Image Processing Reference
In-Depth Information
12.11 Further Reading
Roughly, the types of motion estimation can be categorized by whether they use
sparse
local image data, called feature points, or
all
local image data. Those using
sparse data rely heavily upon existence of discriminatory local images that can be
identified from local information and their relative positions to other feature points.
Typically, in computer vision and cartography, various correlates of lack of linear
symmetry are utilized to identify these points [28, 74, 97]. An alternative approach
is to try to identify the presence of a specific symmetry of the local image, e.g., see
Sect. 11.11, which, in addition to detection, delivers the geometric orientation of the
pattern the target of tracking. By its nature, this approach is two-dimensional [198].
Combined with snakes and energy minimization techniques, it can cope with tracking
deformable objects as well as deformable boundaries, e.g. [148]. The problem of
correspondence, i.e., which sparse point corresponds to which between two frames,
if at all present in both, is, however, still a nontrivial issue along with the occlusion
of points by moving objects.
In this presentation, we have mainly dwelled on dense motion estimation tech-
niques, known as optical flow fields. Such motion estimations are used in numerous
applications. Probably one of the most widely used application is in image com-
pression, where the displacements fields serve to reduce the redundancy by qualified
guesses as to where an image patch will likely go to in the next frame. This is called
prediction which of course is never perfect but it is sufficient if the guess is roughly
correct, because then the error will have less variations than the original sequence
due to almost correct guesseses. Coding a function that has lower variations results
in compression of the data necessary to represent the image sequence [120].
A basic assumption in the dense translational motion field estimation is that a 2D
image undergoes motion with its pattern basically intact, i.e., the gray levels and their
geometic distributions are conserved, leading to the BCC equation. This is, however,
not enough to solve for the velocity and must be regularized [15]. We have presented
two effective regularizations, tensor averaging in 3D and differential averaging in 2D.
However, other approaches to regularization exist, e.g., those, using the membrane
differential equation, [110], adding gradient propagation, [167], combining BCC and
local feature invariance, [200]. An alternative approach to the partial derivative-based
techniques is to estimate the translational motion in the local spectral domain. As has
been discussed, the motion of points and lines are concentrated to a plane and a line
in the spectrum. The 3D local spectrum can, however, be sampled by means of a
Gabor decomposition, which reveals whether or not there is a certain concentration
of the spectral energy, and hence the motion information. The study in [101] has
proposed an algorithm for detecting optical flow using the magnitude of 3D Gabor
filters on the basis of the extracted spectral energy via a set of Gabor filters. A plane
is fit to the power spectrum by a full search of the tilt parameters. Using an analogue
of the tensor approach discussed in Sect. 10.13, but in 3D, [138] does a similar fit
to the power spectrum. The advantage is a full search is avoided. The report of [73]
solves the same tilt estimation problem by using the Gabor filter phase, where phase-
