31-10-2012, 11:21 AM
RATE-DISTORTION OPTIMIZED IMAGE COMPRESSION USING WEDGELETS
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ABSTRACT
Most wavelet-based image coders fail to model the joint coherent
behavior of wavelet coefficients near edges. Wedgelets offer
a convenient parameterization for the edges in an image, but they
have yet to yield a viable compression algorithm. In this paper,
we propose an extension of the zerotree-based Space-Frequency
Quantization (SFQ) algorithm by adding a wedgelet symbol to its
tree-pruning optimization. This incorporates wedgelets into a ratedistortion
compression framework and allows simple, coherent descriptions
of the wavelet coefficients near edges. The resulting
method yields improved visual quality and increased compression
efficiency over the standard SFQ technique.
INTRODUCTION
Edges are the dominant features in images, with great importance
both for perception and for compression. Edges are well known to
convey significant information to the viewer, but they have a dramatic
impact on compression performance as well: edges account
for a significant amount of energy in the frequency domain.
Many of today’s leading image coders, ranging from the zerotree
(EZW) algorithm [1] to the new JPEG-2000 standard, rely
on wavelets to transform and compress the image. Nonetheless,
wavelets actually offer inefficient descriptions of edges in images:
many wavelet coefficients are required to describe a single edge.
A coherency exists among these coefficients which must be preserved
during quantization in order to prevent ringing artifacts.
Modeling the joint behavior of the coefficients is actually quite
difficult, however, and most coders fail to fully capture the joint
dependency of wavelet coefficients near edges.
SPACE-FREQUENCY QUANTIZATION
The SFQ coder [5] is based on a zerotree quantization framework.
The dyadic quadtree of wavelet coefficients is transmitted in a single
pass from the top down, and each directional subband is treated
independently.1 Each node ni of the quadtree includes a binary
map symbol. A 0 symbol indicates a zerotree: all of the descendants
of node ni are quantized to zero. A 1 symbol indicates that
the node’s four children are significant: their quantization bins
are coded along with an additional map symbol for each. Thus,
the quantization scheme for a given wavelet coefficient is actually
specified by the map symbol of its parent (or a higher ancestor, in
the case of a zerotree); the map symbol transmitted at a given node
refers only to the quantization of wavelet coefficients descending
from that node. All significant wavelet coefficients are quantized
uniformly by a common scalar quantizer; the quantization stepsize
q is optimized for the target bitrate.
WEDGELETS AND SFQ
Despite its success, the SFQ coder fails to model the joint behavior
of wavelet coefficients along an edge. A standard SFQ optimization
generally results in the use of zerotree symbols to represent
smooth regions of the image, with scalar quantization used
to code other features such as edges (see Fig. 3). In this section,
we propose wedgelets as a third option (symbol 2) in the SFQ
tree-pruning. With this extension, wedgelet symbols allow efficient
descriptions of the wavelet coefficients surrounding an edge;
scalar quantization can be reserved for more complicated texture
regions. Moreover, wedgelets implicitly model the joint behavior
of the wavelet coefficients, a property that should minimize visual
artifacts at low bitrates.
We first describe a method for coding a wedgelet at a node ni.
We then explain how it may be translated into a subtree of wavelet
coefficients. Finally, we describe the rate-distortion effects which
must be considered during the W-SFQ optimization.
CONCLUSION
We have proposed a method for integrating wedgelets into a ratedistortion
image compression framework. This technique allows
us to take advantage of the simple parameterization of wedgelets,
as well as the natural coherency they imply among wavelet coefficients.
By extending the SFQ tree-pruning with the addition of a
wedgelet symbol, we notice improved visual performance with an
increase in PSNR. Presently, though, the usefulness of such an approach
is limited to low bitrates and to images containing strong,
sharp edges.