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Unformatted text preview: IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 2. NO. 3, SEPTEMBER 1992 285 MotionCompensated Wavelet Transform
Coding for Color Video Compression YaQin Zhang, Member, IEEE, and Sohail Zafar, Student Member, IEEE Abstract—A video compression scheme based on the wavelet
representation and multiresolution motion compensation
(MRMC) is presented in this paper. The multiresolution/
multifrequency nature of the discrete wavelet transform is an
ideal tool for representing images and video signals. Wavelet
transform decomposes a video frame into a set of subframes
with different resolutions corresponding to different frequency
bands. These multiresolution frames also provide a representa
tion of the global motion structure of the video signal at differ
ent scales. The motion activities for a particular subframe at
different resolutions are different but highly correlated since
they actually specify the same motion structure at different
scales. In the multiresolution motion compensation approach,
motion vectors in higher resolution are predicted by the motion
vectors in the lower resolution and are reﬁned at each step. In
this paper, we propose a variable blocksize MRMC scheme in
which the size of a block is adapted to its level in the wavelet
pyramid. This scheme not only considerably reduces the search
ing and matching time but also provides a meaningful charac—
terization of the intrinsic motion structure. The variable block
size MRMC approach also avoids the drawback of the
constantsize MRMC in describing small object motion activi
ties. After wavelet decomposition, each scaled subframe tends to
have different statistical properties. An adaptive truncation pro
cess was implemented and a bit allocation scheme similar to
that in the transform coding is examined by adapting to the
local variance distribution in each scaled subframe. Based on
the wavelet representation, variable blocksize MRMC approach
and a uniform quantization scheme, four variations of the
proposed motioncompensated wavelet video compression sys
tem are identiﬁed. It is shown that the motioncompensated
wavelet transform coding approach has a superior performance
in terms of the peaktopeak signaltonoise ratio as well as the
subjective quality. I. INTRODUCTION E discrete wavelet transform (DWT) has recently
received considerable attention in the context of im age processing due to its ﬂexibility in representing nonsta
tionary image signals and its ability in adapting to human
visual characteristics. Its relationships to the Gabor trans
form, windowed Fourier transform and other intermediate
spatial—frequency representations have been studied
[1]—[5]. The wavelet representation provides a multireso— Manuscript received September 5, 1991; revised February 13, 1992.
This paper was presented in part at the SPIE Visual Communications
and Image Processing Conference [21], Nov. 10—15, 1991, Boston, MA.
Paper was recommended by Associate Editor Yrjo Neuvo. Y.—Q. Zhang is with GTE Laboratories, Inc., Waltham, MA 02254.
Author to whom correspondence should be addressed. S. Zafar is with the Dept. of Electrical Engineering, University of
Maryland, College Park, MD 20742. IEEE Log Number 9201709. 10518215/9230390 lution/multifrequency expression of a signal with localiza
tion in both time and frequency. This property is very
desirable in image and Video coding applications. First,
realworld image and video signals are nonstationary in
nature. A wavelet transform decomposes a nonstationary
signal into a set of multiscaled wavelets where each com—
ponent becomes relatively more stationary and hence
easier to code. Also, coding schemes and parameters can
be adapted to the statistical properties of each wavelet,
and hence coding each stationary component is more
efﬁcient than coding the whole nonstationary signal. In
addition, the wavelet representation matches to the spa
tially tuned frequencymodulated properties experienced
in early human vision as indicated by the research results
in psychophysics and physiology [6]. The discrete wavelet theory is found to be closely
related to the framework of multiresolution analysis and
subband decomposition, which have been successfully used
in image processing for a decade [7][10]. In the multires
olution analysis, an image is represented as a limit of
successive approximations, each of which is a smoothed
version of the image at the given resolution. All the
smoothed versions of the image at different resolutions
form a pyramid structure. An example is so called the
Gaussian pyramid in which the Gaussian function is used
as the smoothing ﬁlter at each step. However, there exists
some redundancies among different levels of the pyramid.
A Laplacian pyramid is formed to reduce the redundancy
by taking the difference between successive layers of the
Gaussian pyramid [7]. The Laplacian pyramid representa
tion results in a considerable compression although the
image size actually expands after the decomposition. In
subband coding, the frequency band of an image signal is
decomposed into a number of subbands by a bank of
bandpass ﬁlters. Each subband is then translated to base
band by downsampling and is encoded separately. For
reconstruction, the subband signals are decoded and up
sampled back to the original frequency band by interpola
tion. The signals are then summed up to give a close
replica of the original signal. The subband coding ap
proach provides a signalto—noise ratio comparable to the
transform coding approach and yields a superior subjec
tive perception due to the lack of the “blocking effect” [9]. The multiresolution representation and the subband
approach are recently integrated into the framework of
the wavelet theory [2], [3]. The wavelet theory provides a
systematic way to construct a set of ﬁlter banks with a © 1992 IEEE 286 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 2, NO. 3, SEPTEMBER l992 regularity condition and compact support [1]. In the
wavelet representation, the overall number of image sam
ples is conserved after the decomposition due to the
orthogonality of wavelet basis at different scales (this is
referred to as a critically sampled system). Wavelet theory
has been applied to image coding in a similar way to the
subband coding approach. Schemes using different types
of wavelets and quantization schemes have been proposed
[2], [3], [11], [12]. There appears to be little efforts in the
application of wavelet theory to real—time video compres—
sion. In [13], the Laplacian pyramid, subband coding, and
wavelet decomposition were compared and used to de
compose a sequence of images, but no coding results were
reported. This paper applies the wavelet theory to com
press fullmotion color video signals using a variable
blocksize multircsolution motion—compensated predic
tion. Video signals are nonstationary in nature. In video
coding, some type of interframe prediction is often used
to remove the interframe redundancy. Motioncom
pensated prediction has been used as an efﬁcient scheme
for temporal prediction. After motion compensation, the
residual video signal still tends to be highly nonstationary.
In the transform coding approach, such as in the CCITT
H.261 recommendations and the MPEG proposal [14],
[15], the residual video signals are divided into many small
rectangular blocks. The reason is that with a small block
size, it becomes feasible and advantageous to be imple
mented in hardware. Also, coding parameters can be
adapted to each locally stationary block. A detailed and
excellent coverage of transformbased coding approach
for video signals can be found in [16]. The block transform coding approach suffers from the
“blocking effect” in low bit rate applications. The wavelet
decomposition provides an alternative approach in repre
senting the nonstationary video signals and the residual
signals after prediction. Compared to the transform cod—
ing, the wavelet representation is more ﬂexible and can be
easily adapted to the nature of human visual system. It is
also free from the blocking artifacts due to the nature of
its global decomposition. In Section II, the dyadic wavelet
theory is reviewed and its extension to twodimensional
cases is brieﬂy described. Video coding often involves
some kind of format conversions by subsampling and
interpolation. The generalized wavelet—based subsampling
and interpolation procedure is discussed in Section III.
Wavelet transform decomposes a video frame into a set of
subframes with different resolutions corresponding to
different frequency bands. These multircsolution frames
also provide a representation of motion structure at dif—
ferent scales. The motion activities for a particular sub
frame at different resolutions are hence highly correlated
since they actually specify the same motion structure at
different scales. In the multircsolution motion compensa—
tion scheme (MRMC) described in Section IV, motion
vectors at higher resolution are predicted by the motion
vectors at the lower resolution and are reﬁned at each
step. We propose a variable blocksize MRMC scheme in which the size of a block is adapted to its scale. This
scheme not only considerably reduces the searching and
matching time but also provides a meaningful characteri
zation of the intrinsic motion structure. The variablesize
MRMC approach also avoids the drawback of the con—
stant—size MRMC in describing small object motion activi
ties. The MRMC scheme described here can also be well
adapted to the motioncompensated interpolation. After
wavelet decomposition, each scaled subframe tends to
have different statistical properties. An adaptive trunca
tion process similar to [17] is implemented and a bit
allocation scheme similar to that being used in the trans
form coding is examined by adapting to the local variance
distribution in each scaled subframe. Based on the wavelet
representation, the variable—size MRMC approach, and a
uniform quantization scheme, four variations of the pro
posed motioncompensated wavelet video compression
system are identiﬁed in Section VI. Comparative results
for the four different results are presented in Section VII. II. WAVELET DECOMPOSITION AND RECONSTRUCTION In this section, a special class of the discrete orthonor—
mal wavelet transform with a resolution step of 2, i.e., the
discrete dyadic wavelet transform, is brieﬂy introduced for
image decomposition and reconstruction. Dyadic wavelets
are a set of functions generated from one singlebasis
wavelet w() by dilations and translations [2]: t
wmn(t) =2'('”/2)w(2—m —n) (m,n) EZ. For any square integrable function f(t) E L2(R), its
wavelet transform Wf(m, n) is deﬁned as Wf(mm) =<f(t).w...(z)> = firmwmmdz which gives an approximation of f(t) at the resolution (or
scale) 2'" at the location n. Conversely, any square inte
grable function f(t) E L2(R) can be represented in terms
of a set of wavelet basis that covers all the scales at every
location: f0) = Z Wf(m,")wanI In other words, any function can be decomposed into a set
of wavelets at various scales, and it can also be recon—
structed by the superposition of all the scaled wavelets.
The condition for perfect reconstruction is f: lW(2’"w)l2 = 1 m=—oc (1) which ensures that the wavelet transform provides a com
plete representation covering all frequency axis, where
W(w) is the Fourier transform of w(t). It has been shown that the wavelet basis can be con
structed from the multircsolution analysis procedure. In
the multiresolution analysis, a scaling function ¢(t) is
introduced. Let Um denote the vector space spanned by ZHANG AND ZAFAR: MOTIONCOMPENSATED WAVELET TRANSFORM CODING 287 ¢m‘ﬂ(t), which is generated by the dilation and translation
of the scaling function 42(1‘): ¢m.(r) = 2*<m/2>¢(2im —n]. Therefore, {Um}m E Z represents the successive approxima
tions at resolutions {2’"},,IE Z and Um constitutes a subset
of Um, 1 for m E Z. If the scaling function ¢(t) and the
basic wavelet function w(t) are chosen to satisfy the
following conditions ¢(t) = 26.14%” — n) and we) = Z(—1)"c...¢(2r + n) then, wmn(t) are the functions that span the orthogonal
compliment of Um_1 and Um. Hence, (f,wmn(t)> repre
sents the difference of information between the resolution
2”"1 and 2’", which is the “new” information conveyed
between the successive approximations. In practice, the input signal f(t) is measured at a ﬁnite
resolution. A ﬁnite dyadic wavelet transform of a given
function f(t) is introduced between the scales {2’"; m =
1,2,, M}. Imposing the condition that i lW(2”’w)l2 m=M+1 léz”(w)l2 = ensures that the condition in (1) holds true.
We denote the wavelet at scale 2”‘ by Wmf= {Wf(m,n); n EZ} or only W2". in case of no ambiguity.
Therefore, a ﬁnite wavelet transform of f(t) between
the scale 21 and 2’” can be represented as {52Mf= W21va WzMaf,,W21f} forOSmsM where SZMf:<f(t).¢2M(z)> = [powwow is the smoothed version of f(t) spanned by the scaling
function at the resolution 2“. Relating the wavelet to the multiresolution analysis
results in a fast computation algorithm that has long been
used in signal processing applications. The algorithm is
described as follows: m=0
while (m <M)
{ W2m+1f= Ssz*Gm
S2m+1f= Ssz*Hm
m =m + 1 } where S 1 f = f is the original signal. The ﬁlter pair H and G corresponds to the expansion
of the scaling function and the wavelet function, respec
tively. The coefﬁcients of an orthonormal wavelet trans
form satisfy the following conditions: ZhUI) = \5 ZgUl) = 0 801) = (—1)"h(1 — n) (2) The reconstruction basically reverses the decomposition
procedure: m =M
while (m > 0)
{ 82m‘1f= W2mf*G~m—l + S2mf*Hm—1
m = m +1 } where H and G are the conjugate ﬁlters of H and G,
respectively. Conditions in (2) are also the requirements for a class
of perfect reconstruction ﬁlters, that is, quadrature mirror
ﬁlters (QMF), which have been extensively used in sub
band image coding applications [8], [9]. Wavelet theory
provides a systematic way to the construction of QMF.
Wavelet theory also explicitly imposes a regularity condi—
tion in the QMF coefﬁcients [1]. The regularity condition
corresponds to the degree of differentiability of the
wavelet functions, which is determined by the number of
zeros of the wavelet ﬁlters at w = 77. In practical applica
tions, it is desirable to have a continuous and smooth
wavelet representation, which is guaranteed by regularity
conditions. In this paper, we use a set of orthonormal bases with
compactly supported wavelets developed in [1]. Compact
support implies a ﬁnite length for ﬁlters H and C. There
is a compromise between the degree of compactness and
the degree of regularity. The wavelet function becomes
more regular as the number of taps in H increases, which
results in more computations. The Daubechies6 coefﬁ
cient set is used in this work since it shows an adequate
energy concentration in the lowfrequency subimage. The extension of the 1D wavelet transform to 2D is
straightforward. A separable wavelet transform is the one
whose 2D scaling function CID(t1,t2) can be expressed as (DUNE) : q)(t1)¢(tz) It can be easily shown that the wavelet at a given resolu—
tion 2’" can be completely represented by three separable
orthogonal wavelet basis functions in L2(R X R): W21m(t17t2) = ¢2m(t1)W2m(12)
W22m(t17t2): w2’”(tl)¢2”'(t2)
W23m(ti,12) = W2m(t1)wzm(t2) Therefore, a 2D dyadic wavelet transform of image f(x, y)
between the scale 21 and 2M can be represented as a 288 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 2, N0. 3, SEPTEMBER 1992 sequence of subimages: (ssz,[WfM f]/=1,2.3""9lW7{‘ flj=1.2.3} The 2D separable wavelet decomposition can be imple
mented ﬁrst in columns and then in rows independently.
The decomposed image data structure and the corre
sponding frequency bands are depicted in Figs. 1 and 2,
respectively. In Fig. 1, the decomposed image forms a
pyramid structure up to three layers with three subimages
in each layer. The resolution decreases by a factor of 4 (2
in the horizontal direction and 2 in the vertical direction)
with each layer increased. Separable transform is easy to implement but is limited
in orientations. Some nonseparable extensions can also be
used such as the Quincunx pyramid where the scaling
function has the form of q)(t1’t2) = ¢(L(t1,t2))
where L(tl, t2) = (t1 + t2, t1 — t2) is a linear transform. III. FORMAT CONVERSION BY GENERALIZED
SUBSAMPLING AND INTERPOLATION Wavelet representation can also be used as a tool for
subsampling and interpolation. As illustrated in Fig. 1, an
image can be represented in terms of a pyramid structure
after wavelet decomposition. The sequence {52m f }m : up M,
represents approximations of a given image at different
resolutions. S2." f gives the optimum representation at
resolution 2’“ in the sense that it gives the best human
visual perception [3]. Video applications often involve
some form of format conversion through subsampling and
interpolation. For example, in the CCITT H.261 standard,
all incoming video signals are converted to a common
intermediate format (CIF) or a quarter of CIF (QCIF)
format depending on the available channel rate. In cer
tain MPEG speciﬁcation, the CCIR 601 resolution has to
be subsampled to meet the target rate of 1.5 Mb / 5. There
are many subsampling and interpolation schemes. The
easiest method is the uniform subsampling in which every
other samples (say for 2: 1 sampling) are discarded. Some
nonuniform subsampling techniques were also developed
to discard samples in terms of its local activity. In the
receiver, different linear or nonlinear interpolation
schemes are engaged to retrieve the video signals. The
drawback of this type of sample discarding is the “aliasing
effect,” caused by the inadequacy of the sampling rate.
Some ﬁltering techniques developed in image coding and
enhancement can also be used as generalized subsampling
and interpolation tools. Examples include Burt’s pyra
mids, Watson’s cortex transform, and QMF’s used in
subband coding [7], [8], [18]. In these schemes, ﬁltering
and decimating process is recursively implemented to
obtain the desired representation at a given resolution.
The process ﬁlters out the higher frequency components
and conﬁnes the frequency distribution to a lower band.
Therefore, it is free from the “aliasing effect” since the
subsampling rate in the lower frequency subimages satis ﬁes the Nyquist rate provided that the original sampling
rate does. The wavelet representation essentially uses the
same approach, but the coefﬁcients of wavelet ﬁlters are
chosen to satisfy certain constraints. An example of the
generalized subsampling and interpolation process is de
picted in Fig. 3. IV. MULTIRESOLUTION MOTION
ESTIMATION / COMPENSATION As Figs. 1 and 2 illustrate, a video frame is decomposed
into multiple layers with different resolutions and differ
ent frequency bands. Motion activities at different layers
of the pyramid are different but highly correlated since
they actually characterize the same motion structure at
different scales and different frequency ranges. In a mul
tiresolution motion estimation (MRME) scheme, the mo
tion ﬁeld is ﬁrst calculated for the lowest resolution
subimage, which sits on the top of the pyramid [19]. Then,
motion vectors at lower layers of the pyramid are reﬁned
using the motion information obtained at higher layers.
This scheme can be considered to be a multiresolution
version of the predictive motion estimation scheme pro
posed in [20]. The motivation for using the MRME ap
proach is the inherent structure of the wavelet represen
tation. MRME schemes signiﬁcantly reduce the searching
and matching time and provide a smooth motion vector
ﬁeld. A video frame is decomposed up to three levels in our
work. A total of 10 subimages are obtained with 3 subim
ages at ﬁrst two levels, and 4 on the top including the
subimage $8 with the lowest frequency band. It is well
known that human vision is more perceptible to errors in
lower frequencies than those incurred in higher bands and
tends to be selective in spatial orientation and positioning,
e.g., errors in smooth areas are more disturbing to a
viewer than those near edges. The subimage S8 also
contains a large percent of the total energy though it is
only 1 /64th of the original video frame size. In addition,
errors in higher layer subimages will be propagated and
expanded to all subsequent lower layer subimages. In this
section, a variable blocksize MRME scheme is proposed
to take all these factors into considerations. The basic multiresolution motion estimation scheme
proposed in this paper is similar to the one used in [19].
The main difference is that the size of blocks varies with
resolutions in our scheme, where the size of the motion
blocks is kept constant for all resolutions in [19]. We use a
block size of p  2"“ for the mthlevel subimage, i.e., the
lower is the resolution (corresponding to higher level in
the pyramid), the smaller is the motion block size. The
constant p is the size of the block used at the lowest
resolution (e.g., p equals one for pel recursive case and
equals two for a blocksize of 2 X 2 for the highest layer
subimages). With this structure, the number of motion
blocks for all subimages is constant because a block at
one resolution corresponds to the same position and the
same object at another resolution. In other words, all
scaled subimages have the same number of motion blocks ZHANG AND ZAFAR: MOTIONCOMPENSATED WAVELET TRANSFORM CODING A 289 I ___..__ I Layer30—————
I \ 1 2 3\,
“W‘20‘ \ Fig. 1 . Fig. 2. Frequency band distribution of wavelet decompositions. that characterize the global motion structure in different
grids and frequency ranges. The variable block—size ap
proach appropriately weights the importance of different
layers and matches the human visual perception to dif—
ferent frequency at different resolutions. It can detect
motions for small objects at the highest level of the
pyramid. The constantblock MRME approach ignores
the motion activities (even high motion) for small objects
at the higher levels of the pyramid. The variable blocksize
MRMC approach also requires fewer computations since
no interpolation is needed as the grid reﬁnes. In the
variable blocksize MRME, an accurate characterization
of motion information at the highest layer subimage pro
duces very low energy in the displaced residual subimagcs
and results in a “cleaner” propagation process for the
motion estimation in lower layer subimages. In a con
stantblock MRME, “clean” copies of lower layer subim
ages are obtained by interpolation and reﬁnements. Let the value of the video frame i at location (x1, y1) be
denoted by I,(x1, yl). The basic principle of motion com
pensation is to ﬁnd the motion vector I/l(x, y) that recon
struct Ii(x1,y1) from Ii_1(x1 +x,yl +y) with minimum
error. In other words, we try to ﬁnd the “best match” for
1,.(x1, yl) in the previous frame (i — 1), which is displaced The pyramid structure of wavelet decomposition and reconstruction. from the original location of (xhyl) by V,(x,y). The
range of x and y is called the search area and is denoted
by S). In a blockbased matching scheme, the idea is to
divide the image in small blocks of size X X Y (2 X 2 for
components at the highest level M in our case), and then
for each block in the current frame i to ﬁnd a block in the
previous frame (1' — 1) within a deﬁned search area (1 to
minimize the prespeciﬁed distortion function. The process
of the blockmatching motion estimation is shown in
Fig. 4. An example of the proposed variable blocksize MRME
scheme is illustrated in Fig. 5. First, the motion vectors for
the highest layer subimage 58 are estimated by full search
with a block size of 2 X 2. A pelrecursive scheme with
large number of iterations can also be employed. These
motion vectors are then sealed appropriately to be used as
initial estimates for motion estimation in higher resolu—
tion subimagcs. Using ZM‘m times the motion vectors for
level M as a bias, the motion vectors for level m are
reﬁned by using full search but with a relatively small
search area 0. There are several possible variations since the motion
activities for subimages Wj’ {for i = 1,2,3 and j 2 2,4, 8}
represent frequencysegmented motion structure of the
global motion activity, motion vectors at different layers
are hence highly correlated. An example of exploiting the
motion redundancy is illustrated in Fig. 6, where the
estimation path is indicated by three directions (horizon—
tal, vertical, and diagonal) corresponding to the direc
tional characteristics of the three 2D wavelet ﬁlters. Let
Kay/(x, y) represent the motion vectors centered at (x, y)
for the subimagc WJ' {for i = 1,2,3 and j = 2, 4, 8}. Then
this estimation scheme is given by Vi.,‘(xa)’) = 21/121064) + A(6x’ 5”) [or i = 1,2,3 and j = 2,4. This conﬁguration produces very low energies in all the
displaced residual subimagcs but with a comparatively
large overhead and more computations. Certainly, this
scheme can be simpliﬁed by using independent motion
vectors obtained for subimage S8 as initial bias and then
reﬁned for all lower layer subimagcs using the fullsearch
algorithm with a smaller search area. With this scheme,
the block is ﬁrst displaced by VLJ(x, y) in the previous
frame and the motion searching algorithm is then imple 290 IEEE TRANSACTIONS ON CIRCUITS ANT) SYSTEMS FOR VIDFO TECHNOLOGY, VOL. 2. N0. 3, SEPTEMBER 1992 2:1 Row
sampling 2:1 Column
sampling 2:1 Column
Interpo. Fig. 3. An example of generalized subsanlpling and interpolation. Fig. 4. Blockbased motion searching and matching scheme. mented to ﬁnd A(5x, 8y). This is equivalent to ﬁnding
A(5x,5y) 1 X/Z Y/z
= argMin — Z Z
5x,5y€0 p=,X/2q= y/Z ‘[i(x1+P7YI+ q) *Ii_1(x1+p+x+8x,yl +q+y+ 5y). The motion vectors at level m are given by YslanYm’==\%s(xi ) 2M’m + A(5x,sy)
f0r{i=1,2,3;j= 2,4,8} where V0’8(x, y)(M) is the motion vector for the subimage
$8 and A( 5x, 6y) is the incremental motion vector found
by a full search with reduced search area. This scheme
provides a meaningful characterization of the intrinsic
motion structure and gives very smooth motion vectors
from block to block. Motion overhead and computation can be reduced dra
matically if the motion vectors for each subimage are not
reﬁned. This scheme is illustrated in Fig. 5 by making all
A( 6x, 5y) identically equal to zero, i.e., 5x = By = 0. V. BIT ALLOCATION AND QUANTIZATION Quantization is an important part of a video compres
sion system. As a matter of fact, in most video coding
systems, quantization is the only process that introduces
distortion and hence achieves a data rate far less than the
entropy limit. An efﬁcient quantizer matches to the un—
derlying probability distribution of the coefﬁcients in the displaced residual subimages (DRS) at different scales
and different frequency bands. In this section, two schemes
are presented to quantize the DRS video signals. The ﬁrst
method uses a bit allocation scheme followed by an uni—
form quantizer, which is similar to that being used in
some existing transform coding and subband coding
schemes [9], [16]. The difference here, however, is to
multiply a proper weighting factor to each subimage ac
cording to its importance in the pyramid. The second
scheme is similar to the adaptive truncation process used
in the scene adaptive coder [17]. The bit allocation process can be divided into two parts.
Bits are ﬁrst assigned among each subimage, and then the
assigned number of bits will be distributed within each
individual subimage. Let {Rig m = 1,',M; k = 1,2,3}
be the number of bits associated with subimages {W,,’f;
m = 1,',M; k = 1,2, 3} and RM represent the number
of bits for subimage S M, then the total number of bits R
13 M 3
R=RM+Z ZR; 0) m:lk:l The assignment should be done to minimize the overall
distortion in the reconstructed image, which is repre—
sented as M 3
D = ZZMDM + z E 2MB];
m—l k: l
where {D,’,‘,; m = 1,,M; k = 1,2, 3} is the distortion
associated with subimages {W,,f; m = 1,', M; k = 1,2,3}
and DM represents the distortion introduced in the
subimage SM. Appropriate weighting factor 22’" is intro
duced in the above distortion criterion, which means that
errors incurred at the higher layer subimages are weighted
to have more impact on the overall distortion. The prob
lem is to minimize (4) subject to the bit constraint in (3).
The constrained problem can be converted to uncon—
strained problem by forming the following function: J=D+AR where A is the Lagrangian multiplier. The solution is
obtained by taking the derivative of J with respect to R M (4) ZHANG AND ZAFAR: MOTION—COMPENSATED WAVELET TRANSFORM CODING 291 . HE”.
IEJIII IELJ
IIIIII..
IIIIII III "
I ' “ Si distortionrate function given by [8] is
2—r(1+R,*,,) 0,:(R) = 77lflﬁ<nlm+ldxlm (6) where {fmk(x); m = 1;", M; k = 1,2, 3} is the PDF associ
ated with wavelets {WW/1‘; m = 1,~, M; k = 1,2,3}. For
simpliﬁcation we let r+ 1
Fig. 6. Variable blocksize MRME‘using independent motion estima K _ k 1/ r+1
tion for (5,,ng {i = 1,2,3). am  flfm(x)] dx . Substituting these values in (5) we have '9 {xwam—A[R— Em,” =0. (7) and {R,’§,; m = 1,~,M; k = 1,2,3} and setting it to zero. M 3 M 3 6R + 1
J=22MDM+ )3 222m0,:+)t(RM+ 2 2R5). '" m r
m=1 k=1 m=1 k=1 Solving (7) obtains the value of Rm:
To simplify the notation we will assume that for any X R _ 1 l (r In 2) amZZMﬁr
M 3 m _ r ng A(r + 1)
_ k
§Xm _ XM + 21 [(21 Xm and Substituting this value of Rm in the constraint equation
"I _ (3), we get the value of A,
M 3
1‘le =XM l_l l—lep A = rln22~(r+l(7ReMX3M+5)])
m m=1 k=1 r + 1
Thus, the partial derivative can be written as and, ﬁnally, we get the optimal bit allocation for each
a wavelet:
ER—[D(R) — A{R ~ 21cm” = 0, (5) R _ R _ M(3M + 5) ﬂ
’" m m 3M + 1 r(3M + 1) r If a difference distortion measure with power r is used, 1 a m
D(x) =Ix — q(x)r r 21 + _ logl 1/(3M+1) ' (8)
where q(x) is the quantization of x. The asymptotic ] 292 The result is quite intuitive, as the bit allocation is nearly
uniform among all subimages. Since the size of higher
layer subimages is much smaller than that of lower layer
subimages, this means that more bits are assigned to the
higher layer subimages in terms of average bits per pixel.
This is consistent with the inherit structure of the wavelet
pyramid shown in Fig. 1. Bit allocation within each subim
age is the same as the conventional scheme used in
transform coding and will not be elaborated here [16]. The second quantization technique is based on the
adaptive truncation scheme [17]. This scheme only in
volves a ﬂoatingtointeger conversion process and is very
simple to implement. It was originally used for quantizing
discrete cosine transform coefﬁcients. We are using this
technique by adjusting the normalization factor to the
wavelet pyramid. The scheme consists of three steps. The
ﬁrst is to apply a threshold to all subimages {SM,W,,’f;
m = 1,~,M; k = 1,2,3} to reduce the number of coef
ﬁcients to be quantized, i.e., make all the coefﬁcients
below a deﬁned value zero. It should be pointed out that
the dynamic range of the values in different subimages of
the DRS varies and highly depends on the motion activi
ties and the accuracies of motion estimation scheme asso—
ciated with each subimagc. Therefore, the threshold could
be chosen in terms of dynamic range and the level in the
pyramid. In this paper, a ﬁxed threshold T is used for all
subimages for the sake of simplicity. The threshold is then subtracted from the remaining
nonzero coefﬁcients. k . . . k . .
Wﬂi’j) = WALD T if Wm(t,1) > T
0 1f W,,’;( i, j) s T
whereOsigX/Zm—l and Osng/2m71 and X
and Y are the video frame size.
The next step is to scale the coefﬁcients by a normaliz
ing factor Dm based on their levels in the pyramid. The
choice of BM is based on the same principle stated in Section IV. A larger value Dm corresponds to a coarser
quantization. In our work, Dm =DM2M’”' is chosen, where DM is the normalization factor for
{SM7W~117WA3’WA3}‘
TW"(i,j)
NTW" =—"‘ .
m(l DMzM—m After normalization, the values are rounded to the next
integer values by RNTW,,’f(i,j) = integer{NTW,,f(i,/) + 0.5} Then RNTan(i, j) is entropy coded and transmitted. At
the receiver, the decoded values are inversely normalized,
added to the threshold, and inversely transformed to
reconstruct the image. This simple adaptive truncation
process results in a variable bit rate but a nearly constant
quality. For constant bit rate output, Dm should be a
function of the degree of buffer fullness at the output of
the coder. Relating Dm to the variance distribution of
different subimages should also improve the performance. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 2, NO. 3, SEPTEMBER 1992 VI. DESCRIPTION OF THE VIDEO CODING SCHEMES The compression scheme we implemented in our work
is basically an interframe hybrid DPCM/DWT scheme.
Wavelet decomposition can be operated either on the
original video samples before the motion compensation or
on the residual video samples after motion compensation.
Fig. 7 depicts a typical video coding system where original
video source S is ﬁrst decomposed into subimages
{SM,W,,’,‘; m = 1,~,M; k = 1,2,3}. After using the vari
able blocksize MRMC, the DRS frames {R M, R5,; in =
1,, M; k = l, 2,3} are coded and transmitted. The ener—
gies of DRS may be further compacted by a mapping that
intends to localize the energy distribution within each
subimagc. The mapping can be any conventional trans
form or a predictive coder. Of course, a simple PCM
coder followed by an entropy coding is also expected to
perform well. These two variations are illustrated in Fig. 7
where dashed lines represent a DCT mapping being used.
Alternatively, wavelet decomposition can take place in the
residual video signal after a conventional motioncom
pensated prediction scheme, shown in Fig. 8. Therefore,
four variations of the proposed algorithm are identiﬁed in
terms of the domain of wavelet decomposition and the
choice of mapping strategies: 1) Wavelet decomposition a multiresolution motion
compensation “a multiscale quantization —> entropy
encoder 2) Wavelet decomposition —+ multiresolution motion
compensation —> DCT —> uniform quantization —>
entropy encoder 3) Motion compensation —> wavelet decomposition —>
multiscale quantization —> entropy encoder 4) Motion compensation > wavelet decomposition a
DCT —> uniform quantization —> entropy encoder In scheme 1), the original video frames are ﬁrst decom
posed into wavelets in different scales and resolutions,
Then DRS frames are formed using the variable blocksize
MRMC prediction scheme. The DRS frames are then
quantized using the adaptive truncation process (ATP)
with a multiscale normalization factor described in Sec
tion V. The coding chain of this scheme is expressed as
DWT/MRMC/ATP. Scheme 2) also decomposes the
original video frame using the wavelet transform; how
ever, the energy of the DRS frames is further compacted
using a conventional DCT and the DCT coefﬁcients are
quantized by an uniform quantizer. The coding chain of
this scheme is expressed as DWT/MRMC/DCF/UQ. In
schemes 3) and 4), the wavelet decomposition is per
formed on the residual video frame (the displaced frame
difference (DFD)) using a conventional motioncom
pensated prediction scheme. A multiscale quantizer is
used in scheme 3), whereas in scheme 4) DCT is used for
all DFD’s followed by a uniform quantizer. These strate—
gies can be expressed as MC/DWT/ATP and
MC /DWT/DCT /UQ, respectively. In all four cases, mo
tion vectors are DPCMcoded and all quantities are en
tropycoded prior to the transmission. ZHANG AND ZAFAR: MOTIONCOMPENSATED WAVELET TRANSFORM CODING 293 Entropy Coding Entropy Coding Fig. 8. Motion estimation (ME) and discrete wavelet transform (DWT). VII. TEST RESULTS The proposed video coding system is implemented in
the video compression testbed at GTE Laboratories,
Waltham, MA. The testbed includes a digital video
recorder that allows a realtime acquisition and playback
of 25 3 digital video in CCIR 601 format. The recorder is
interfaced to a host machine in which the compression
software resides. By using software simulation of the
compression and decompression algorithms, we can re—
construct video segments to compare with the original
signal via realtime playback. Therefore, compression per
formance, quality degradation, and computational efﬁ
ciency can be evaluated for different coding algorithms. The test sequence “CAR” we use in this paper is a
fullmotion interlaced color video sequence in CCIR 601
format with 720 X 480 per frame and 16 b /pixel. It is a
fast camerapanning sequence and ideal for testing vari
ous motion compensation schemes. Experimental results are also obtained for other sequences including the
“CHEERLEADERS” and “FOOTBALL” sequences used for the MPEG testing. All the results and parameters
follow the same pattern although actual numbers may
turn out to be different. Table I shows the energy distribution among different
subimages before and after the proposed variable block
size MRMC for a typical video frame in the “CAR”
sequence. Four variations of the MRME schemes de
scribed in Section V are compared. “S8 only” means that
only fullmotion searching in S8 is implemented and all
other subimages use the same or scaled motion vectors
obtained in S8 (A = 0 in Fig. 5). “SS, Wat only” means that
fullmotion searching in layer 3 of the wavelet pyramid is
conducted and directionally propagated to lower layer
subimages without reﬁnement (see Fig. 6). “S8 + reﬁne”
means that full searching is used for SS, and motion
vectors of all other wavelets are predicted based on the
motion information obtained for S8 (Fig. 5). Finally,
“$8,W8‘ + reﬁne” is an extension of the scheme illus
trated in Fig. 6 by using motion vectors of “SS, as
initial predictions. 294 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 2, NO. 3, SEPTEMBER 1992 TABLE I
ENERGY DISTRIBUTION AMONG DIFFERENT SUBIMAGES FOR A TYPICAL FRAME IN “CAR” SEQUENCE
Energy 58 W81 w; w,3 m1 W42 W,‘ W; W22 W23
Original signal 4958723 7361.20 452.91 148.47 1391.86 65.89 18.46 203.53 7.48 331
S8 only 336.00 848.63 155.74 193.20 428.40 53.07 37.12 110.65 5.26 1.28
SB,W8‘ only 336.00 195.58 44.32 28.34 414.99 44.54 21.62 97.47 4.31 0.55
S8 + reﬁne 336.00 186.16 44.56 29.01 138.83 13.58 4.65 39.96 1.02 0.05
S8, Ws‘ + reﬁne 336.00 195.58 44.32 28.34 139.71 15.14 7.37 38.61 0.78 0.19 The means of all the DRS’s are very small, ranging
from as low as 0.01 to a maximum of 3.75. However, the
variance depends on the motion activity and the accuracy
of the motion prediction algorithm. With high motion the
variances of all the subimages increase. The accuracy of
motion vectors contributes signiﬁcantly to the energy in
the displaced residual subimages. It can be seen from Table I that the decomposition
compacts most of the energy in S8 for the original video
signal. After the variable blocksize MRMC, energies or
variances in most subimages are considerably reduced.
The reduction in the highest layer subimages (especially
for SS) is rather signiﬁcant. This is due to the fact that a
very accurate motion estimation scheme is used for this
layer and the variations between successive frames are
well compensated. This layer is the most important layer
in terms of visual perception and is appropriately treated
in the proposed variable blocksize MRMC approach.
Also, it can be easily observed that the “S8 + reﬁne” and
the “$8, W + reﬁne” schemes produce less energies than
the other two schemes. The distribution of energies among
different subimages in both U and V components of the
color signal follows the similar pattern as that in the Y
component. The luminance signal contains more than
60% of the total energy of the original signal and U and
then V components have less than 20% of the total
energy, respectively. The normalizing factor for quantiza—
tion is, therefore, set to a lower level for the Y component
than that for the U and V components. The four different scenarios 1—4 of the proposed wavelet
video compression scheme described in Section VI are
implemented. A classiﬁed vector quantization scheme
(V0) is also used to quantize the variablesize MRMC
residual video frames (scenario (e) in Fig. 9). For schemes
(a) and (b), the “SS, W; + refine” MRMC scheme is used
to ﬁnd the motion vectors since it gives the best perfor
mance as shown in Table I. The conventional fullsearch
MC scheme using a block size of 8 X 8 is employed in
schemes (c) and (d). Fig. 9 illustrates the peaktopeak
signaltonoise ratio (SNR) for these ﬁve scenarios at an
average bit rate of 3 Mb / s. A normalizing factor (DM) of
8.0 for Y and 16.0 for U and V is used for schemes (a)
and (c). For schemes (b) and (d) the same quantization
tables as that being used in the JPEG speciﬁcation are
used to quantize the DCT coefﬁcients. Fig. 9 indicates that DWT working on the original video
domain incorporated with the proposed variable block—size
MRMC scheme has a better performance than DWT
operating on the DFD compensated by a conventional WT/MRMC/AQ (A) Peak SNR In dB WT/MRMC/DCT/Q
MCNVT/AQ
MC/WT/DCT/O
WT/MRMCNO a. \ 02468101214 Frame Number 16 18 2O 22 24 Fig. 9. Peaktopeak signaltonoise ratios for schemes (a) through (c)
at 3 Mb/s. (21) WT/MRMC/AQ. (b) WT/MRC/DCT/Q. (0)
MC /WT/AQ. (d) MC /WT /DCT/Q. (e) WT/MRMC/VQ. fullsearching scheme. We can also see that DCT mapping
after DWT does not compact energies as one might
expect for original video samples, instead it has an inverse
effect on the overall performance. Scheme (a) clearly
outperforms schemes (b), (c), and ((1). V0 gives further
gain in the peaktopeak signaltonoise ratio. These ob
servations are also supported by subjective evaluations.
We observe some “blocking effect” and other artifacts
inherent to the block DCT approach when using schemes
(b) and (d) although they are not as pronounced as using a
simple interframe block DCT scheme [20]. Schemes (a)
and (c) are basically free from the “blocking effect.” This
is due to the fact that the wavelet decomposition involves
a global transform, and hence the distortion is randomly
distributed among the whole picture, which is less annoy
ing than the periodic “blocking effect” for human viewers.
It should be pointed out that appropriate quantization
tables (rather than the JPEG default tables used in this
paper) for DCT coefﬁcients in residual subimages may
improve the performance for scenarios (b) and (d) since
residual subimages have a completely different statistical
properties from original video samples. VIII. SUMMARY, CONCLUSIONS, AND FUTURE WORK In this paper, application of the discrete wavelet trans
form (DWT) to fullmotion video compression was exam
ined. DWT decomposes a video signal into a pyramid
structure with multiple layers that characterize the video
signal in different scales with different frequency ranges. ZHANG AND ZAFAR: MOTIONeCOMPENSATED WAVELET TRANSFORM CODING This representation matches to the intrinsic properties of
human vision structure in early stages as speculated in
current research in the ﬁeld. Based on a set of wavelet
coefﬁcients developed by Daubechies [1] and a variable
blocksize MRMC scheme, a video compression system
was presented. A bitallocation assignment formula was
derived based on a weighted distortion criterion. The
adaptive truncation process used in this paper is similar to
the scheme used in Chen’s sceneadaptive coder, but the
normalization factor was appropriately adjusted to match
the “importance” level of subimages in the pyramid struc—
ture. Four variations of the proposed video compression
scheme were implemented and compared in terms of the
peaktopeak signaltonoise ratio. Our results indicated that DWT working on the original
video domain incorporated with the proposed variable
block—size MRMC scheme outperforms the DWT operat
ing on the DFD compensated by a conventional full
scarching scheme. We also observed that DCT mapping
after DWT does not compact energies as one might
expect for original video samples, instead it has an inverse
effect on the overall performance. These observations are
also supported by subjective evaluations. We observe some
“blocking effect” and other artifacts inherent to the block
DCT approach when using schemes 2 and 4 although they
are not as pronounced as with a simple interframe block
DCT scheme. Schemes 1 and 3 are basically free from the
“blocking effect.” This is due to the fact that the wavelet
decomposition involves a global transform and hence the
distortion is randomly distributed among the whole pic
ture, which is less annoying than the periodic “blocking
effect” for human viewers. In addition, a classiﬁed VQ
scheme was used to quantize the displaced residual
subimages after the proposed variablesize MRMC and
considerable gain in the peak—topeak signal—tonoise ratio
was obtained. Recently, biorthogonal wavelets with linear phase and
nonseparable wavelets functions such as the quincunx and
hexagonal wavelets have been developed and applied to
image coding applications. The extensions to video com
pression are straightforward by using the proposed motion
prediction schemes or other existing methods. The direc
tional properties of the nonseparable wavelets may fur—
ther improve the motion prediction performance in the
proposed MRMC scheme as indicated in Fig. 6. Also,
comparisons should be made between the 3D wavelet
representation approach and the motion—compensated
wavelet approach. The advantages of the 3D approach
are 1) it is more computationally efﬁcient since no motion
estimation needs to be implemented, 2) no refreshing
frames need to be sent. The disadvantages of the 3D
approach are 1) larger buffers are needed and 2) it is
difﬁcult to handle scene changes. It is not clear which
approach performs better. However, these two approaches
can be used in different scenarios. For example, the 3D
wavelet approach can be used in interactive video commu
nication environments such as videotelephony since it is
symmetric in nature where the MRMC 2D approach can 295 be used in oneway broadcasting and video—ondemand
applications since the decoder structure is much simpler.
Future studies should be directed to these areas. Finally,
the combination of 3D wavelet/subband representation
with the proposed multiresolution motion compensation
by using the ﬁlter banks along the motion trajectory
should also improve the performance. These topics de
serve further study. ACKNOWLEDGMENT The authors would like to thank Dr. D. Le Gall from
CCube Microsystems for providing us the original Video
sequence “CAR.” Assistance from Dr. I. Daubechies from
AT&T Bell Laboratories is greatly appreciated. Com
ments from reviewers are also helpful in improving the
presentation of this material. This work was carried out at
the video techniques and system engineering department
of GTE Laboratories. The authors would like to acknowl—
edge the consistent supports and interests from S. Walker
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coding for color video compression," SPIE Visual Communications and Image Processing, pp. 301316, Boston, MA, Nov. 10715, 1991. [20] [21] YaQin Zhang was born in 1966 in Taiyuan,
China. He received the BS. and MS. degrees in
electrical engineering from the China University
of Science and Technology (USTC), Hefei,
China, in 1983 and 1985, respectively. He re
ceived the Doctor of Science (ScD) degree in
electrical engineering from the George Wash
ington University, Washington, DC, in 1989. He has been a Senior Member of Technical
Staff at the video techniques and system engi
neering department of GTE Laboratories, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 2, NO. 3, SEPTEMBER 1992 Waltham, MA since May, 1991. Previously, he was a Member of TCChni
cal Staff at Contel Technology Center, Chantilly, VA. He was on the
parttime faculty of George Washington University in 1990. He has
published more than 40 papers in medical imaging and image /video
communications. He received the Merwin Ph.D. award sponsored by the
Industrial Liaison Program for his academic achievements in 1989. Sohail Zafar (8’87) was born in Lahore, Pak—
istan, on November 3, 1960. He received the
B.Sc degree in electrical engineering from Uni
versity of Engineering and Technology. Lahore,
Pakistan, in 1981, and the MS. degree from
Columbia University, New York, in 1988, Since
1989, he has been working as a Graduate Re
search Assistant at University of Maryland, Col
lege Park, MD, where he is pursuing the PhD.
degree. He has worked as a Member of Technical
Staff at Contel Technology Center, Chantilly, VA, during the summer of
1989 and 1990. He is working as a summer Member of Technical Staff at
GTE Laboratories, Waltham, MA. His research interests include neural
networks, parallel processing, and video coding and transmission. ...
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