WO2003049420A2 - Restauration d'image a partir de donnees de composants transformes - Google Patents

Restauration d'image a partir de donnees de composants transformes Download PDF

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Publication number
WO2003049420A2
WO2003049420A2 PCT/US2002/038958 US0238958W WO03049420A2 WO 2003049420 A2 WO2003049420 A2 WO 2003049420A2 US 0238958 W US0238958 W US 0238958W WO 03049420 A2 WO03049420 A2 WO 03049420A2
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image
data
domain
marker
base
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PCT/US2002/038958
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WO2003049420A3 (fr
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Hal H. Ottesen
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Regents Of The University Of Minnesota
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Priority claimed from US10/124,547 external-priority patent/US6873744B2/en
Application filed by Regents Of The University Of Minnesota filed Critical Regents Of The University Of Minnesota
Priority to AU2002346675A priority Critical patent/AU2002346675A1/en
Publication of WO2003049420A2 publication Critical patent/WO2003049420A2/fr
Publication of WO2003049420A3 publication Critical patent/WO2003049420A3/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T9/00—Image coding
    • G06T9/007—Transform coding, e.g. discrete cosine transform

Definitions

  • the present invention relates to image data processing, and more particularly concerns restoring an image from a transformed version including less than all components of the transformed data.
  • the magnitude component of the transform contains half the information of the image from the spatial base domain, and the complementary phase component contains the other half.
  • the ability to restore or reconstruct an image from only one of these frequency components could save the bandwidth and/or time required to transmit both components, or to transmit the image in its spatial or other base-domain form.
  • Storing only a single transform component would also substantially reduce the space required to hold a representation of a transform- domain image on a disk or other medium. These reductions are especially significant in the normal case where transform-domain data requires a double- precision floating-point format.
  • the present invention offers an iterative technique for restoring or reconstructing an image, given only a component of the data from a transformed version of the original image and one or more known marker values.
  • the transformed image component is combined with a complementary component of the current restored image for multiple iterations.
  • the known marker(s) are reinserted into the current restored image to enhance convergence.
  • the invention also includes a technique for marking an original image in a way that the restoring technique converges without imposing any special constraints upon the original image.
  • the Drawing Fig. 1 illustrates an overall system for communicating an image in component form.
  • Fig. 2 shows a method for preparing image data of Fig. 1 for restoration.
  • Figs. 3A-C represent image data layouts for Fig. 2.
  • Fig. 4 outlines a method for restoring an image.
  • Fig. 5 is a graph illustrating convergence of a restoration method.
  • Fig. 6 shows how to prepare transformed component image data for restoration.
  • the following description and the drawing figures describe some specific embodiments of the invention sufficiently to enable those skilled in the art to practice it. Alternative embodiments may incorporate structural, logical, process, and other changes. Examples merely typify possible variations. Individual structures and functions are optional unless explicitly required, and the relative sequence of operations may vary. Portions and features of some embodiments may be included in or substituted for those of others. The scope of the invention encompasses the full ambit of the appended claims and all available equivalents.
  • I(n,,n 2 ) is the original (N, x N 2 ) image.
  • rF(k,,k 2 ) is the (N, x N 2 ) DFT of the original image I(n familiarn 2 ).
  • ⁇ (n,,n 2 ) is the padded (2 N, * 2 N 2 ) image, where I(n,,n 2 ) is the upper left quadrant of the padded image matrix.
  • HF(k authorityk 2 ) is the (2 N, x 2 N 2 ) DFT of the padded image ⁇ (n familiarn 2 ).
  • JJ(n,,n 2 ) is a padded (2 N, x 2 N 2 ) image used during the iterations.
  • JJF(k accountk 2 ) is the (2 N, 2 N 2 ) DFT of the padded iteration JJ(n familiarn 2 ).
  • Some images are directly available for viewing at the data source, since both the magnitude and phase components are present in the frequency transformed source data, although the invention permits storing only the magnitude component, slicing the storage requirement by 50%.
  • a pixel marker I, ⁇ can be embedded in the original image I(n,,n 2 ) before its DFT IF(k,,k 2 ) is computed.
  • the pixel marker can also be embedded directly in the magnitude component — and must be, where only that component is available. In these cases, a pixel value embedded in an (N, x N 2 ) matrix of zeros is transformed and its transform is added to the magnitude component of the source data.
  • the value of I max is typically more than twice the value of the sum of all the pixels in the original image I(n,,n 2 ).
  • the location of the pixel marker could, for example, be in any of the four corners of the original image. The location and the value of the pixel marker follow a user-defined convention. The purpose of the marker is to enforce convergence in the magnitude-only image restoration algorithm regardless of the characteristics of the original image.
  • the unpadded DFT magnitude component of IF(k,,k 2 ), with the embedded pixel marker, is converted to a padded magnitude component of IIF(k householdk 2 ). Padding provides a bounded support for the image function. This is the complete DFT magnitude response, called MIIF(k 1 ,k 2 ), for the algorithm for the phase restoration.
  • the magnitude-only restoration method can be invoked.
  • Mask(n,,n 2 ) has all ' 1' values in the upper left quadrant.
  • the remaining mask entries are all '0'.
  • the initial iterated padded image JJ(n,,n 2 ) is set equal to Mask(n,,n 2 ).
  • the 2D DFT JJF(k,,k 2 ) of the iterated padded image JJ(n,,n 2 ) is computed, and the 2D DFT phase component PJJF(k,,k 2 ) is extracted.
  • the real part of the inverse DFT of JJF is calculated to obtain a new iterated padded image JJ(n,,n 2 ).
  • the iteration number q is compared to the specified total number of iterations Q.
  • x(n) is the sequence index and k is the index for the one-dimensional DFT, X(k).
  • x(n) is the original N - point row or column sequence.
  • x,(n) is the original sequence with y max as a preamble, x(n)].
  • XX, (k) is the padded 2(N+1) - point DFT of x,(n) where x,(n) is in the first half of the padded sequence.
  • the rest of the entries in the 2(N+1) - point padded sequence X ⁇ (n) are '0'.
  • yy(n) is the padded (2 N) - point sequence used during the iteration.
  • YY(k) is the (2N) - point DFT of the padded yy(n).
  • the magnitude-only restoration method can also be applied to a two- dimensional image in a row-wise or a column-wise mode. Since all the pixel values within the image are non-negative, each row or column will have non- negative values.
  • the proper DFT magnitude component MX of the one- dimensional N - point sequence x(n) is computed.
  • the marker could also be embedded into the sequence x(n), either in front or at the end of the sequence.
  • the location and the value of the sequence marker follow a user-defined convention.
  • the value of y max is typically more than twice as large as the sum of the pixels values in the row sequence x(n).
  • the 2(N+1) - point DFT XX ⁇ (k) of the zero-padded row-sequence x,(n) is computed, and the corresponding DFT magnitude component MXX of XXj(k) is extracted.
  • the initial conditions for the iterated padded sequence yy(n) are set equal to the Mask(n).
  • the DFT YY(k) of the iterated padded sequence yy(n) is computed, as well as the DFT phase PYY (in radians).
  • the real part of the inverse DFT of YY is calculated to obtain a new iterated padded sequence yy(n).
  • sequence marker y max for example, at yy(l) is removed.
  • the restored magnitude-only sequence y(n) is finally output.
  • the top row and left column are then trimmed from restored image J(n,,n 2 ).
  • the restored image J(n familiarn 2 ) can be trimmed such that the resultant image is a [(Nl-1) x (N2-1)] image.
  • Fig. 1 shows an example of a system 100 for hosting the invention.
  • the invention can be implemented in software, hardware, or any combination.
  • a computer-readable storage or communication medium such as 101 or 102 may hold or transmit some or all of any computer instructions or data for executing the invention.
  • a number of different sources 110 in an input section may provide an image or other data. Some produce an original image in the base image domain such as space or time.
  • MRI scanner 11 1 for example, generate data representing two-dimensional spatial images. This data may be sent on in two- dimensional form, or may be converted to one-dimensional rows or columns.
  • Other sensors, such as spectrometer 112 may generate data that is inherently one- dimensional, having time as its base domain, and the data points corresponding to image pixels have temporal locations.
  • Some sources may generate component data in a transform domain.
  • Weather satellite 113 may produce both spatial images and frequency observations.
  • Astronomical sensor 114 for a telescope is capable of outputting only one component (power or magnitude) data for different wavelengths in a frequency transform domain, and cannot determine the phase component.
  • Other magnitude-only sensors include those for X-ray crystallography, electron microscopy, and coherence theory.
  • Module 120 modifies data from a base-domain source to add one or more markers for later restoration of the original image.
  • Transform generator 130 converts the data to a transform domain, unless the image is already in that domain. Frequency-transformed data are usually stored in floating-point double- precision format.
  • a digital signal processor may implement a discrete Fourier transform to produce frequency and phase components. However, module 130 may send only the magnitude component — or a derivative such as magnitude squared — as data 131 representing the original image. (Line 132 symbolically represents discarded complementary phase-component data.)
  • Channel 140 communicates the modified partial data 131 from any of the sources 110 to be restored directly, or stores it for later restoration. Communication may take the form of direct transmission from one physical location to another over a medium such as 101, or of storage in a medium such as 102. Medium 102 may temporary or archival, and may occur at any physical location or facility.
  • Image data that has already passed through marker module 120 can pass directly to a module 121 that further modifies the image by inserting padding into it in the transform domain.
  • Padding could have been inserted into the image in the base domain before transmission or storage in channel 140.
  • padding increases the image size, and may significantly increase the storage size or transmission time required for the transformed partial data.
  • padding can be inserted at any point, many applications favor performing this operation after storage or transmission in the transform domain.
  • module 120' marks the data in the transform domain before passing it to padding module 121. Because it does not significantly increase the size of the transform data, transform-domain marking may occur before or after storage or transmission in channel 140.
  • Data from sources 111-113 could alternatively be marked in the transform domain by a module such as 120', instead of being marked in the base domain before transformation.
  • transform-domain marking involves direct manipulation of the transform-domain image, such marking has a corresponding representation in the base image domain, and will sometimes be described from that viewpoint.
  • Restore module 150 calculates complementary component data from the current iterated approximation, combines it with the received transformed component data, and takes an inverse transform to convert the data to the base domain of the original image.
  • Line 151 represents iteration through the module.
  • Module 150 reinserts the known marker value(s) and padding at the correct locations in the image data during every iteration, so as to coerce convergence toward the correct image. It may also scale or otherwise manipulate the iteration data.
  • Storage 160 holds the transformed image from channel 140, and initial and interim data representing the iterated restored image. It may also hold parameters such as markers and pad locations.
  • Output modifier 170 performs ancillary operations upon base-domain data representing the final iteration of the restored image. These operations may include scaling or normalizing data values, trimming away padding, and interpolating pixel values.
  • the final restored image then proceeds to various output devices 180 such as displays 181, printers 182, and data analyzers 183 for presentation to a user or for further processing.
  • Fig. 2 outlines one of the methods for modifying original image data for communication and restoration.
  • Modules such as 120, 120', and/or 130, Fig. 1, may implement method 200.
  • Block 201 receives an original image 300, Fig. 3 A, in the form of a large number of pixels 301 or other data points each representing an intensity or other characteristic at a certain location in the image.
  • Fig. 3A depicts Image 300 as a two-dimensional (2D) spatial image having pixel locations designated by x and y coordinates.
  • Image 300 may be treated as a two- dimensional image.
  • its rows or columns may be operated upon separately as a sequence of one-dimensional (ID) images; this may simplify implementing the calculations in an integrated circuit.
  • the spatial form of the image is the base domain of the image in this example.
  • Operation 210 sets a marker value, from characteristics of the image data.
  • the marker value may be selected as a constant K times the sum of all the pixels values in a 2D restoration, or the sum of all pixel values in a row or a column for a ID restoration.
  • K>1 insures that the resulting transformed data sequence is characteristically minimum-phase.
  • Block 211 applies the calculated marker value to image 300.
  • the marker represents one or more designated image locations, it can physically be inserted anywhere, added as further pixel locations, sent separately from the image, or be made known to the system in some other way. Some situations may employ multiple marker values and/or locations. For example, some high-contrast images may restore more easily when a normal marker pixel value is followed by another marker pixel having a '0' value. These two markers may be added as, e.g., a preamble to each row or column of a ID image.
  • Operation 220 applies padding to provide a bounded support for image 300.
  • Fig. 3B shows the original image 300 embedded in one quadrant of a modified image 310, Fig. 3B.
  • the other three quadrants 311 have pixels 312 with predetermined values, conveniently all zeros. There are other ways to provide appropriate mathematical support for the present purposes.
  • Fig. 3C shows another format for a modified image.
  • Each stream may contain its own marker 322 and its own one-dimensional padding 323 as an appended sequence of known pixel values. This example appends a number of zeros equal to the number of data pixels in the row.
  • a single marked and padded row can alternatively represent an entire one-dimensional image.
  • Other image formats can be accommodated as well. Some environments gain an advantage by applying the padding after conversion to the transform domain, perhaps at the physical location of the restoration process.
  • the purpose of the padding is to provide mathematical support for bounding the image. Any operation that achieves this end may serve in block 220; in some cases, the original image may already possess a border or other area that makes it unnecessary to add further padding. Operation 230 applies a transform to the padded and marked image.
  • a two-dimensional image format such as 310 may employ a two-dimensional transform.
  • a one-dimensional image such as 320 may use a separate one- dimensional transform for each row 321, or a single one-dimensional transform that aggregates all the rows together as a single data sequence. This example supposes a discrete Fourier transform (DFT). Other forms of Fourier transform, and transforms other than Fourier, may also be suitable.
  • DFT discrete Fourier transform
  • the DFT and other such transforms produce multiple separable components.
  • the DFT generates complementary sets of coefficient data representing magnitudes and phases. These components are separable; that is, either may be stored or processed independently of the other.
  • Operation 231 selects less than all components of the transformed image data as the transform- domain representation of the image — in this illustration, only the magnitude component. Operation 231 may also perform functions such as scaling to remove negative data values from the original image, or selecting only the most significant portion of the magnitude coefficients for communication.
  • Matrix 232 symbolizes the output data stream of transform-domain data for the image.
  • Block 233 symbolizes ancillary data that might or might not be sent with the image data, including a header and image parameters such as values or locations for the marker(s) or padding.
  • Fig. 4 implements one of a number of methods for restoring a modified image from only a component of data in a transform domain.
  • Software or hardware modules 150-160, Fig. 1 may carry out method 400.
  • method 400 can be thought of as a phase-retrieval process; that is, it regenerates the missing phase component.
  • padding is sometimes preferably applied to the image in the transform domain, rather than in the base domain.
  • Padding usually increases the size of the image in the transform domain as well as in the base domain, requiring extra storage space and/or communication time for the transform-magnitude representation of the image in channel 140, Fig. 1. In such applications, padding can be delayed until the reconstruction of the image.
  • Block 220' in Fig. 4 performs this operation in process 400 whenever it has not already been performed as a part of process 200, or as a part of process 600, Fig. 6. Example methods for creating desired base-domain padding by manipulations in the transform domain will be described for process 600, Fig. 6.
  • Operation 410 generates a mask as an initial iteration of a padded image in the base domain of the image.
  • This example supposes a spatial base domain in a two-dimensional format such as image 310, Fig. 3 A.
  • a convenient mask assigns a '1' value to each pixel at the locations of the original unpadded image.
  • the padded areas contain the known pad values at the known locations of the padding.
  • the marker location contains the known marker value, possibly received from data 232; e.g., if method 200 had applied a marker value of 2 18 at location ⁇ 0,0 ⁇ of the original image, then block 410 sets mask location (0,0 ⁇ to 2 18 .
  • Operation 420 transforms the padded and marked iteration to the transform domain, e.g., to magnitude and phase components in the frequency domain.
  • the magnitude component is discarded.
  • the first iteration is the mask from block 410; subsequent iterations arrive from block 450.
  • Operation 430 receives the phase component of the transformed iteration, and combines it with the magnitude component of the transformed and modified original image.
  • the result represents an image in the transform domain having magnitude values from the image to be restored, but having phase values from an approximation — possibly quite inaccurate — to that image.
  • this operation may constitute a complex multiplication Me ) ⁇ where M represents the magnitude component from received data 232 and ⁇ is the phase component from block 420.
  • Operation 431 takes an inverse transform of the combined transform- domain image to produce an image iteration in the base domain having the format of 310 or 320, Fig. 3B-C.
  • An inverse DFT may produce complex values; block 431 selects the real parts of such values to represent the pixels of the iterated image.
  • Operation 440 then reinstates the known pixels of the pad areas such as 311 in Fig. 3B.
  • the pad areas such as 311 in Fig. 3B.
  • the inverse transform may have generated some untoward results, such as pixels outside the permitted range of values, or negative pixels.
  • Block 441 scales the pixel data from block 440 into a desired form for further processing. Scaling functions may include renormalizing the magnitude range, translating the levels up or down, and taking absolute values.
  • Block 442 inserts the known marker value(s) at the predetermined known location(s) in the base- domain version of the iterated restored image.
  • Block 442 could alternatively recompute the marker value, e.g., by multiplying the known constant K times the sum of all the pixels values in the data from block 441.
  • the absolute value of the scaled values from block 441 can be calculated after the marker is applied in block 442, as well as before.
  • Block 450 determines whether or not the current iteration is the final one.
  • line 451 returns control to block 411, using the output of operation 442 as the next iteration of the restored image. Many images converge sufficiently after 15 to 20 iterations.
  • Every iteration of method 400 corrects the base-domain image with known data values at certain locations. With a suitably chosen marker value, replacing the marker location with its known fixed value repeatedly during the iterations anchors the process, ensuring that the iterated restored image will in fact converge regardless of any special conditions or characteristics of the original image.
  • the padding provides functional support for the image field, if required.
  • Operation 460 trims the padding from the final iteration of the base- domain image, converting it back to the format of the original. For an image such as 310, block 460 strips off the pad locations 311, leaving the image field 300. Other formats such as 320 strip pad areas 323 in a similar manner. Inserting a marker value into the transmitted image obliterates the original value of the pixel at the marker location.
  • Operation 461 replaces that pixel with a value hopefully more nearly approaching that of the original image.
  • block 461 averages the values of pixels near the marker location and replaces that pixel with the interpolated value.
  • a simple interpolation averages the values of the pixels surrounding the marker location. Under some conditions, interpolation of the marker bit may interfere with convergence.
  • the original image 310 could have been augmented by a row of pixels at the top and a column at the left side, then the restored image trimmed to remove them.
  • Block 462 outputs the restored image in its base domain for further manipulation or storage.
  • Method 400 pertains to images in other formats, such as 320, Fig. 3C. Converting a two-dimensional image to a sequence of one-dimensional row or column data in the base domain may reduce computation time and storage space during restoration, and may facilitate implementation in an integrated circuit. Again, methods 200 and 400 are broadly useful for images in any format, and for data other than spatial images. Manipulation of the image in the base domain is transparent to restoration according to the invention. For example, the original image 300, Fig. 3 A, could have been compressed by any of a number of conventional algorithms. When the image is later restored, applying an inverse algorithm at block 462 recovers the original image in uncompressed form. Listings I and ⁇ , below, contain code in the Matlab® programming language, available from The Math Works, Inc.
  • Listing I implements a routine for restoring a two-dimensional image such as 320, Fig. 3B.
  • Listing II illustrates a routine for restoring one-dimensional data such as one of the rows 321 of image 320, Fig. 3C.
  • the function names f f t2 and f f tl respectively represent two-dimensional and one-dimensional discrete fast Fourier transforms.
  • Fig. 5 demonstrates the performance of method 400, Fig. 4, in restoring a representative image.
  • the abscissa of graph 500 denotes number of iterations.
  • the ordinate is calibrated in terms of the base- 10 logarithm of percentage normalized mean squared error (NMSE).
  • NMSE percentage normalized mean squared error
  • Figure 5 demonstrates two convergence performance curves of method 400, Fig. 4, in restoring two representative images.
  • the abscissa of graph 500 denotes number of iterations.
  • the ordinate is calibrated in terms of the base- 10 logarithm of percentage normalized mean squared error (NMSE).
  • NMSE percentage normalized mean squared error
  • the curves indicate that the convergence rates, i.e., NMSE per iteration, are similar for both images.
  • Fig. 6 illustrates an alternative method for modifying an image for restoration by a method such as 400, Fig. 4.
  • the nature of the sensor precludes modifying the original image in the base domain, ruling out a modification process similar to 200, Fig. 2.
  • Sensor 114, Fig. 1 offers an example. Even when both components of a transformed image or other signal are available, some applications may severely distort one component, leaving reliable data only in the other component. For example, blind convolution attempts to restore data from an unknown signal convolved with noise or filtered through an unknown system. In other environments, the base and/or complete transformed image data may be available and satisfactory, but there are no convenient facilities to modify it prior to transforming and sending it.
  • Method 600 modifies a transform magnitude component of an image directly in the transform domain, instead of modifying a base-domain image first and then transforming it as in method 200. This method is employed when the image is not available in base-domain form; however, it may also be employed when the base-domain image is available but had not been marked for some reason.
  • Block 601 receives the available component of an arbitrary image or other data in a transform domain. This example employs a magnitude component of a Fourier transform of a two-dimensional image.
  • Block 610 selects a marker value.
  • This base-domain value may be the same as for block 210, Fig. 2, although it must be calculated from the transformed image in this case.
  • Block 611 inserts the marker.
  • the base-domain marker value from block 610 may be converted to the transform domain and inserted into the magnitude data at an appropriate pixel location.
  • the base-domain value can be represented as a high- valued delta function at the marker location. This can be implemented by adding the argument value of the delta function to each of the components of the image data in the transform domain, in block 211, Fig. 2.
  • the marker may be sent in base-domain form as separate data 233. Calculating and inserting the marker may occur when and where the image data is generated, or at the time and location that the image is reconstructed. Although inserting the marker is usually easier in the base domain when the original image is available in that domain, the marker could be inserted in the transform domain in that case as well, if desired.
  • Block 620 applies padding to the transform component directly in the transform domain by adding a value to each of the magnitude coefficients in the transform domain. This is an approximation that produces a negligible error in the reconstruction.
  • One way to add known padding values at known locations in the base domain of a one-dimensional image sequence such as 320, Fig. 3C, is to catenate the magnitude component of a Fourier transform to itself. This forces alternate pixel locations in the base image domain to a '0' value. These locations then become the padding. Folding the component coefficients to create a symmetry is another example of a way to introduce padding directly in the transform domain. Operation 460, Fig. 4 can easily accommodate stripping such locations from the restored image. Similar techniques exist for other data formats.
  • Method 800 outputs the same image data 232 as does method 200, Fig. 2.
  • Ancillary data 233 may be generated as well in some cases.
  • JP2 angle (JJX); % Phase in radians
  • JJX IM2.*exp(j*JP2) ; % Compose new XJ
  • JJ real (ifft2 (JJX) ) ;
  • J JJ(1:N1, 1:N2) ;

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Abstract

L'invention concerne un procédé et un système de restauration d'image, dans lesquels une image dans un domaine source (spatial, par exemple) est restaurée à partir d'un seul composant (d'amplitude, par exemple) d'une image à domaine de transformée (de Fourier, par exemple), selon une technique consistant à combiner ce composant avec un composant complémentaire (de phase, par exemple) d'une itération précédente transformée. Cette technique consiste ensuite à transformer chaque itération en domaine source et à appliquer à nouveau des données de marque et de remplissage prédéfinis et déterminés à l'itération, durant chaque itération, à des fins de convergence. L'image restaurée peut être réduite et ajustée et la position de la marque interpolée. L'image de départ à restaurer est modifiée de façon à ce qu'elle contienne la marque déterminée et le remplissage déterminé, à des emplacements déterminés. Ces derniers peuvent être introduits dans le domaine source ou dans le domaine de transformée.
PCT/US2002/038958 2001-12-05 2002-12-05 Restauration d'image a partir de donnees de composants transformes WO2003049420A2 (fr)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5825892A (en) * 1996-10-28 1998-10-20 International Business Machines Corporation Protecting images with an image watermark
US6178271B1 (en) * 1996-04-29 2001-01-23 The Mclean Hospital Corporation Methods and systems for registering image data
US6195465B1 (en) * 1994-09-21 2001-02-27 Ricoh Company, Ltd. Method and apparatus for compression using reversible wavelet transforms and an embedded codestream
US6427028B1 (en) * 1996-08-14 2002-07-30 France Telecome Method for the transformation of images signals on arbitrarily- shaped segments

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6195465B1 (en) * 1994-09-21 2001-02-27 Ricoh Company, Ltd. Method and apparatus for compression using reversible wavelet transforms and an embedded codestream
US6178271B1 (en) * 1996-04-29 2001-01-23 The Mclean Hospital Corporation Methods and systems for registering image data
US6427028B1 (en) * 1996-08-14 2002-07-30 France Telecome Method for the transformation of images signals on arbitrarily- shaped segments
US5825892A (en) * 1996-10-28 1998-10-20 International Business Machines Corporation Protecting images with an image watermark

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