Page 127 - Video Coding for Mobile Communications Efficiency, Complexity, and Resilience

104 Chapter 4. Basic Motion Estimation Techniques

noise. In particular, the use of the 2-D DFT instead of the 2-D FT results in
the following e ects [10]:

• The boundary e ect: In order to obtain a perfect impulse, the transla-
tional displacement must be cyclic. In other words, objects disappearing
at one end of the moving area must reappear at the other end. In practice
this does not happen, which leads to the degeneration of the impulse
into peaks. Furthermore, the DFT assumes periodicity in both directions.
In practice, however, discontinuities occur from left to right and from
top to bottom, introducing spurious peaks.
• Spectral leakage: In order to obtain a perfect impulse, the translational
displacement must correspond to an integer multiple of the fundamental
frequency. In practice, noninteger motion vectors may not satisfy this
condition, leading to the well-known spectral leakage phenomenon [89],
which degenerates the impulse into peaks.
• Displacement wrapping: The 2-D DFT is periodic with the area size
(N x ;N y ). Negative estimates will be wrapped and will appear as positive
displacements. To accommodate negative displacements, the estimated
displacement needs to be unwrapped as follows [10]:
 ˆ ˆ

 d i if |d i |≤ N i and N i is even
2

ˆ
ˆ
d i = or if |d i |≤ N i −1 and N i is odd; (4.27)
 2


ˆ
d i − N i ; otherwise:
This means that the range of estimates is limited to [ −N i +1; ] for N i
N i
2
2
even.
The phase correlation motion estimation method was rst reported by Kuglin
and Hines in 1975 [90]. It was later extensively studied by Thomas [91]. In
his study, Thomas analyzed the properties of the phase correlation function.
He suggested using a weighting function to smooth the correlation surface and
suppress spurious peaks. He also proposed a second stage to the method, in
which smaller moving areas are used and more than one dominant peak from
the rst stage are considered and compared. Girod [92] augmented this by a
third stage, in which the estimated integer-pel motion displacement is re ned
to subpel accuracy.
The phase correlation method has a number of desirable properties. It has a
small computational complexity, especially with the use of fast Fourier trans-
forms (FFTs). In addition, it is relatively insensitive to illumination changes
because shifts in the mean value or multiplication by a constant do not a ect
the Fourier phase. Furthermore, the method can detect multiple moving objects,