Abstract: A method for transmitting fractal transform parameters generated by a variety of compressors using different fractal transform parameters is disclosed. The method includes generating an universal header having image reference data, color space data, fractal transform region reference data, and file decoding data and generating a fractal transform data segment having fractal transform parameters for domains and ranges used by a compressor to generate fractal transform parameters. The image reference data includes image dimensions expressed in physical size units so that the regeneration of the image at a decompressor is resolution independent. The color space parameters include identification of the original image color space and may include identification of a color space into which the original image is converted.

Abstract: A system and method for compressing and decompressing datastreams with fractal coding is disclosed. The method includes the generation of an optimal data set transformation function corresponding to a representative datastream captured from a data source. The data set transformation function is determined by ordering the digits of the representative datastream to order the intervals of an attractor. The ordered intervals are then used to determine the mapping functions which define an optimal data set transformation function. The nodes or graphical representation of the data set transformation function are incorporated in a compressor/decompressor combination. The compressor receives data symbols from a data source and determines the next interval of an attractor using a composition operation. The address or a portion of the address is shifted out as a number representative of the data symbols. Preferably, the interval is renormalized so the interval may be represented in sixteen bits.

Abstract: A system and method are disclosed for representing a data set by selecting a data transformation function and a data masking function. Preferably, the data set transformation and data masking functions are used to generate an attractor that more accurately represents the data set than an attractor generated by the data transformation function alone. The data masking function is a set of exclusionary data elements which are used to terminate data transformations for data elements which generate the attractor. Preferably, the data masking function is defined as a polygon for a two dimensional space. When the data masking function is incorporated with the data transformation function, the attractor normally produced by the data set transformation function is constrained to more accurately represent the data set.

Abstract: A method of fractally interpolating intensity values for a color component array derived from a single chip charge-coupled-device (CCD) is disclosed. The method includes selection of a domain area about an array element not having a value for the color component array. A plurality of range areas are selected which are larger than the domain area. Additional range areas may be generated by range area transformations and intensity value scaling and shifting. A difference measurement between each domain area and range area is determined and the range area corresponding to the smallest distance measurement is selected. The intensity values of the selected range area are then used to generate an interpolated intensity value for the domain area.

Abstract: A method and apparatus are described for-encoding a three-dimensional array of data representing a physical entity, such as an image (or sequence of frames), by means of its local symmetries. This encoding yields both compression and a resolution-independent description which allows reconstruction of the image to an arbitrary scale. Spatial zooming and interframe interpolation can be achieved without significant loss of information.

Abstract: A system and method for analyzing a set of data elements is disclosed. The method includes the steps of transforming data elements of a transform data space using the states of data elements comprising a data set and determining whether the transformed data elements have structure in the transform data space. The transformation of the data elements is performed by iteratively selecting mapping transformations corresponding to the states of successive data elements in the data set and applying the mapping transformations to successive transformations in the transform data space. By viewing the transformations in the transform data space, structure may be ascertained and evaluated to obtain information about the data set. The inventive system includes a transformer that changes state in response to the state of the next data element received from the data set and transforms the last transformation stored in the transform data space.

Abstract: Digital image data compression apparatus includes a controller circuit for receiving digital image data and for processing the image data into blocks. The controller circuit supplies processed image data to a plurality of transform circuits and to a feeder circuit. The transform circuits receive data from the controller circuit and the feeder circuit, and provide parallel processing to compare blocks of image data and generate fractal transform values representing the image data in a compressed form.

Abstract: Digital image data compression apparatus includes a controller circuit for receiving digital image data and for processing the image data into blocks. The controller circuit supplies processed image data to a plurality of transform circuits and to a feeder circuit. The transform circuits receive data from the controller circuit and the feeder circuit, and provide parallel processing to compare blocks of image data and generate fractal transform values representing the image data in a compressed form.

Abstract: Digital image data is automatically processed by dividing stored image data into domain blocks and range blocks. The range blocks are subjected to processes such as a shrinking process to obtain mapped range blocks. The range blocks or domain blocks may also be processed by processes such as affine transforms. Then, for each domain block, the mapped range block which is most similar to the domain block is determined, and the address of that range block and the processes the blocks were subjected to are combined as an identifier which is appended to a list of identifiers for other domain blocks. The list of identifiers for all domain blocks is called a fractal transform and constitutes a compressed representation of the input image. To decompress the fractal transform and recover the input image, an arbitrary input image is formed into range blocks and the range blocks processed in a manner specified by the identifiers to form a representation of the original input image.

Abstract: Digital image data is automatically processed by dividing stored image data into domain blocks and range blocks. The range blocks are subjected to processes such as a shrinking process to obtain a mapped range blocks. Then, for each domain block, the mapped range block which is most similar to the domain block is determined, and the address of that range block and the processes the block was subjected to are combined as an identifier which is appended to a list of identifiers for other domain blocks. The list of identifiers for all domain blocks is called a fractal transform and constitutes a compressed representation of the input image. To decompress the fractal transform and recover the input image, an arbitrary input image is formed into range blocks and the range blocks processed in a manner specified by the identifiers to form a representation of the original input image.

Abstract: A method and apparatus for obtaining highly compressed images employing an iterated function system (IFS). An original input or target image is subdivided into regions having similar characteristics. Contractive copies or maps of a particular region, which are the results of affine transformations to the region, are generated and tiled with respect to the input image until the entire region is covered and a collage is formed. Each region is processed in like manner. The affine transformation coefficients or IFS codes completely represent the input image, and are stored or transmitted. To generate an image from the IFS codes, a decoding system is disclosed. One disclosed method involves a chaotic dynamical system. A random iteration of the IFS codes is performed until an attractor, which is the target image, emerges and stabilizes. Another disclosed deterministic method repeatedly and successively applies the IFS codes to an arbitrary starting image until the attractor emerges.