3 Estimating Large Velocities

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

 

   
Figure 2: Cathy Sequence

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).

   
Figure 3: Recovering Large Motions