25-08-2012, 04:01 PM
Image compression
1Image compression [.docx (Size: 328.19 KB / Downloads: 41)
INTRODUCTION
Image compression is a process of reducing or eliminating redundant or irrelevant data. So, this reduces the amount of data required to represent an image. Data redundancy is the irrelevant data or data which is repeated. Images often require a large number of bits to represent them, and if the image needs to be transmitted or stored, it is impractical to do so without somehow reducing the number of bits. The problem of transmitting or storing an image affects all of us daily. Image compression plays a key role in many important applications, including image database, image communications, remote sensing.
FUNDAMENTALS
The term data compression refers to the process of reducing the amount of data required to represent a given quantity of information. In this definition, data and information is not the same thing; data are the means by which information is conveyed. Because various amounts of data can be used to represent the same amount of information, representations that contain irrelevant or repeated information are said to contain redundant data. If we let b and b´ denote the number of bits (or information-carrying units) in two representations (usually before, and after compression respectively) of the same information
LOSSLESS VS LOSSY IMAGE COMPRESSION
A compression algorithm is lossless (or information preserving, or reversible) if the decompressed image is identical with the original. Respectively, a compression method is lossy (or irreversible) if the reconstructed image is only an approximation of the original one.
Lossless files like TIFF, GIF and PNG are saved using algorithms that reduce file size but do so without losing image quality. Unfortunately, the compression ratios are quite a bit weaker than lossy. Lossy files like JPEG and JPEG2000 discard information when they are saved. The amount of information that is discarded directly influences the size of the file. It's important to note that once we save a lossy file, we can never go back to the previous state. Each time the file is opened and saved as a JPEG, it will lose more and more data which will cause the image to become pixelated. The table below presents the differences among the lossy and lossless image compression.
FRACTAL IMAGE COMPRESSION
The term fractal was first coined by Benoit Mandelbrot [1] in 1975.He named fractal from the Latin adjective fractus. The corresponding Latin verb franger means “to break:”to create irregular fragments. Mandelbrot did not actually consider fractals for compression. He showed that they could be used for modelling real life objects like trees, mountains or clouds. The images generated by fractals were also used in a Hollywood movie named Beast and Beauty [2].
There are two main groups of fractals: linear and nonlinear. The latter are typified by the popular Mandelbrot set and Julia sets, which are fractals of the complex plane. However, the fractals used in image compression are linear, and of the real plane. So, the fractals used are not chaotic; in other words, they are not sensitive to initial conditions. They are the fractals from Iterated Function Theory. An Iterated Function System (IFS) is simply a set of contractive affine transformations. IFSs may efficiently produce shapes such as ferns, leaves and trees.
This presented an intriguing possibility; since fractal mathematics is good for generating natural looking images, could it not, in the reverse direction, be used to compress images
1Image compression [.docx (Size: 328.19 KB / Downloads: 41)
INTRODUCTION
Image compression is a process of reducing or eliminating redundant or irrelevant data. So, this reduces the amount of data required to represent an image. Data redundancy is the irrelevant data or data which is repeated. Images often require a large number of bits to represent them, and if the image needs to be transmitted or stored, it is impractical to do so without somehow reducing the number of bits. The problem of transmitting or storing an image affects all of us daily. Image compression plays a key role in many important applications, including image database, image communications, remote sensing.
FUNDAMENTALS
The term data compression refers to the process of reducing the amount of data required to represent a given quantity of information. In this definition, data and information is not the same thing; data are the means by which information is conveyed. Because various amounts of data can be used to represent the same amount of information, representations that contain irrelevant or repeated information are said to contain redundant data. If we let b and b´ denote the number of bits (or information-carrying units) in two representations (usually before, and after compression respectively) of the same information
LOSSLESS VS LOSSY IMAGE COMPRESSION
A compression algorithm is lossless (or information preserving, or reversible) if the decompressed image is identical with the original. Respectively, a compression method is lossy (or irreversible) if the reconstructed image is only an approximation of the original one.
Lossless files like TIFF, GIF and PNG are saved using algorithms that reduce file size but do so without losing image quality. Unfortunately, the compression ratios are quite a bit weaker than lossy. Lossy files like JPEG and JPEG2000 discard information when they are saved. The amount of information that is discarded directly influences the size of the file. It's important to note that once we save a lossy file, we can never go back to the previous state. Each time the file is opened and saved as a JPEG, it will lose more and more data which will cause the image to become pixelated. The table below presents the differences among the lossy and lossless image compression.
FRACTAL IMAGE COMPRESSION
The term fractal was first coined by Benoit Mandelbrot [1] in 1975.He named fractal from the Latin adjective fractus. The corresponding Latin verb franger means “to break:”to create irregular fragments. Mandelbrot did not actually consider fractals for compression. He showed that they could be used for modelling real life objects like trees, mountains or clouds. The images generated by fractals were also used in a Hollywood movie named Beast and Beauty [2].
There are two main groups of fractals: linear and nonlinear. The latter are typified by the popular Mandelbrot set and Julia sets, which are fractals of the complex plane. However, the fractals used in image compression are linear, and of the real plane. So, the fractals used are not chaotic; in other words, they are not sensitive to initial conditions. They are the fractals from Iterated Function Theory. An Iterated Function System (IFS) is simply a set of contractive affine transformations. IFSs may efficiently produce shapes such as ferns, leaves and trees.
This presented an intriguing possibility; since fractal mathematics is good for generating natural looking images, could it not, in the reverse direction, be used to compress images