Estimates displacement vector fields for two images. For example, given
two 2-D images f(x1,x2) and g(x1,x2), a shift finder estimates two vector
components of displacement u1(x1,x2) and u2(x1,x2) such that
f(x1,x2) ~ g(x1+u1(x1,x2),x2+u2(x1,x2)).
Like the images f and g, the components of displacement are sampled
functions of coordinates x1 and x2. That is, displacements may vary
from sample to sample. The components u1 and u2 represent displacements
in the x1 and x2 coordinate directions, respectively.
This shift finder estimates each component of displacement using local
cross-correlations. For each image sample, the estimated shift is that
which yields the maximum correlation coefficient. This coefficient is
found by quadratic interpolation of correlation functions sampled at
integer lags.
The peak (maximum) correlation coefficient may be used to measure
quality of an estimated shift. However, because a correlation function
may have more than one peak (local maxima), a better measure of quality
may be the difference between the coefficients for the correlation peak
and next highest peak. Both the peak coefficient and this difference may
be computed with the shifts.
Methods are provided to find and compensate for each component of shift
sequentially. As each component is found, that component can be removed
from the image g before estimating another component. For example, again
for 2-D images f(x1,x2) and g(x1,x2), we might first estimate u1(x1,x2).
If we then compute an image h(x1,x2) = g(x1+u1(x1,x2),x2), we can use
f(x1,x2) and h(x1,x2) to estimate u2(x1,x2). By repeating this process
sequentially, we obtain estimates for both u1(x1,x2) and u2(x1,x2) such
that f(x1,x2) ~ g(x1+u1(x1,x2),x2+u2(x1,x2)).
Methods are also provided to whiten 2-D and 3-D images before estimating
displacement vectors. This (spectral) whitening improves estimates of
displacements parallel to image features that may be otherwise poorly
resolved. Whitening is performed with local prediction error filters
computed from local auto-correlations.