Fractal coding of data

A method of fractal coding of data relating to at least one of an image, speech, handwriting and information on various physical forms representing various phenomena, the method being performed using a processing apparatus, and the method comprising:

• dividing the data into domains,
• applying analysis to the data for the domains to determine a set of transformations relating the domains to the data in such a manner so as to minimize error between the data and an approximation of the data, wherein the analysis step includes resolving the data for the domains into equations to determine the set of transformations, and
• providing an expression including quantized fractal transformation coefficients characterizing the transformations, wherein the quantized fractal transformation coefficients are derived in linear time.

A method of fractal coding of data relating to an image, the method being performed using a processing apparatus, and the method comprising:

• dividing the data into domains,
• applying analysis to the data for the domains to determine a set of transformations relating the domains to the data in such a manner as to minimize error between the data and an approximation of the data, wherein the analysis step is accomplished by resolving the data for the domains into equations, and wherein determining the set of transformations so as to minimize the error involves solving the equations, and
• providing an expression including quantized fractal transformation coefficients characterizing the transformations, the quantized fractal transformation coefficients being determined based on a linear relationship between coding complexity and image size.

A programmable apparatus for fractal coding of data relating to at least one of an image, speech, handwriting and information on various physical forms representing various phenomena, the apparatus comprising:

• partitioning means for dividing the data into domains,
• analysis means and co-operative transformation means for determining a set of transformations relating the domains to the data in such a manner so as to minimize error between the data and an approximation to the data, wherein the analysis means resolves the data for the domains into equations, and wherein determining the set of transformations so as to minimize the error involves solving the equations, and
• quantization means for providing an expression including quantized fractal transformation coefficients characterizing the transformations.

A computer implemented system for coding images and to compress image data comprising:

• partitioning means for dividing the image data into domains,
• analysis means and co-operative transformation means for determining a set of transformations relating the domains to the image data in such a manner so as to minimize error between the image data and an approximation to the image data, wherein the analysis means resolves the image data for the domains into equations, and wherein determining the set of transformations so as to minimize the error involves solving the equations, and
• quantization means for providing an expression including quantized fractal transformation coefficients characterizing the transformations so as to compress the image data to an order of 12:1.

A computer implemented system for coding image pixels comprising:

• partitioning means for dividing image data into domains,
• analysis means and co-operative transformation means for determining a set of transformations relating the domains to the image data in such a manner so as to minimize error between the image data and an approximation to the image data, wherein the analysis means resolves the image data for the domains into equations to determine the set of transformations, and
• quantization means for providing an expression including quantized fractal transformation coefficients characterizing the set of transformations so that computational efficiency is linearly proportional to the number of image pixels.

A storage medium recorded with a fractal coding of data obtained by a method wherein data relating to at least one of an image, speech, handwriting and information on various physical forms representing various phenomena is fractal coded, and the method comprising:

• dividing the data into domains,
• applying analysis to the data for the domains to determine a set of transformations relating the domains to the data in such a manner so as to minimize error between the data and an approximation of the data, wherein the analysis step includes resolving the data for the domains into equations, and wherein determining the set of transformations so as to minimize the error involves solving the equations, and
• providing an expression including quantized fractal transformation coefficients characterizing the transformations.