02-03-2011, 03:19 PM
presented by:
Meeramol T.K.
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ABSTRACT
Edges are dominant features in images,with great importance both for perception and compression.
Most wavelet-based image coders fail to model the joint coherent behavior of wavelet coefficients near edges.
Wedgelet is introduced as a geometric tool for image compression.
Wedgelets offer a convenient parameterization for the edges in an image.
Wedgelets offer piecewiselinear approximations of edge contours and can be efficiently encoded.
INTRODUCTION
Uncompressed multimedia data requires considerable storage capacity and transmission bandwidth.
The recent growth of data intensive multimedia based web applications have not only sustained the need for more efficientways to encode signals and images but have made compression of such signals central to storage and communication technology.
For still image compression, the JPEG standard has been established by ISO and IEC .
The performance of these coders generally degrades at low bit-rates.
A variety of powerful and sophisticated wavelet-based schemes for image compression, have been developed.
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.
IMAGE COMPRESSION
In most images, the neighboring pixels are correlated.
The foremost task is to find less correlated representation of the image.
Two fundamental components of compression are
redundancy reduction and
irrelevancy reduction
In general, three types of redundancy can be identified:
Spatial Redundancy
Spectral Redundancy
Temporal Redundancy
Image compression research aims at reducing the number of bits needed to represent an image.
WAVELET CODER
What is a Wavelet Transform ?
functions defined over a finite interval and having an average value of zero.
The basic idea is to represent any arbitrary function ƒ(t) as a superposition of a set of wavelets
These basis functions are obtained from a single prototype wavelet
Discrete Wavelet Transform of a finite length signal x(n) having N components, is expressed by an N x N matrix.
NEED OF WAVELET-BASED COMPRESSION
Blocking artifacts of JPEG
Wavelet transformation has been widely accepted in image compression
There is no need to block the input image
Robust under transmission and decoding errors
Better matched to the HVS characteristics
Suitable for applications where scalability and tolerable degradation are important.
GEOMETRY BASED TECHNIQUE
Edges represent abrupt changes in intensity.
Smooth regions are characterized by slowly varying intensities
Textures contain a collection of localized intensity changes.
Edges are of particular interest for compression.
Wavelets are well-suited to represent smooth and textured regions of images, but waveletbased descriptions of edges are highly inefficient.
a simple twofold approach to compression.
A geometry-based compression scheme to compresses edge information
Wavelets to compress the smooth and textured regions.
Better compression performance
PSNR
WEDGELETS
Wedgelets is a tool for compression of edge information.
Wedgelets approximate curved contours using an adaptive piecewise-linear representation.
Wedgelets were first introduced by Donoho.
A wedgelet is a piecewise constant function on a dyadic square with a linear discontinuity.
These dyadic blocks contains a single straight edge with arbitrary orientation.
Each wedgelet by itself can represent a straight edge within a certain region of the image.
Smooth contours can be represented by concatenating individual wedgelets from this decomposition.
WEDGELET DICTIONARY
A wedgelet is a square, dyadic block of pixels containing a picture of a single straight edge.
Wedgelet is parameterized by five numbers:
d : edge location
θ : edge orientation
m1, m2 : shading
N: block size
wedgelet dictionary is the dyadically organized collection of all possible wedgelets.
A compression scheme based on the wedgelet representation requires a model which captures the dependency among neighboring wedgelet fits; this can be referred as “geometric modeling”.
Wedgelet Decomposition
Approximate edge contours by partitioning dyadic blocks along lines
WEDGELET ESTIMATION
Requires a technique for estimating wedgelet parameters which fit the pixelized data.
A standard criterion, is to seek the set of parameters which minimize the distance l2 from the wedgelet approximation to an N*N block of pixel data.
The set of possible wedgelets forms a nonlinear four dimensional subspace
Finding the best wedgelet fit reduces to projecting the data onto this subspace.
Accurate estimates may be obtained through an analysis of the block’s Radon transform.
By restricting the wedgelet dictionary to a carefully chosen discrete set of orientations and locations, the inner products of all wedgelets may be quickly computed.
COMPRESSION VIA EDGE CARTOON
Two stage scheme
The image = {edge cartoon} + {texture}
f(x,y) = c(x,y) + t(x,y)
The edge cartoon contains the dominant edges of the image
Two-stage scheme produces compressed images with clean, sharp edges at low bitrates.
ESTIMATION AND COMPRESSION OF THE EDGE CARTOON
Wedgelet decomposition offers a piecewise-linear approximation to a contour.
Resulting image resembles a “cartoon sketch”
It contains approximations of the image’s dominant edges, and spaces between the edges are filled with constant values.
The sizes of wedgelet blocks should be chosen intelligently
Begin with a full dyadic tree of wedgelets.
Each node n of the tree is associated with the wedgelet parameters which give the best l2 fit to the data in the corresponding image block.
WEDGELET QUADTREE
ESTIMATION AND COMPRESSION OF THE EDGE CARTOON…
Three types of information must be sent:
(1) a symbol from {E, I, C}
(2) edge parameters (d, θ)
(3) grayscale values (m) or (m1, m2)
For a given node, we predict its edge parameters and grayscale values based on the previously coded parameters of its parent
We make the prediction based on a simple spatial ntuition:
The parent’s wedgelet is divided dyadically to predict the wedgelets of its four children
After coding the pruned wedgelet tree, we translate it into the cartoon sketch
MULTISCALE WEDGELET PREDICION
IMPROVING THE COMPRESSION SCHEME
The wedgelet-based cartoon compression scheme, can be combined with the tapered masking scheme for wavelet compression of the residual image.
geometric modeling to attain improvements in visual quality and PSNR
The wedgelet decomposition in Stage I has been optimized only locally.
The consideration of placing wedgelets is made without knowledge of any residual compression scheme to follow.
The resulting wedgelet placements often create residual artifacts.
Wedgelets should be placed only when they actually improve the overall rate-distortion performance of the coder
Achieving global rate-distortion optimality requires sharing information between the geometry-based coder and the residual coder.
W-SFQ: Geometric Modeling with Rate-Distortion Optimization
Geometric modeling and compression of edge contours must be very effective.
A natural image coder should wisely apply its geometric techniques in a rate-distortion sense
Here introduces a method which uses a simple wedgelet-based geometric representation
Wedgelets are used only when they actually increase the final rate-distortion performance of the coder.
THE SFQ COMPRESSION FRAMEWORK
SFQ FUNDAMENTALS
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.
Each node includes a binary map symbol.
A symbol indicates a zerotree: descendants are quantized to zero.
A symbol indicates that the node’s four children are significant: their quantization bins are coded with an additional map symbol
Thus, the quantization scheme for a given wavelet coefficient is actually specified by the map symbol of its parent
Themap 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 is optimized for the target bitrate.
