is error-prone when motion deviates from the basic
assumption of 2D translation. In addition, the complexity of the
method is proportional to the square of the magnitude of the
largest visual motion. Corner matching [8] gives
good initial motion estimates from correspondences between
corners (features exhibiting high curvature and contrast) in
two consecutive images, thus providing motion vectors for the
corners that can be interpolated over the rest of the image.
The tolerance to large scale motions is demonstrated using the
image pair shown in figure 2. For this 
test pair, the foreground motion of the actress is
approximately 10 pixels/frame, while the
background motion is approximately 2 pixels/frame. The motion
model is applied to 
neighbourhoods. The spatial
derivatives are computed after a pre-smoothing using a Gaussian
filter with standard deviation 0.5 pixels. The motion model
employed is a simple affine formulation with no temporal
components. Thus the displacement field may be defined as
To illustrate the quality of the results produced by any estimator, the resultant displacement fields are used to predict the current image from the previous. Figure 3(a) presents the image predicted using the displacements produced by a standard three-layer implementation of a multi-resolution algorithm[1]. While the bulk of the lower motion background is predicted very well with median greylevel difference of 3.2 greylevels, the higher speed foreground figure is poorly estimated.
Our estimator given by equation 9 must be supplied with an initial displacement field. This is generated by a simple block matching scheme applied to subsampled versions of the previous and current frames for speed. The quality of the generated displacement fields may be inspected by comparing the predicted frame of figure 3(b) with the current image in figure 2(a). Although the block structure of the method is clearly evident in the result, the displacement fields align the previous and current images to a reasonable accuracy. The median greylevel difference produced using the initial displacement field generated by the block matcher is shown in figure 3(c).
The plot in figure 3(c) shows the convergence of the proposed estimator. With each successive iteration the error reduces initially very quickly with small subsequent improvement. In fact given reasonably accurate initial displacement fields, convergence is quickly achieved in usually 2-3 iterations. The accuracy of the resultant displacement field is shown by comparing the predicted image of 3(d) with the current image in figure 2(a).
