Classifications

• • H—ELECTRICITY
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  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/60—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding
  • H04N19/63—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets
  • H04N19/635—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets characterised by filter definition or implementation details
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
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  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
  • H04N19/12—Selection from among a plurality of transforms or standards, e.g. selection between discrete cosine transform [DCT] and sub-band transform or selection between H.263 and H.264
  • H04N19/122—Selection of transform size, e.g. 8x8 or 2x4x8 DCT; Selection of sub-band transforms of varying structure or type
• • H—ELECTRICITY
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  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
  • H04N19/17—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object
  • H04N19/172—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object the region being a picture, frame or field
• • H—ELECTRICITY
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  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
  • H04N19/186—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being a colour or a chrominance component
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/60—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding
  • H04N19/61—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding in combination with predictive coding
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/60—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding
  • H04N19/63—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/60—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding
  • H04N19/63—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets
  • H04N19/64—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets characterised by ordering of coefficients or of bits for transmission
  • H04N19/647—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets characterised by ordering of coefficients or of bits for transmission using significance based coding, e.g. Embedded Zerotrees of Wavelets [EZW] or Set Partitioning in Hierarchical Trees [SPIHT]
• • H—ELECTRICITY
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  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
  • H04N19/115—Selection of the code volume for a coding unit prior to coding
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
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  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
  • H04N19/124—Quantisation
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  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
  • H04N19/134—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or criterion affecting or controlling the adaptive coding
  • H04N19/146—Data rate or code amount at the encoder output
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  • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
  • H04N19/42—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals characterised by implementation details or hardware specially adapted for video compression or decompression, e.g. dedicated software implementation

Definitions

• the present invention generally relates to the field of digital image compression, and more particularly to a method and apparatus for digital image compression which operates on dynamical systems, such as cellular automata (CA).
• CA cellular automata
• a communications network such as public or private computer networks (e.g., the Internet), the Plain Old Telephone System (POTS); Cellular Wireless Networks; Local Area Networks (LAN); Wide Area Networks (WAN); and Satellite Communications Systems.
• POTS Plain Old Telephone System
• LAN Local Area Networks
• WAN Wide Area Networks
• Satellite Communications Systems Many applications also require digital image data to be stored on electronic devices such as magnetic media, optical disks and flash memories.
• the volume of data required to encode raw image data is large.
• a 1024x1024 color photograph digitized at the rate of 24 bits per pixel (bpp).
• Such a digitized image contains 25,165,824 bits of data.
• To transmit such an image file over 56 kilobits per second (kps) communications channel e.g., the rate supported by most POTS through modems
• the best approach for dealing with the bandwidth limitation and also reduce huge storage requirement is to compress the data.
• One popular technique for compressing image data combines transform approaches (e.g. the Discrete Cosine Transform, DCT) with psycho-visual techniques.
• DCT Discrete Cosine Transform
• JPEG Joint Photographic Expert Group
• the present invention use a dynamical system, such as cellular automata transforms (CAT).
• CAT cellular automata transforms
• the evolving fields of cellular automata are used to generate "building blocks" for image data.
• the rules governing the evolution of the dynamical system can be adjusted to produce "building blocks" that satisfy the requirements of a low-bit rate image compression process.
• cellular automata transform (CAT) was first taught in U.S. Patent No. 5,677,956 by Lafe for encrypting and decrypting data.
• the present invention uses more complex dynamical systems, that produce efficient "building blocks" for encoding image data.
• the present invention also uses a psycho-visual method developed specially for the sub-band encoding process arising from the cellular automata transfomi.
• a special bit allocation scheme that also facilitates compressed data streaming is provided as an efficient means for encoding the quantized transform coefficients obtained after the cellular automata transform process.
• a method of compressing image data comprising: determining a multi-state dynamical rule set and an associated transform basis function, receiving input image data, and performing a forward transform using the transform basis function to obtain transform coefficients suitable for reconstructing the input image data.
• a method for zooming an image comprising: determining a multi-state dynamical rule set and an associated transform basis function, receiving input image data, performing a sub-band forward transfomi using the transform basis function to obtain a set of low frequency transform coefficients, and performing an inverse transform using the transfomi basis function and the set of low frequency transfomi coefficients, wherein the resulting image data is a zoomed down version of the input image data.
• a method for zooming an image comprising: determining a multi-state dynamical rule set and an associated transform basis function receiving input image data, performing a sub-band forward transform using the transform basis function to obtain a set of low frequency transform coefficients, performing a forward transfomi using the transform basis function and the set of low frequency transform coefficients to generate second transform coefficients, wherein the set of low frequency transfomi coefficients are used as the input image data, and performing an inverse transform using the transfomi basis function and the second transfomi coefficients, wherein the resulting image data is a zoomed up version of the input image data.
• an apparatus for compressing image data comprising: means for determining a multi-state dynamical rule set and an associated transfomi basis function, means for receiving input image data, and means for performing a forward transfomi using the transform basis function to obtain transform coefficients suitable for reconstructing the input image data.
• an apparatus for zooming an image comprising: means for determining a multi- state dynamical rule set and an associated transform basis function, means for receiving input image data means for performing a sub-band forward transform using the transform basis function to obtain a set of low frequency transform coefficients, and means for performing an inverse transform using the transform basis function and the set of low frequency transform coefficients, wherein the resulting image data is a zoomed down version of the input image data.
• an apparatus for zooming an image comprising: means for determining a multi- state dynamical rule set and an associated transform basis function, means for receiving input image data means for performing a sub-band forward transform using the transfo i basis function to obtain a set of low frequency transfomi coefficients, means for performing a forward transfomi using the transfomi basis function and the set of low frequency transfomi coefficients to generate second transfomi coefficients, wherein the set of low frequency transform coefficients are used as the input image data, and means for performing an inverse transform using the transform basis function and the second transform coefficients, wherein the resulting image data is a zoomed up version of the input image data.
• a method of edge detection comprising: determining a multi-state dynamical rule set and an associated transform basis function, receiving input image data performing a sub-band forward transfomi using the transform basis function to obtain a set of high frequency transfomi coefficients, and performing an inverse transform using the transfomi basis function and the set of high frequency transform coefficients, wherein the resulting image data provides edge detection of the input image data.
• an apparatus for edge detection comprising: means for determining a multi-state dynamical rule set and an associated transform basis function, means for receiving input image data means for performing a sub-band forward transform using the transfomi basis function to obtain a set of high frequency transform coefficients, and means for performing an inverse transfo i using the transform basis function and the set of high frequency transform coefficients, wherein the resulting image data provides edge detection of the input image data.
• An advantage of the present invention is the provision of a method and apparatus for digital image compression which provides improvements in the efficiency of digital media storage.
• Another advantage of the present invention is the provision of a method and apparatus for digital image compression which provides faster data transmission through communication channels.
• Fig. 1 illustrates a one-dimensional multi-state dynamical system
• Fig. 2 illustrates the layout of a cellular automata lattice space for a Class I Scheme
• Fig. 3 illustrates the layout of a cellular automata lattice space for Class II Scheme
• Fig. 4 illustrates a one-dimensional sub-band transform of a data sequence of length L
• Fig. 5 is a flow chart illustrating the steps involved in generating efficient image building blocks, according to a preferred embodiment of the present invention
• Fig. 6 is a flow diagram illustrating an encoding, quantization, and embedded stream processes, according to a preferred embodiment of the present invention
• Fig. 7 is a flow diagram illustrating a decoding process, according to a preferred embodiment of the present invention.
• Fig. 8 illustrates interrelated factors that influence the compression process
• Fig. 9 illustrates decomposition of CAT transform coefficients into 4 bands, according to a preferred embodiment of the present invention
• Fig. 10 illustrates the image formed by the Group I components of Fig. 9 as further CAT decomposed and sorted into another 4 groups at a lower resolution;
• Fig. 11 shows an original image of a ba
• Fig. 12 shows the image of Fig. 1 1 reproduced by using only CAT transfomi coefficients in Groups II, III, and IV components of Fig. 9 at the highest resolution;
• Fig. 13 shows an original image of a 319x215 Tiger
• Fig. 14 shows a zoomed down 159x107 image of the Tiger of Fig. 13
• Fig. 15 shows a zoomed up 638x430 image of the Tiger of Fig. 13;
• Fig. 16a shows an original image of Lena
• Figs. 16b - 16h show the image of Fig. 16a at different levels of compression
• Fig. 17 shows an original image of a Tiger at 921 ,654 bytes (1 :1);
• Fig. 18 shows a compressed of the Tiger of Fig. 17 at 20,320 bytes (45:1 );
• Fig. 19 is a block diagram of an exemplary apparatus of the present invention, in accordance with a preferred embodiment.
• the present invention teaches the use of a transform basis function (also referred to as a "filter") to transform image data for the purpose of more efficient storage on digital media or faster transmission through communications channels.
• the transform basis function is comprised of a plurality of "building blocks,” also referred to herein as "elements” or “transform bases.”
• the elements of the transform basis function are obtained from the evolving field of cellular automata.
• the mles of evolution are selected to favor those that result in an "orthogonal" transform basis function.
• a special psycho- visual model is utilized to quantize the ensuing transfomi coefficients.
• the quantized transfomi coefficients are preferably stored/transmitted using a hybrid run-length- based/Huffman/embedded stream coder.
• the encoding technique of the present invention allows sequences of image data to be streamed continuously across communications networks.
• Fig. 8 illustrates some of the costs involved in data compression techniques which seek to remove or minimize the inherent redundancy within a data string.
• compression costs pertain to three interrelated factors:
• Fig. 8 degenerates into a dual-factor relationship in which more compression is typically achieved at the expense of computational ease.
• a classic example is the family of adaptive encoders.
• Data that is perceived can often be compressed with some degree of loss in the reconstructed data. Greater compression is achieved at the expense of signal fidelity.
• a successful encoding strategy will produce an error profile that cannot be perceived by the human eye (digital images and video) or ear (digital audio).
• Perceptual coding becomes a key and integral part of the encoding process.
• Cellular Automata are dynamical systems in which space and time are discrete.
• the cells are arranged in the form of a regular lattice structure and must each have a finite number of states. These states are updated synchronously according to a specified local rule of interaction.
• a simple 2-state 1 -dimensional cellular automaton will consist of a line of cells/sites, each of which can take value 0 or /.
• a specified rule usually deterministic
• the values are updated synchronously in discrete time steps for all cells.
• each cell can take any of the integer values between 0 and K - 1.
• the rule governing the evolution of the cellular automaton will encompass m sites up to a finite distance r away.
• the cellular automaton is referred to as a Estate, m-site neighborhood CA.
• Fig. 1 illustrates a multi- state 1 -dimensional cellular automaton. It will be appreciated that the number of dynamical system rules available for a given compression problem can be astronomical even for a modest lattice space, neighborhood size, and CA state. Therefore, in order to develop practical applications, a system must be developed for addressing the pertinent CA rules.
• a T-state N-node cellular automaton with m 2r+I points per neighborhood.
• 0 ⁇ W ⁇ K and ⁇ . are made up of the permutations (and products) of the states of the cells in the neighborhood.
• the states of the cells are (from left-to-right) a 0t ,a lp a 2l at time t.
• the state of the middle cell at time t+1 is:
• each set of W results in a given rule of evolution.
• the chief advantage of the above rule-numbering scheme is that the number of integers is a function of the neighborhood size; it is independent of the maximum state, K, and the shape/size of the lattice.
• transform basis function B is the inverse of transform basis function ⁇ .
• orthogonal transform basis functions are preferable on account of their computational efficiency and elegance.
• the forward and inverse transform basis functions A and B are generated from the evolving states a of the cellular automata. Below is a general description of how these transform basis functions are generated.
• a given CA transform basis function is characterized or classified by one (or a combination) of the following features:
• transfomi basis functions are those with transfomi coefficients (1,-1) and are usually derived from dual-state cellular automata. Some transfomi basis functions are generated from the instantaneous point density of the evolving field of the cellular automata. Other transform basis functions are generated from a multiple-cell-averaged density of the evolving automata. Construction of CA transform bases will now be described in detail.
• One- dimensional ( D ⁇ 1 ) cellular spaces offer the simplest environment for generating CA transform bases. They offer several advantages, including:
• N- cells are evolved over T time steps.
• One major advantage of the latter approach is the flexibility to tie the precision of the elements of the transition basis function to the evolution time T.
• the bottom base states (with N 2 cells) shown in Fig. 3 form the initial configuration of the cellular automata.
• T yP e 1 : a + ⁇ a ik + ( ⁇ - -,) i ⁇ '
• transfomi bases A lk should satisfy:
• CA states will generally not be orthogonal.
• Fig. 5 there is shown a flow chart illustrating the steps involved in generating an efficient transform basis function (comprised of "building blocks"), according to a preferred embodiment of the present invention.
• Testlmage data is input into a dynamical system as the initial configuration of the automaton, and a maximum iteration is selected.
• an objective function is determined, namely fixed file size/minimize error or fixed error/minimize file size (step 504).
• Typical rule set parameters include CA rule of interaction, maximum number of states per cell, number of cells per neighborhood, number of cells in the lattice, initial configuration of the cells, boundary configuration, geometric stmcture of the CA space (e.g., one-dimensional, square and hexagonal), dimensionality of the CA space, type of the CA transform (e.g., standard orthogonal, progressive orthogonal, non-orthogonal and self-generating), and type of the CA transfomi basis functions.
• the rule set includes:
• Boundary conditions (BC) to be imposed.
• the dynamical system is a finite system, and therefore has extremities (i.e., end points).
• extremities i.e., end points.
• the nodes of the dynamical system in proximity to the boundaries must be dealt with.
• One approach is to create artificial neighbors for the "end point” nodes, and impose a state thereupon.
• Another common approach is to apply cyclic conditions that are imposed on both "end point” boundaries. Accordingly, the last data point is an immediate neighbor of the first.
• the boundary conditions are fixed. Those skilled in the art will understand other suitable variations of the boundary conditions.
• the dynamical system is then evolved for T time steps in accordance with the rule set parameters (step 510).
• the resulting dynamical field is mapped into the transfomi bases (i.e., "building blocks"), a forward transform is performed to obtain transfomi coefficients.
• the resulting transform coefficients are quantized to eliminate insignificant transform coefficients (and/or to scale transfomi coefficients), and the quantized transfomi coefficients are stored.
• an inverse transfomi is performed to reconstruct the original test data (using the transform bases and transfomi coefficients) in a decoding process (step 512).
• the error size and file size are calculated to determine whether the resulting error size and file size are closer to the selected objective function than any previously obtained results (step 514).
• new W-set coefficients are selected.
• one or more of the other dynamical system parameters may be modified in addition to, or instead of, the W-set coefficients (return to step 508). If the resulting error size and file size are closer to the selected objective function than any previously obtained results, then store the coefficient set W as BestW and store the transform bases as Best Building Blocks (step 516). Continue with steps 508-518 until the number of iterations exceeds the selected maximum iteration (step 518). Thereafter, store and/or transmit N, m, K, T, BC and BestW, and Best Building Blocks (step 520). One or more of these values will then be used to compress/decompress actual image data, as will be described in detail below.
• the initial configuration of the dynamical system, or the resulting dynamical field may be stored/transmitted instead of the Best Building Blocks (i.e., transform bases). This may be preferred where use of storage space is to be minimized. In this case, further processing will be necessary in the encoding process to derive the building blocks (i.e., transfomi bases).
• the CA filter i.e., transform basis function
• the CA filters are applied in a non-overlapping manner.
• the input data is divided into segments, where none of the segments overlap.
• the filter of size Nx N is applied in the form:
• the transfomi coefficients for points belonging to a particular segment are obtained solely from data points belonging to that segment.
• CA filters can also be evolved as overlapping filters.
• the condition at the end of the segment when / > -N is handled by either zero padding or the usual assumption that the data is cyclic.
• Overlapped filters allow the natural connectivity that exists in a given data to be preserved through the transform process. Overlapping filters generally produce smooth reconstructed signals even after a heavy decimation of a large number of the transfo ⁇ n coefficients. This property is important in the compression of digital images, audio and video signals.
• the building blocks comprising a transform basis function are received (step 602). These building blocks are determined in accordance with the procedure described in connection with Fig. 5.
• Image data to be compressed is input (step 604).
• a forward transform (as described above) is performed to obtain transform coefficients (step 606). It should be appreciated that this step may optionally include performing a "sub-band" forward transform, as will be explained below.
• c k is determined directly from the building blocks obtained in the procedure described in connection with Fig. 5, or by first deriving the building blocks from a set of CA "gateway keys" or rule set parameters which are used to derive transform basis function A and its inverse B.
• the transfomi coefficients are quantized (e.g., using a
• the transform coefficients are quantized to discard negligible transform coefficients.
• the search is for a CA transform basis function that will maximize the number of negligible transform coefficients. The energy of the transform will be concentrated on a few of the retained transform coefficients.
• the quantized transfomi coefficients are stored and/or transmitted.
• the quantized transfo i coefficients are preferably coded (step 612).
• a coding scheme such as embedded band- based threshold coding, bit packing, run length coding and/or special dual-coefficient Huffman coding is employed.
• Embedded band-based coding will be described in further detail below.
• the quantized transform coefficients form the compressed image data that is transmitted/stored.
• steps 608, 610 and 612 may be collectively referred to as the "quantizing" steps of the foregoing process, and may occur nearly simultaneously.
• the quantized transform coefficients are transmitted to a receiving system which has the appropriate building blocks, or has the appropriate information to derive the building blocks. Accordingly, the receiving device uses the transfer function and received quantized transform coefficients to recreate the original image data.
• Fig. 7 there is shown a summary of the process for decoding the compressed image data.
• coded transform coefficients are decoded (step 702), e.g., in accordance with an embedded decoding process (step 702) to recover the original quantized transform coefficients (step 704).
• An inverse transform (equation 3) is performed using the appropriate transfo ⁇ n function basis and the quantized transform coefficients (step 706). Accordingly, the image data is recovered and stored and/or transmitted (step 708). It should be appreciated that a "sub-band" inverse transform may be optionally performed at step 706, if a "sub-band” transform was performed during the encoding process described above.
• the quantization strategy is a function of how the data will be perceived. For digital images and video, low frequencies are given a higher priority than high frequencies because of the way the human eye perceives visual info ⁇ uation. For digital audio both low and high frequencies are important and the transform coefficient decimation will be guided by a psycho-acoustics-based profile.
• Sub-band coding is a characteristic of a large class of cellular automata transforms.
• Sub-band coding which is also a feature of many existing transform techniques (e.g., wavelets), allows a signal to be decomposed into both low and high frequency components. It provides a tool for conducting the multi-resolution analysis of a data sequence.
• Fig. 4 shows a one-dimensional sub-band transfo ⁇ n of a data sequence of length L.
• the data is transformed by selecting M segments of the data at a time.
• the resulting transform coefficients are sorted into two groups, namely, the transform coefficients in the even locations (which constitute the low frequencies in the data) fall into one group, and the transform coefficients in the odd locations fall into a second group.
• the transform coefficients in the even locations which constitute the low frequencies in the data
• the transform coefficients in the odd locations fall into a second group.
• the "even” group is further transformed (i.e., the "even” group of transform coefficients become the new input data to the transform) and the resulting 2" ⁇ ' transform coefficients are sorted into two groups of even and odd located values.
• the odd group is added to the odd group in the first stage; and the even group is again transformed. This process continues until the residual odd and even group is of size of N/2.
• the N/2 transfo ⁇ n coefficients belonging to the odd group is added to the set of all odd-located transfomi coefficients, while the last N/2 even-located group transform coefficients form the transform coefficients at the coarsest level. This last group is equivalent to the lowest CAT frequencies of the signal.
• the rules of evolution of the CA, and the initial configuration can be selected such that the above conditions are automatically satisfied.
• the above conditions can be obtained for a large class of CA rule sets by re-scaling of the transfomi bases.
• Multi-dimensional, non-overlapping filters are easy to obtain by using canonical products of the orthogonal one-dimensional filters. Such products may not be automatically derivable in the case of overlapping filters.
• the CA has been evolved over 8 time steps.
• the following scaled transfomi coefficients are obtained from the states of the cellular automata evolved by using the above rule.
• the inverse filters are obtained via a numerical inversion from the forward overlapping filters.
• the redundancy is identified by transforming the data into the CA space.
• the principal strength of CAT- based compression is the large number of transfomi basis functions available. Use is made of CA transfo ⁇ n basis functions that maximize the number of transform coefficients with insignificant magnitudes. It may also be desirable to have a transform that always provides a predictable global pattern in the transfomi coefficients. This predictability can be taken advantage of in optimal bit assignment for the transform coefficients.
• CA CAT permits the selection of transform basis functions that can be adapted to the peculiarities of the data.
• a principal strength of CA encoding is the parallel and integer-based character of the computational process involved in evolving states of the integer-based character of the computational process involved in evolving states of the cellular automata. This can translate into an enormous computational speed in a well- designed CAT-based encoder.
• CAT Apart from the compression of data, CAT also provides excellent tools for performing numerous data processing chores, such as digital image processing (e.g., image segmentation, edge detection, image enhancement) and data encryption.
• digital image processing e.g., image segmentation, edge detection, image enhancement
• data encryption e.g., data encryption
• the low frequency, Group I, components can be further transformed.
• the ensuing transform coefficients are again subdivided into 4 groups, as illustrated by Fig. 10. Those in Groups II, III, and IV are stored while Group I is further CAT-decomposed and sorted into another 4 groups at the lower resolution.
• the hierarchical transformation can continue until Group I contains only one-quarter of the filter size.
• the sub-band coding will be limited to n R levels.
• Fig. 9 represents the transfo ⁇ n data at the finest resolution.
• the last transformation, at the n R -th level is the coarsest resolution.
• Figs. 11 and 12 show the use of dual-coefficient CAT filters in detecting the edge of a bam.
• Fig. 11 shows the original image
• Fig. 12 shows the image of Fig. 11 reproduced by using only CAT transform coefficients in Groups II, III, and IV at the highest resolution.
• the Group I low frequency transform coefficients provide the tool for zooming up or down on an image.
• Group I transform coefficients (with proper normalization ) form the zoomed down image.
• the original image is assumed to be the Group I transfo ⁇ n coefficients of the new larger image to be formed.
• the transform coefficients in Groups II, III and IV are set to zero.
• An inverse CA transfomi is carried out to recover a new image that is four times the original (Fig. 15). The process can be repeated to produce an image that is sixteen times the original.
• transfomi coefficients derived from a sub-band CAT coder makes it possible to impose objective conditions based on either: 1 ) a target compression ratio; or 2) a target error bound.
• the encoding philosophy for a sub- band coder is intricately tied to the cascade of transform coefficient Groups I, II, III, and IV shown in Figs. 9 and 10.
• the coding scheme is hierarchical. Bands at the coarsest levels typically contain transfomi coefficients with the largest magnitudes. Hence, the coding scheme gives the highest priority to bands with the largest transform coefficient magnitudes.
• T max magnitude of transform coefficient with the largest value throughout all the bands
• step (i) if InputSize ⁇ TargetSize.
• T ma magnitude of transfo ⁇ n coefficient with the largest value throughout all the bands
• Arithmetic Code, Huffman, Dictionary-based Codes Otherwise the packed bytes can be run-length coded and then the ensuing data is further entropy encoded using a dual- coefficient Huffman Code.
• the examples shown below utilized the latter approach.
• the data / is a vector of three components representing the primary colors such as RED (R), GREEN (G), and BLUE (B).
• Each of the colors can have any value between 0 and 2 b - 1 , where b is the number of bits per pixel.
• Each color component is treated the same way a grayscale data is processed. It is most convenient to work with the YIQ model, the standard for color television transmission.
• the Y- component stands for the luminance of the display, while the I- and Q-components denote chrominance.
• the luminance is derived from the RGB model using
• the chrominance components are computed from:
• the advantage of the YIQ-model is the freedom to encode the components using different degrees of fidelity.
• the luminance represents the magnitude of light being deciphered by the human eye.
• the I- and Q- components represent the color information.
• the chrominance components can be encoded with a much lower degree of fidelity than the luminance portion.
• the Original 512x512 color Lena image (Fig. 16a) has been selected for sselling the CAT image compression approach.
• the CAT filters used are those shown in Tables 2 and 3.
• the compressed files are shown to one-quarter scale in Figs. 16b-i.
• the chief strength of CAT compression is the ability to maintain relatively smooth non- pixelized images at very low bit rates (See Figs. 16e-16h).
• Fig. 19 is a block diagram of an apparatus 100, according to a preferred embodiment of the present invention. It should be appreciated that other apparatus types, such as a general purpose computers, may be used to implement a dynamical system.
• Apparatus 100 is comprised of a receiver 102, an input device 105, a programmed control interface 104, control read only memory (“ROM”) 108, control random access memory (“RAM”) 106, process parameter memory 1 10, processing unit (PU)116, cell state RAM 114, coefficient RAM 120, disk storage 122, and transmitter 124.
• Receiver 102 receives image data from a transmitting data source for real-time (or batch) processing of information.
• image data awaiting processing by the present invention are stored in disk storage 122.
• the present invention performs info ⁇ nation processing according to programmed control instructions stored in control ROM 108 and/or control RAM 106.
• Information processing steps that are not fully specified by instructions loaded into control ROM 108 may be dynamically specified by a user using an input device 105 such as a keyboard.
• a programmed control interface 104 provides a means to load additional instructions into control RAM 106.
• Process parameters received from input device 105 and programmed control interface 104 that are needed for the execution of the programmed control instructions are stored in process parameter memory 110.
• rule set parameters needed to evolve the dynamical system and any default process parameters can be preloaded into process parameter memory 110.
• Transmitter 124 provides a means to transmit the results of computations performed by apparatus 100 and process parameters used during computation.
• the preferred apparatus 100 includes at least one module 112 comprising a processing unit (PU) 1 16 and a cell state RAM 1 14.
• Module 112 is a physical manifestation of the CA cell. In an alternate embodiment more than one cell state RAM may share a PU.
• the apparatus 100 shown in FIG. 19 can be readily implemented in parallel processing computer architectures. In a parallel processing implementation, processing units and cell state RAM pairs, or clusters of processing units and cell state RAMs, are distributed to individual processors in a distributed memory multiprocessor parallel architecture.
• the present invention has been described with reference to a preferred embodiment. Obviously, modifications and alterations will occur to others upon a reading and understanding of this specification. It is intended that all such modifications and alterations be included insofar as they come within the scope of the appended claims or the equivalents thereof.

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• 2000
  • 2000-03-03 US US09/518,347 patent/US6393154B1/en not_active Expired - Fee Related
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