IMAGE COMPRESSION USING WEDGELETS
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02-03-2011, 03:19 PM


presented by:
Meeramol T.K.


.ppt   IMAGE COMPRESSION USING WEDGELETS.ppt (Size: 132.5 KB / Downloads: 202)
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 project and implimentationing 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.

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03-05-2011, 09:51 AM

ABSTRACT
Images typically contain strong geometric features, such as edges, that impose astructure on pixel values and wavelet coefficients. Modeling the joint coherentbehavior of wavelet coefficients is difficult, and standard image coders fail to fullyexploit this geometric regularity. i.e. Most wavelet-based image coders fail tomodel the joint coherent behavior of wavelet coefficients near edges. Wedgelet isintroduced as a geometric tool for image compression. Wedgelets offer aconvenient parameterization for the edges in an image, Wedgelets offer piecewiselinearapproximations of edge contours and can be efficiently encoded
1. Image compression
1.1 Introduction

Uncompressed multimedia (graphics, audio and video) data requiresconsiderable storage capacity and transmission bandwidth. Despite rapidprogress in mass-storage density, processor speeds, and digitalcommunication system performance, demand for data storage capacity anddata-transmission bandwidth continues to surpass the capabilities ofavailable technologies. The recent growth of data intensive multimediabasedweb applications have not only sustained the need for more efficientways to encode signals and images but have made compression of suchsignals central to storage and communication technology.For still image compression, the `Joint Photographic Experts Group' or JPEGstandard has been established by ISO (International Standards Organization) andIEC (International Electro-Technical Commission). The performance of thesecoders generally degrades at low bit-rates mainly because of the underlyingblock-based Discrete Cosine Transform (DCT) scheme. More recently, thewavelet transform has emerged as a cutting edge technology, within the field ofimage compression. Wavelet-based coding provides substantial improvements inpicture quality at higher compression ratios. Over the past few years, a variety ofpowerful and sophisticated wavelet-based schemes for image compression, havebeen developed and implemented.
1.3 The principles behind compression:
A common characteristic of most images is that the neighboring pixels arecorrelated and therefore contain unnecessary information. The foremost taskthen is to find less correlated representation of the image. Two fundamentalcomponents of compression are redundancy and irrelevancy reduction.Redundancy reduction aims at removing duplication from the signal source(image/video). Irrelevancy reduction omits parts of the signal that will not benoticed by the signal receiver, namely the Human Visual System (HVS). Ingeneral, three types of redundancy can be identified:Spatial Redundancy or correlation between neighboring pixel values.Spectral Redundancy or correlation between different color planes orspectral bands.Temporal Redundancy or correlation between adjacent frames in asequence of images (in video applications).Image compression research aims at reducing the number of bitsneeded to represent an image by removing the spatial and spectralredundancies as much as possible. Since we will focus only on still imagecompression, we will not worry about temporal redundancy.
1.4 Typical image coder
Compression is accomplished by applying a linear transform to decorrelate the image data, quantizing the resulting transformcoefficients, and entropy coding the quantized values.A typical image coder therefore consists of three closely connected components namely (a) Source Encoder (b) Quantizer, and ©Entropy Encoder.
1.4.1 JPEG : DCT-Based Image Coding Standard
The discovery of DCT (Discrete Cosine Transform) in 1974 is an importantachievement for the research community working on image compression. It is atechnique for converting a signal into elementary frequency components. DCT is realvaluedand provides a better approximation of a signal with fewer coefficients.In 1992, JPEG established the first international standard for still imagecompression where the encoders and decoders are DCT-based. The JPEGstandard specifies three modes namely sequential, progressive, andhierarchical for lossy encoding, and one mode of lossless encoding. Thebaseline JPEG coder' which is the sequential encoding in its simplest form.Color image compression can be approximately regarded as compression ofmultiple grayscale images, which are either compressed entirely one at atime, or are compressed by alternately interleaving 8x8 sample blocks fromeach in turn.The DCT-based encoder can be thought of as essentially compressionof a stream of 8x8 blocks of image samples. Each 8x8 block makes its waythrough each processing step, and yields output in compressed form into thedata stream. Because adjacent image pixels are highly correlated, the`forward' DCT (FDCT) processing step lays the foundation for achievingdata compression by concentrating most of the signal in the lower spatialfrequencies. For a typical 8x8 sample block from a typical source image,most of the spatial frequencies have zero or near-zero amplitude and neednot be encoded. In principle, the DCT introduces no loss to the source imagesamples; it merely transforms them to a domain in which they can be moreefficiently encoded.After output from the FDCT, each of the 64 DCT coefficients isuniformly quantized in conjunction with a carefully designed 64-elementQuantization Table (QT). At the decoder, the quantized values are multipliedby the corresponding QT elements to recover the original unquantizedvalues. After quantization, all of the quantized coefficients are ordered. Thisordering helps to facilitate entropy encoding by placing low-frequency nonzerocoefficients before high-frequency coefficients. The DC coefficient,which contains a significant fraction of the total image energy, isdifferentially encoded.


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09-05-2011, 02:44 PM


.ppt   IMAGE COMPRESSION USING WEDGELETS.ppt (Size: 635.5 KB / Downloads: 83)
IMAGE COMPRESSION USING WEDGELETS
INTRODUCTION
IMAGE COMPRESSION
NEED OF COMPRESSION

THE PRINCIPLES BEHIND COMPRESSION
Typical image coder
JPEG : DCT-Based Image Coding Standard
Wavelet Coder
Need of Wavelet-based Compression
Geometry Based Technique
WEDGELETS
The Wedgelet Dictionary
Wedgelet Estimation
THE WEDGELET DICTIONARY
a)Parameterization of a wedgelet on an N*N image block
orientation θ ,offset d & grayscale intensity values m1, m2
b)Example of a wedgelet for pixelized image block, N=16
a) Artificial Image
b) Wedgelet decomposition. Each dyadic
block in the tiling is constant or contains
a single straight line.
COMPRESSION VIA EDGE CARTOON
ESTIMATION AND COMPRESSION OF THE EDGE CARTOON

Pruned wedgelet quadtree.
Interior nodes I, Leaf nodes E (edge) and C (contant).
The cartoon sketch is drawn according to leaf nodes.
Cartoon sketch C obtained from the coded wedgelet parameters. (Blocking artifacts at the wedgelet borders).
Final coded cartoon sketch C . Smoothing removes blocking artifacts while preserving coded edge.
Residual Texture Image
Wavelet compressed residual image coded cartoon sketch PSNR 28.48db
ZEROTREE COMPRESSION
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19-07-2011, 03:39 PM

ABSTRACT
Images typically contain strong geometric features, such as edges, that impose a structure on pixel values and wavelet coefficients. Modeling the joint coherent behavior of wavelet coefficients is difficult, and standard image coders fail to fully exploit this geometric regularity. i.e. 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.
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