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.
download full report
http://dspace.cusat.acdspace/bitstream/1...GELETS.pdf
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.
download full report
http://dspace.cusat.acdspace/bitstream/1...GELETS.pdf
