Abstract:
A system for watermarking an image file selects coefficients using a selection procedure that is kept secret, and assigns the selected coefficients to coefficient pairs. The difference between the coefficients of the pairs is biased by a value that varies, preferably in a pseudo-random manner, and the biased differences are used to generate signature bits that characterize the authentic image at different locations. To detect an unauthorized alteration after the image file has been watermarked, coefficient pairs are selected using the same secret procedure that was originally used to generate the signature bits. The difference between the coefficients of the pairs is then biased and checked against the signature bits. Using a varying bias value permits a tolerance band for reducing false alarms to be used without the risk that would otherwise exist that evidence of an attack on the original image might be hidden in the tolerance band.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     The present invention is directed to a method and a system for watermarking an electronically depicted file, particularly an image file, so that unauthorized alterations in the file can be detected.  
         [0002]     A colored photograph of a scene such as a bowl of fruit typically contains many variations in color and shading. The apple may be predominantly red but have regions of a brownish or yellowish hue, and perhaps areas that are still green to one degree or another. The bananas are various shades of yellow and brown, with maybe some green, too, and the grapes are purple. Shadows and highlights suggest the curvature of the fruit. Despite this visual complexity, though, every spot on the photograph can be depicted by a point in a color space defined by a red axis, a green axis that is orthogonal to the red axis, and a blue axis that is orthogonal to both the red and green axes. At the origin of this RGB coordinate system, where all three colors have the value of zero, the visual impression is black. At some maximum value along the red axis, green axis, and blue axis, the visual impression is white. Between black at the origin and white at some common, maximum value along all three axes, a line can be drawn that depicts various shades of gray.  
         [0003]     This line that depicts various shades of gray can be used to establish an axis in a new color space. This axis is called the luminance axis (generally designated by the letter Y), and it is accompanied in the new color space by a red chrominance axis (commonly designated Cr or V) and a blue chrominance axis (commonly represented by Cr or U). Just as every spot on the photograph could be represented in the RGB color space, every spot can be represented in the YCrCb color space. Simple equations for translating from the RGB color space to the YCrCb and vice versa are well known. Other color spaces are also known and used on occasion.  
         [0004]     The human eye is much more sensitive to changes in the gray level than it is to changes in color. This means that the luminance information is more important than the chrominance information or, in other words, the apparent quality of an image falls only slowly as chrominance information is discarded. Various image encoding techniques (which also typically permit data compression) exploit this fact in order to reduce the file size of an image without a commensurate loss in the apparent quality of the image.  
         [0005]     One such encoding technique is the original JPEG technique, introduced by the Joint Photographic Experts Group in the early 1990s. It is described in the standard ISO/IEC 10918-1. The original JPEG technique (occasionally called “JPEG-original” hereafter) will now be summarized with reference to  FIGS. 1A and 1B .  
         [0006]     In  FIG. 1A , an image encoder  20  receives an input signal from an image source unit  22 , such as a digital camera, a scanner, or a memory that stores the image. It will be assumed that the input signal is a digital signal with red, green, and blue components. The encoder  20  includes a color space converter  24  that converts the red, green, and blue components of the input signal to a YCrCb color space. The luminance (or Y) component is fed to a luminance branch  26 . The red chrominance (or Cr) component is fed to a red chrominance branch  28 , and the blue chrominance (or Cb) component is fed to a blue chrominance branch  30 . The branch  26  for the luminance component includes a subdivision unit  32 , a discrete cosine transform (DCT) unit  34 , a quantizer  36 , and an entropy encoder  38  (a Huffman encoder, which reduces the file size by assigning codes to data words, with the shorter codes being assigned to the data words that are more likely to be present and with longer codes being assigned to less likely data words).  
         [0007]     The subdivision unit  32  divides the luminance component into blocks that are 8 pixels wide and 8 pixels high. The DCT unit  34  performs a discrete cosine transform or DCT on each of these blocks. The discrete cosine transform, which is related to the Fourier transform, results in sixty four coefficients for weighting sixty four basis functions, or basis images. The sixty four basis functions employed in the discrete cosine transform essentially represent patterns that are coextensive with the original block and that depict the frequency of changes in the horizontal direction of the block and in the vertical direction of the block. Here, “frequency” refers to the rate of variations with respect to space, not time. The portion of the original image that is represented by the 64 pixel values in the 8×8 block is equivalent to the sum of the sixty four basis functions, weighted by the coefficients generated via the discrete cosine transform.  
         [0008]     The sixty four coefficients that are generated by DCT unit  34  for each block are placed in array, in a predetermined order, and provided to the quantizer  36 . It is the quantizer  36  (along with the quantizers in the chrominance branches) that is the primary engine for data compression. The quantizer  36  employs a quantization table having sixty four quantization values, one for each of the sixty four DCT coefficients. Different quantizing tables may be selected depending upon the desired quality of the compressed image. The higher the quality, the less the compression. The quantizing values in the selected table are integers (some of which are typically the same). The quantizer  36  quantizes the DCT coefficients by dividing each coefficient by its corresponding quantizing value and then rounding down to the nearest imager, discarding any fractional results. Since the DCT coefficients for basis functions with higher frequency variations tend to be small, in practice, and also since the quantizing values for these coefficients are larger in magnitude than the quantizing values for coefficients corresponding to lower frequency basis functions, the DCT coefficients for the higher frequency basis functions are frequency quantized to 0. The elimination of fractional results during the quantization process and the likelihood that a substantial number of the quantized coefficients will turnout to be 0, in practice, means that substantial data compression is achieved by the quantizer  36 . Further data compression is achieved by the encoder  38 , which entropy encodes the quantized DCT coefficients and supplies them to a formatting unit  40 .  
         [0009]     The branches  28  and  30  for the chrominance components are the same, in general, as the branch  26  described above for the luminance component. The primary difference is in the quantizers. Since the human eye is less sensitive to spatial variations in color than it is to spatial variations in luminance, the quantizing tables used by the quantizers in branches  28  and  30  have quantizing values that are larger in magnitude than the quantizing values in the table employed in quantizer  36 . The result is that the amount of data discarded in the chrominance branches is larger than the amount discarded in the luminance branch, without this increased loss of data degrading the apparent quality of the compressed image significantly. The quantized-and-encoded DCT coefficients in the chrominance branches, like the quantized-and-encoded DCT coefficients in the luminance branch, are supplied to the formatting unit  40 .  
         [0010]     The formatting unit  40  assembles the quantized-and-encoded coefficients into an encoded image data frame. It provides the frame with a header having various information, including information about the quantization tables employed and the encoding by the encoders  38 , so that the encoded image can be reconstructed. The frame is then delivered to a utilization unit  42 , such as a storage device, an interface to a transmission medium which conveys the frame to another location, or a decoder to reconstruct the image for immediate presentation on a display.  
         [0011]     An image decoder  44  for reconstructing the image is shown in  FIG. 1B . It receives the encoded image data frame from an encoded image source  46 , and includes a payload extractor  48  which delivers the quantized-and-encoded coefficients for luminance to a luminance branch  50 , the quantized-and-encoded coefficients for red chrominance to a red chrominance branch  52 , and the quantized-and-encoded coefficients for blue chrominance to a blue chrominance branch  54 . The payload extractor  48  also retrieves information about quantization and encoding from the header of the frame and supplies this information to the branches  50 - 54 . Each of these branches basically performs operations that are the inverse of the operations performed by the corresponding branches of the image encoder  20  in  FIG. 1A . For example, the luminance branch  50  includes a decoder  56  that expands the data encoded by encoder  38 . The expanded data is provided to an inverse quantizer  58 , which multiplies the quantized coefficients by the same quantization value by which they were divided in the quantizer  36 . The results are provided to an inverse transform unit  60 , which performs an inverse discrete cosine transform in order to regenerate 8×8 blocks of pixel values that approximate the original 8×8 blocks. Such blocks are assembled into a total luminance image by a subdivision assembly unit  62 . The total luminance image, together with total chrominance images from the branches  52  and  54 , are then supplied to a color space converter  64 , which transforms the image back to RGB space. The reconstructed image can then be shown on a utilization device  66  such as a display device.  
         [0012]     Photo editing software is available which permits image files to be manipulated in a wide variety of ways. An image may be cropped, for example, or altered by replacing a portion of the image with content taken from a different image. Other editing possibilities include increasing the compression, adjusting the colors, copying one portion of an image over a second portion in order to obliterate the second portion, and so forth. Such alterations may have a benign purpose, as when a blemish is removed from a portrait, or they may have a malicious purpose, as when the picture of an automobile accident is altered in an attempt to avoid responsibility by deception. Regardless of the purpose, alteration of an image can be characterized as an attack on the integrity of the image. It is desirable to be able to detect such an attack. An image is said to be watermarked if means are provided for detecting an attack, other than perhaps an acceptable degree of compression (which carries with it corresponding reduction in image quality), or adjustment of brightness or colors.  
         [0013]     The springboard for the present invention is a watermarking technique described by Ching-Yung Lin and Shih-Fu Chang (who is one of the co-inventors herein) in an article entitled “Semi-Fragile Watermarking for Authenticating JPEG Visual Content,” Proc. SPIE, Security and Watermarking of Multimedia Contents, San Jose, Calif., pp. 140-151, January 2000. Here, “semi-fragile” means that the watermarking technique is sufficiently flexible to accommodate acceptable manipulation of the image, such as a modest degree of compression, but has a low tolerance for other other types of image manipulation.  
         [0014]     In the watermarking technique described in the above-noted article by Lin and Chang, so-called “signature” bits are generated from an image and then embedded in the image. To generate the signature bits, 8×8 blocks of an image are grouped in pairs of blocks using a secret mapping function. For each block pair, predetermined DCT coefficients are selected. The signature bits are generated on the basis of the relationship between the magnitude of the selected coefficients for one block of a pair and the magnitude of the selected coefficients for the other block of the pair. More specifically, if a given coefficient for the first block of a pair is smaller than the given coefficient for the second block of the pair, a signature bit of 0 is generated; and otherwise, a signature bit of 1 is generated. This can be expressed as: 
 
S i =1 if  F   i (block 1)− F   i (block 2)≧0, and 
 
S i =0 if  F   i (block 1)− F   i (block 2)&lt;0  Equations (1) 
 
 Here, S i  is the i-th signature bit, which characterizes the relationship between the i-th DCT coefficients F i  generated from block 1 and block 2 of a two-block pair. 
 
         [0015]     The signature bits S i  are embedded by using a secret mapping function to select to serve as hosts for the embedding. The embedding is accomplished by adjusting the least significant bits of the host coefficients in accordance with the signature bits.  
         [0016]     This procedure for generating signature bits and selecting host coefficients in which they will be embedded will now be illustrated by an example, with reference to  FIGS. 2A-2C .  FIG. 2A  shows an image  68  of a house and the sun in the sky above it. Using a first secret mapping function, 8-pixel by 8-pixel blocks  70 ,  72 , and  74  are selected and are paired with 8-pixel by 8-pixel blocks  76 ,  78 , and  80 .  FIG. 2B  illustrates an array  70 ′ for receiving the sixty four DCT coefficients generated from, say, the luminance component of block  70 . Summarily,  FIG. 2C  illustrates an array  76 ′ for receiving the sixty-four DCT coefficients generated from the luminance component of block  76 , which is paired with block  70 . Using further mapping rules, signature-source coefficients in the arrays  70 ′ and  76 ′ that are to be used for generating signature bits are selected, and host coefficients where the signature bits are to be embedded are selected as well. This is illustrated, in this example, by using circles in  FIGS. 2B and 2C  to designate source coefficients selected for generating signature bits. Hexagons are used to designate host coefficients selected for embedding the signature bits.  
         [0017]     For purposes of illustration, suppose that the first signature bit S 1  for the block pair  70 ,  76  is to be generated from the coefficient at row number 1, column number 1 of array  70 ′ and the corresponding coefficient at row number 1, column number 1 of array  76 ′, and that this signature bit is to be embedded in the coefficient at row 6, column 5 of array  70 ′. Applying Equations 1, the signature bit to be embedded would be S 1 =1 if the coefficient at row 1 column 1 in array  70 ′ is as large or larger than the coefficient at row 1, column 1 of array  76 ′, and S 1 =0 if the coefficient at row 1, column 1 of array  70 ′ is smaller than the coefficient at column 1, row 1 of array  76 ′.  
         [0018]     The embedding operation described in the above-noted article by Lin and Chang is conducted by replacing the DCT coefficient F 6,5  that would normally appear at row 6, column 5 of array  70 ′ (that is, the host coefficient in this example) by a modified value F* 6,5 , called a reference coefficient. It is calculated a two-step procedure from F 6,5 , the signature bit S i  (where i=1 in this example), and the quantization value Q 6,5  by which F 6,5  would normally be divided during the subsequent quantization procedure. In the first step, F 6,5  and Q 6,5  are used to calculate an intermediate value, as follows:  
               f     6   ,   5       =     IntegerRound   ⁢           ⁢       F     6   ,   5           Q     6   ,   5       +   1                 Equation   ⁢           ⁢     (   2   )               
 
 Here, “IntegerRound” means rounded up or down to the nearest integer. In the second step, the reference coefficient F* 6,5  is calculated as follows:  
                     F     6   ,   5     *     =       f     6   ,   5       ⁡     (       Q     6   ,   5       +   1     )                           ⁢         if   ⁢           ⁢   the   ⁢           ⁢   LSB   ⁢           ⁢   of   ⁢           ⁢     f     6   ,   5         =     S   i       ,               and               F     6   ,   5     *     =       [       f     6   ,   5       +     sgn   ⁡     (         F     6   ,   5           Q     6   ,   5       +   1       -     f     6   ,   5         )         ]     ⁢     (       Q     6   ,   5       +   1     )                           ⁢       if   ⁢           ⁢   the   ⁢           ⁢   LSB   ⁢           ⁢   of   ⁢           ⁢     f     6   ,   5         ≠     S   i                     Equation   ⁢           ⁢     (   3   )               
 
 Here, “sgn” is minus 1 if the expression following it is negative and plus 1 if the expression following it is not negative. 
 
         [0019]     In the authentication process, signature bits are extracted from the received image and check to see whether they meet criteria set forth in the article by Lin and Chang. The article introduces two theorems, one of which basically provides that there is an invariant relationship, before and after quantization, between DCT coefficients generated from two 8×8 non-overlapping blocks of an image. The second theorem basically provides that, under certain conditions, the exact value of an unquantized coefficient can be reconstructed after quantization. In particular, the second theorem asserts that if a DCT coefficient is modified to an integral multiple of a pre-determined quantization value which is larger than all possible quantization values in subsequent JPEG compression, then this modified coefficient can be exactly reconstructed following JPEG compression by use of the same quantization value that was employed in the original modification. This theorem provides the rationale for using the reference coefficients F*. From Equations 3, it will be apparent that embedding the signature bits as described in the above-noted article by Lin and Chang results in, at worst, a rather small modification in the quantized values. The procedure permits areas where an image has been attacked to be identified, in many cases.  
         [0020]     The Lin and Chang article noted above addresses the possibility of false alarms, and mentions the possibility of using a tolerance bound. Such false alarms may arise due to noise, particularly if the noise is accompanied by acceptable modifications such as editing to adjust brightness. The possibility of a false alarm rises to significant levels if the i-th coefficients for the blocks of a pair have close numerical values when Equations (1) are applied, since in this case the signature bit S i  is determined on the basis of a small positive or negative number. A tolerance bound M can be established, during the signature-checking stage, for withholding judgment about whether an attack has been made if the absolute value of the difference between the coefficients is smaller than M, as follows:  
                           TABLE 1                                   Relationship Range   Signature S i                             F i  (block 1)-F i  (block 2) &gt; M   Only S i  = 0 is acceptable.           |F i  (block 1)-F i  (block 2)| ≦ M   Don&#39;t care.           F i  (block 1)-F i  (block 2) &lt; −M   Only S i  = 1 is acceptable                      
 
         [0021]     This can be illustrated with the aid of  FIG. 2D . The horizontal axis represents the difference between the i-th coefficient of the two blocks of a pair when an image is encoded (that is, on the signature-generation side), and the vertical axis represents the difference as determined when the encoded image is decoded (that is, on the signature-verification side). A signature bit having a value S i =0 is generated on the signature-generation side when the difference is greater than or equal to 0 (see Equations 1), or to the right side of the vertical axis. Without the tolerance bound M, one would expect the difference between the coefficients at the verification site to be 0 or greater in the absence of an attack. What the tolerance bound M does is to provide an indeterminate band of width 2M that follows the horizontal axis in  FIG. 2D .  
         [0022]     While the tolerance bound M reduces false alarms, it also provides a “safe harbor” for attacking an image. The reason is that an attack cannot be detected if the absolute value of the difference between the quantized coefficients is less than M. If attacks which meet this constraint were impossible for even very difficult, this vulnerability could be overlooked. Unfortunately, attacks such as replacing an object from one image with an object from another image, copying a portion of the background in an image over an object to hide the object, deleting text from a white background, inserting an object, or drawing an object on a light background may well result in quantized coefficients whose difference is small.  
         [0023]     Image encoding techniques employing discrete cosine transforms together with compression have proven themselves to be very useful, as evidenced by the widespread success of JPEG-original. Nevertheless, image encoding using other basic approaches continues to attract attention. One of these alternative approaches employs wavelet transforms to generate coefficients, instead of discrete cosine transforms. This approach has been selected for use in JPEG-2000. The specifications for JPEG-2000 have been published as ISO/IEC JTC1/SC29/WG1.  
         [0024]     Like the discrete cosine transform, a wavelet transform is related to the well-known Fourier transform. Unlike a discrete cosine transform, however, a discrete wavelet transform analyzes an input signal with reference to compact functions that have a value of zero outside a limited range. Cosine terms, in contrast, have recurring, non-zero values outside a limited range. In the image encoding field, discrete wavelet transforms typically employ a family of orthogonal wavelengths generated by translating a so-called “mother wavelet” to different positions and by dilating (or expanding) the mother wavelet by factors of two. Various mother wavelets that can be used to generate families of orthogonal or almost-orthogonal wavelets for use in a DWT are known. Using a DWT to analyze an input signal generates coefficients which, basically, provide an index of how well the input signal correlates with the wavelets. The coefficients provide frequency information about the input signal (in view of the dilations) as well as position information (in view of the translations).  
         [0025]      FIG. 3A  illustrates an image encoder  80  which receives an RGB image from an image source unit  82 . The encoder  80  includes a color space converter  84  which converts the image to a luminance (Y) component that is supplied to a luminance branch  86 , a red chrorninance (Cr) component that is supplied to a red chrominance branch  88 , and a blue chrominance (Cb) component that is supplied to a blue chrominance branch  90 . The luminance branch  86  includes a subdivision unit  92  that separates the luminance component into sub-units known as tiles, which are supplied to a discrete wavelet transform unit  94 . The DWT unit  94  generates wavelet coefficients by using digital filters, which have characteristics that are based on the wavelet family employed.  
         [0026]      FIG. 3B  schematically illustrates a conceptual implementation of the DWT unit  94 . The input signal from unit  92 , representing a tile of the luminance component, is supplied to a high pass filter  96 , which filters in the row direction and which is followed by a down-sampler  98 , which down-samples the filtered signal by two (meaning that every other sample is discarded). The filter and down-sampled signal is then supplied to a high pass filter  100 , which filters in the column direction. The result is down-sampled by two by a down-sampler  102 . The result is a set of the DWT coefficients in a so-called 1HH band (“1” indicating the first level of decomposition and “HH” meaning high pass filtration in both the row and column direction). The output of down-sampler  98  is also supplied to a low pass filter  104 , which filters in the column direction, and the filtered output is down-sampled by two by a down-sampler  106 . This provides a set of DWT coefficients for a 1HL band.  
         [0027]     In addition to being high pass filtered in the row direction by the filter  96 , the signal from unit  92  is low pass filtered in the row direction by a filter  108 . The result is down-sampled by two by a down-sampler  110  and then supplied to high pass and low pass filters  112  and  114 , which filter in the column direction. The output of filter  112  is down-sampled by a down-sampler  116  to provide a set of DWT coefficients for a 1LH band. The output of filter  114  is down-sampled at  118  to complete the first level of decomposition of the tile.  FIG. 3C  schematically illustrates the four sub-bands of DWT coefficients resulting from the first level of decomposition.  
         [0028]     The 1LL sub-band represents low frequency information in both filtering directions at various positions. It is down-sampled by two in both directions and thus corresponds generally to a smaller-sized, lower-quality version of the image content in the original tile. The coefficient in the 1HL, 1HH, and 1LH sub-bands represent high frequency information at various positions. This high frequency information could be used at this stage to augment the low frequency information in the 1LL sub-band so as to reconstruct the image content of the original tile. However, it is quite common to continue the decomposition for one or more additional levels.  
         [0029]     In  FIG. 3B , the output of down-sampler  118  (representing the 1LL sub-band) is provided to a high pass filter  120 , which filters in the row direction, and the filtered signal is down-sampled by two at  122  and then supplied to high pass and low pass filters  124  and  126 , both of which filter in the column direction. The filtered results are down-sampled to provide coefficients in the 2HH and 2HL sub-bands. The output of down-sampler  118  is also low pass filtered in the row direction, down-sampled, high pass filtered in the column direction, and down-sampled to provide coefficients in a 2LH sub-band. This process of repeatedly filtering and down-sampling the low pass residue can continue.  FIG. 3D  illustrates sub-bands of coefficients for the second and third levels of decomposition in the region where the 1LL sub-band (see  FIG. 3C ) would have been had only one level of decomposition been employed.  
         [0030]     Returning now to  FIG. 3A , DWT coefficients from unit  94  are arranged in an array and quantized by quantizer  128  in accordance with quantizing values in a quantization table, the table that is selected (that is, the magnitudes of the quantizing values) depending upon the desired degree of compression in conjunction with the amount of image deterioration that can be tolerated to achieve this compression. As was the case with the DCT transform, the values in the selected table are integers which vary in magnitude depending upon the visual significance of the particular coefficients which they are to quantize. A DWT coefficient is quantized by dividing it by its quantization value from the table (some of the quantization values in the table may be numerically the same despite the fact that they are applied to different coefficients) and any remainder is discarded.  
         [0031]     With continuing reference to  FIG. 3A , quantized DWT coefficients are supplied to an entropy encoder  130  and then to a formatting unit  132 , which also receives quantized-and-encoded DWT coefficients for the red and blue chrominance components from branches  88  and  90 . The formatting unit  132  places the quantized-and-encoded coefficients in an encoded image data frame along with various other information, including information for use in regenerating the encoded image. The frame is then supplied to an encoding image utilization unit  134  such as a storage device, a decoder, or a signal transmission unit for conveying the encoded image data frame to some desired destination.  
         [0032]     An image decoder  136  is illustrated in  FIG. 3E . It receives an encoded image data frame from a source  138 . A payload extractor  140  retrieves the information for decoding the image and supplies the quantized and entropy-encoded coefficients for the luminance component to a luminance branch  142 . The quantized and entropy-encoded coefficients for red and blue chrominance are supplied to chrominance branches  144  and  146 . In luminance branch  142 , a decoder  148  expands the entropy-encoded data so as to supply the quantized coefficients for the tiles of the luminance component to an inverse quantizer  150 , which multiplies the quantized coefficients by values in a table. These values match the values by which the coefficients were divided during the quantizing procedure employed by the image encoder  80 . After an inverse DWT transform by a unit  152 , which regenerates pixel values for the tiles of the luminance component from the DWT coefficients, the tiles are combined into a total luminance image by a subdivision assembly unit  154 . Pixel values for the combined tiles of the luminance and chrominance components are converted back to RGB space by a converter  156  and then supplied to a utilization device  158  such as a display apparatus.  
       SUMMARY OF THE INVENTION  
       [0033]     An object to the present invention is to provide a watermarking method and system that has a small error rate but that lacks the vulnerability to attack that has been needed to achieve a small error rate in the prior art.  
         [0034]     Another object of the invention is to provide a watermarking method and system in which a tolerance band for reducing false alarms is effectively moved around, in a plane having one dimension defined by features extracted from a first file (such as a first image file) and having another dimension defined by features extracted from a second file (such as a second image file, which is to be checked for authenticity with respect to the first file), so as to expose evidence of an attack that might otherwise be hidden in the tolerance band. A related object is to move the tolerance band to different positions in this plane in a pseudo-random manner.  
         [0035]     These and other objects that will become apparent during the ensuing detailed description can be attained, in accordance with one aspect of the invention, by providing a method in which groups (such as pairs) of coefficients in a first file are selected using a predetermined selection rule; first calculated values are determined from the coefficients in each group using a predetermined calculation formula (such as subtracting one coefficient in a pair from the other coefficient in the pair); the first calculated values are combined with bias values to generate biased calculated values; the biased calculated values are compared to a predetermined number (such as zero) to calculate signature values for the first file; and the signature values are then preserved, so that they can subsequently be used for determining whether a second file is an authentic version of the first file.  
         [0036]     In accordance with another aspect of the invention, a method is provided in which groups of coefficients in a first file are selected using a predetermined selection rule; first calculated values are determined from the coefficients in each group using a predetermined calculation formula; the first calculated values are combined with bias values to generate first biased calculated values; the first biased calculated values are compared to a predetermined number to generate signature values for the first file; groups of coefficients in the second file are selected using the same predetermined selection rule that was employed for the first file; second calculated values are determined from the coefficients in each group of the second file using the same calculation formula that was employed for the first file; the second calculated values are combined with bias values (the same bias values that were employed with the first file) to generate second biased calculated values; and the second biased calculated values are compared with the signature values. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0037]      FIG. 1A  is a schematic block diagram illustrating a conventional image encoder using discrete cosine transforms;  
         [0038]      FIG. 1B  is a schematic block diagram of a conventional image decoder for regenerating the images encoded by the arrangement of  FIG. 1A ;  
         [0039]      FIG. 2A  illustrates an example of the selection of pairs of blocks in accordance with a prior art technique;  
         [0040]      FIGS. 2B and 2C  illustrate arrays of DCT coefficients in pairs of blocks, with an example of coefficients that are used to generate signature bits and coefficients in which the signature bids are to be embedded in accordance with the prior art technique being marked by circles and hexagons;  
         [0041]      FIG. 2D  is a graph illustrating a tolerance bound to reduce false alarms;  
         [0042]      FIG. 3A  is a schematic block diagram illustrating a conventional image encoder using discrete wavelet transforms;  
         [0043]      FIG. 3B  is a schematic block diagram illustrating a conventional filter and down-sampling arrangement for generating wavelet coefficients;  
         [0044]      FIGS. 3C and 3D  are diagrams illustrating decomposition of an image into sub-bands of wavelet coefficients;  
         [0045]      FIG. 3E  is a schematic block diagram illustrating a conventional image decoder for regenerating an image encoded by the arrangement shown in  FIG. 3A ;  
         [0046]      FIG. 4A  is a schematic block diagram illustrating an image encoder in an accordance with a first embodiment of the present invention;  
         [0047]      FIG. 4B  is a schematic block diagram of a watermarking unit employed in  FIG. 4A ;  
         [0048]      FIG. 4C  illustrates an example of selection of pairs of blocks;  
         [0049]      FIG. 4D  is a schematic block diagram illustrating an image decoder in accordance with the first embodiment of the present invention;  
         [0050]      FIG. 4E  is a schematic block diagram of a signature verifying unit employed in the image decoder of  FIG. 4D ;  
         [0051]      FIGS. 4F-4H  are graphs showing the effect of a varying bias value;  
         [0052]      FIG. 5A  is a schematic block diagram of an image encoder in accordance with a second embodiment of the invention;  
         [0053]      FIG. 5B  illustrates sub-bands in three levels of decomposition of an image using a discrete wavelet transform, and shows an example of a technique for grouping coefficients in a sub-band into pairs;  
         [0054]      FIG. 5C  is a schematic block diagram illustrating a watermarking unit in the image encoder of  FIG. 5A ;  
         [0055]      FIG. 5D  illustrates a matrix of random values selected from a set of seven values; and  
         [0056]      FIG. 5E  is a schematic block diagram illustrating an image decoder for decoding an image that has been encoded by the image encoder of  FIG. 5A .  
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
     First Embodiment  
       [0057]      FIG. 4A  illustrates an image encoder  200  in an imaging encoding system according to a first embodiment of the present intention. The encoder  200  receives a signal representing an RBG image from an image source  202 , such as a digital camera, scanner, or storage device. The RGB color space is converted to a YCbCr color space by a color space converter  204 . The color space converter  204  delivers the luminance (Y) component of the image to a luminance branch  206 . Similarly, the red and blue chrominance components Cr and Cb are supplied to a red chrominance branch  208  and a blue chrominance branch  210 .  
         [0058]     The luminance branch  206  includes a subdivision unit  212  that subdivides the luminance component of the image into blocks of eight-pixels by eight-pixels. These blocks are supplied to a discrete cosine transform (DCT) unit  214  that performs a discrete cosine transform on the pixel values of each block in order to generate sixty four DCT coefficients for each block The sixty four coefficients for each block are grouped into an array and quantized by a quantizer  216  in accordance with a quantization table that is selected on the basis of the apparent image quality that is desired. The quantized coefficients are received by a signal embedding unit  218 , the purpose of which will be discussed later, and are then encoded by an entropy encoder  220 . The quantized-and-encoded coefficients for each block of the luminance component are delivered to a formatting unit  222 .  
         [0059]     The quantizer  216  is connected to a watermarking unit  224 , which generates a set of signature bits S i  (to be discussed later) from the quantized coefficients. The signature bits S i  are supplied to the signal embedding unit  218 .  
         [0060]     The chrominance branches  208  and  210  are similar, but their quantizers use quantization tables having larger quantization values than the quantization table used in the luminance branch  206 .  
         [0061]     The formatting unit  222  forms an encoded image data frame from the quantized-and-encoded coefficients produced by the branches  206 - 210 , and adds information in the header of the frame for use in reconstructing the image (e.g., information identifying the quantization tables, and identifying the encoding employed by the encoder  218  and the un-numbered encoders in the chrominance branches). The completed image data frame is delivered to an encoded image utilization device  226  (such as a data storage device, a means for transmitting the encoded image data frame to another location, or an image decoder which regenerates the image for a display device).  
         [0062]      FIG. 4B  illustrates the watermarking unit  224 . It includes a subtractor  228  that receives the arrays of DCT coefficients for all of the blocks of the luminance component from the quantizer  216  via an input port  230 . The subtractor  228  is also connected to a signature-generation coefficients selector  232 , which identifies coefficient pairs p i  and q i  to the subtractor  228 . These coefficient pairs are selected in accordance with a rule that is kept secret. The subtractor  228  subtracts the value of the coefficient q i  from the value of the coefficient p i  and supplies an i-th difference value (p i −q i ) resulting from the subtraction to an adder  234 . The adder  234  also receives a bias value B i  from a varying bias generator  236 , which receives a signal (not illustrated) indicating the current value of the index and “i” from the selector  232 . The adder  234  biases the difference value p i −q i  by adding the bias value B i  to it, and supplies the biased difference value to a signature generator  238 . The signature generator  238  determines the signature bits S i  in accordance with the following: 
 S i =0 if ( p   i   −q   i   +B   i )≧0 and  S i =1 if ( p   i   −q   i   +B   i )&lt;0  Equations (4)  
 The signature bits S i  are supplied to the signature embedding unit  218  via an output port  240 . The embedder  218  selectively alters the least significant bits of host coefficients as taught by the article by Lin and Chang that is discussed in the “Background of the Invention” section of this document. The host coefficients are chosen in accordance with a selection procedure that is kept secret. 
 
         [0063]     As its name suggests, the varying bias generator  236  generates bias of values B i  that very magnitude. Preferably, they vary in magnitude in a pseudo-random manner, and within a limited range. In the present embodiment, the bias values B i  are integers that range from −16 to +16. Such bias values B i  can be generated, for example, by multiplying a predetermined angle (say, pi/10) by the i-th term in a pseudo-random sequence, taking the sine of the product, multiplying by 16, and rounding to the nearest integer.  
         [0064]     One possibility for a rule that can be employed by the selector  232  in order to identify coefficient pairs p i , q i  will now be discussed with reference to  FIG. 4C . This Figure illustrates an image  242  of a house and the sun shining on the house. Starting blocks P 1 , P 2 , . . . P 1 , . . . P N  are selected, preferably at various locations outward from the central region of the image, in accordance with a predetermined selection list. A random number generator is then employed to generate x and y values that define vectors V 1 , V 2 , . . . , V 1 , . . . V N . Vector addition of the starting blocks P 1  and the random vectors V 1  then yields target blocks Q 1  that are paired with the starting blocks P 1 . It is then necessary to employ some procedure for selecting a particular one of the sixty four DCT coefficient values generated from the pixels in the pair of blocks. One way to do this is to use i mod  64  as a selection criterion. That is, for blocks P 1  and Q 1 , the first of the sixty four coefficients would be selected as the coefficients p 1  and q 1 ; for blocks P 2  and Q 2 , the second of the sixty four coefficients would be selected as P 2  and q 2 ; and so on to blocks P 64  and Q 64 , where the 64th coefficient would be selected from both blocks as p 64  and q 64 . The next coefficient pair, P 65  and q 65 , would start again with the first DCT coefficients generated for the blocks P 65  and Q 65 . It should be noted that more than one pair of coefficients can be selected within the same pair of blocks by selecting the same block P i  and the same vector V i  more than once.  
         [0065]     Turning now the  FIG. 4D , an image decoder  242  for use with the encoder  200  of  FIG. 4A  will now be described. The decoder  242  receives an encoded image data frame from an encoded image source  244 . A payload extractor  246  retrieves the encoded-and-quantized coefficients for the three components from the encoded image data frame, and supplies them respectively to a luminance branch (Y)  248 , a red chrominance branch (Cr)  250 , and a blue chrominance branch (Cb)  252 . The information in the header of the image data frame that is needed for decoding the components (e.g., information identifying the quantization tables employed and the entropy encoding) is also distributed to the branches  248 ,  250 , and  252 .  
         [0066]     The branch  248  includes a decoder  254  for expanding the entropy-encoded values, an inverse quantizer  256 , an inverse DCT unit  258 , and a subdivision assembly unit  260 , which combines the blocks of the luminance component into a total luminance image. The chrominance branches  244  and  246  are similar. A color space converter  262  receives the total luminance image and the total chrominance images and converts them to the RGB color space.  
         [0067]     A signature verifying unit  264  receives the quantized coefficients from decoder  254  and checks whether the signature bits S i  are consistent with the coefficients p i  and q i  as determined on the signature-verifying side (that is, the image decoder  242 ) to generate the signature bits. If not, the unit  264  emits a signal identifying blocks with discrepancies to a marking unit  266 . The marking unit  266  then superimposes markings, on the video image from converter  262 , to identify regions that have been attacked. The video image with superimposed markings (if any) are then supplied to a utilization device  268 , which issue usually a display device but may be an image storage device or a means for transferring the image to another location.  
         [0068]     The construction of the signature verifying unit  264  is shown in  FIG. 4E . A signature generation coefficients selector  270  selects coefficient pairs using the same secret selection procedure that was employed by the image encoder  200 . The coefficient pairs p i , q i  are identified to a subtractor  272 , which receives the coefficients themselves from the decoder  254  via a port  274 . A subtractor  272  finds the difference p i −q i  between the coefficients identified by selector  270  and supplies this difference to an adder  274 . A varying bias generator  276  generates the same bias values B i  that were generated by the generator  236  (see  FIG. 4B ) and supplies this sequence of values to the adder  274 , which supplies the biased difference (that is, p i −q i +B i ) to a criteria checker  276 .  
         [0069]     A host coefficients selector  278  identifies host coefficients to a signature retriever  280 , which also receives the coefficients themselves via a port  275 . The selector  278  selects the host coefficients using the same secret selection procedure that was employed by the signal embedding unit  218  on the signature-generation side. The retriever  280  regenerates the signature bits S i  from the coefficients identified by selector  278 , preferably using the regeneration technique outlined in the above-noted article by Lin and Chang. The signature bits are supplied to a criteria checker  276 , which checks the biased difference values against the signature bids in accordance with Table 2:  
                                 TABLE 2                       Criteria for checking signatures S i         (“M” is a margin value for reducing false alarms       due to loss compression, noise, or variations in       the accuracy of the transforms.)                                    (p i  − q i  + B i ) &gt; M   S i  = 0   Acceptable           (p i  − q i  + B i ) &gt; M   S i  = 1   Not acceptable           |(p i  − q i  + B i ) | ≦ M   S i  = 0 or 1   Acceptable           (p i  − q i  + B i ) &lt; −M   S i  = 0   Not acceptable           (p i  − q i  + B i ) &lt; −M   S i  = 1   Acceptable                      
 
 If any of the biased difference values p i −q i +B i  are not acceptable in light of the signature bit S i , a discrepancies signal is supplied to the marking unit  266  ( FIG. 4C ) via a port  282 . 
 
         [0070]     The significance of Table 2 will now be explored further with reference to  FIGS. 4F-4H .  FIG. 4F  is similar to  FIG. 2D  in that the horizontal axis represents the difference between quantized coefficient pairs when an image is originally encoded (that is, on the signature-generation side) and the vertical axis represents the difference between the quantized coefficient pairs when the encoded image is regenerated (that is, on the signature-verification side). The symbols employed label the axes in  FIG. 4F  diverges from the symbols employed to label the axes and  FIG. 2D , but the physical meaning is the same. Unlike  FIG. 2D , however,  FIG. 4F  shows a group  284  of points, several of which are marked by Xs in the drawing, signaling an attack because the difference between coefficient pairs on the signature-generation side is significantly different from the difference between the same pairs of coefficients on the signature-verification side. However, in  FIG. 4F  this attack cannot be detected because the group  284  lies within the 2M tolerance band that is provided in order to reduce false alarms stemming from noise and minor (acceptable) image manipulation, such as loss compression. In the situation shown in  FIG. 4E , the biased value B i  is 0.  
         [0071]     In  FIG. 4G , the bias value B i  has changed to a negative number, but the attack is still not detectable because the points in the group  284  are consistent with the corresponding signature values S i  and consequently be group  284  does not lie in a zone where an attack can be detected. The bias value B i  has changed again in  FIG. 4H , and this time the group  284  of points is located partially in a zone where an attack can be detected. As the value of the index “i” changes, some of points in the group  284  will be available to signal an attack and others of the points in the group will not. However, it has been found that, in case of an attack, points defined by the difference between coefficient pairs on the signature-generation side and the difference between the same coefficient pairs on the signature-generation side tend to lie in clusters or groups in actual practice. As a result, some of the points in a group resulting from an attack will generally tend to move into an attack-detectable zone when the 2M tolerance band is moved to various locations by a way of the variable bias value B i . The tolerance band still serves its purpose of reducing false alarms, but moving it to different locations with the aid of the variable bias value B i  makes it difficult for malefactor to hide an attack within the tolerance band.  
         [0072]     The second embodiment:  
         [0073]     A second embodiment will now be described with reference to  FIGS. 5A  to  5 E.  FIG. 5A  illustrates an image encoder  286  that receives an RGB image from a source unit  288 . The encoder  286  includes a converter  290  that transforms the RGB image to a YCrCb image. The luminance component is supplied to a luminance branch  292 , and the red and blue chrominance components (Cr and Cb) are delivered to chrominance branches  294  and  296 . The luminance branch  292  includes a subdivision unit  298  that subdivides the luminance component provides tiles of the component to a discrete wavelet transform or DWT unit  300 . The unit  300  performs horizontal and vertical filtration, with down-sampling, using digital filters configured to generate wavelet coefficients as previously discussed with reference to  FIGS. 3A through 3E . For purposes of illustration it will be assumed that the unit  300  executes three levels of decomposition on each tile of the luminance component, and for each tile delivers wavelet coefficients for the sub-bands resulting from this three-level decomposition to a quantizer  302 .  
         [0074]     The quantizer  302  quantizes the coefficients in accordance with quantization values in a table, and supplies the quantized coefficients to an encoder  304 , which entropy-encodes the coefficients for each tile of the luminance component and supplies them to a formatting unit  306 . The quantizer  302  also supplies the wavelet coefficients to a watermarking unit  318 . It identifies coefficients p 1 , p 2 , . . . , p i , . . . , p n  in a given sub-band using a predetermined selection rule, generates a set of vectors v 1 , v 2 , . . . , v i , . . . , v n  using a random number generator, and pairs each of the coefficients p i  with a coefficient q i  by adding the vectors to the locations associated with the coefficients p i , . . . , p n . An example is shown in  FIG. 5B , where a coefficient p i  is paired with a coefficient q i  in the same sub-band (the 1HL sub-band in the drawing). Coefficients in one or more additional sub-bands may be paired in the same way. It should be noted that the pairing is on a sub-band by sub-band basis; coefficients are not paired with coefficients in different sub-bands.  
         [0075]     After the watermarking unit  308  pairs the coefficients, it generates difference values p i −q i  by subtracting each coefficient q i  from its paired coefficient p i , adds a pseudo-random bias value B i  to the difference, and supplies a signature values S i  to the formatting unit  306 . Information identifying the sub-band from which each signature value originated is also supplied to the formatting unit  306 .  
         [0076]     The chrominance branches  294  and  296  are similar, the main difference being that the quantizers in these branches employ quantization tables that, in general, result in larger quantization steps than in the luminance branch  302 . The quantized-and-encoded coefficients, relevant information about the image (such as a file name) and about the encoder  286  (such as information identifying the quantization tables employed and entropy encoder tables), and the signature bits S i  are formatted into an encoded image data frame by the unit  306  and then delivered to an encoded image utilization device  310  (e.g., a storage device for the encoded image data frame, means for transferring it to another location, or an image decoder for restoring the image in preparation for displaying it on display device). Instead of being embedded in host coefficients, as in the first embodiment, the signature bits S i  are placed in the header of the encoded image data frame by the formatting unit  306  in the present embodiment.  
         [0077]      FIG. 5C  illustrates the construction of the watermarking unit  308 . A signature generation coefficient selector  312  identifies coefficient pairs p i , q i  to a subtractor  314 , which receives the coefficients themselves from the quantizer  302  via a port  316 . The selector  312  also identifies the second coefficient of each pair, q i , to a varying bias generator  318 . The subtractor  314  calculates the difference p i −q i  between the coefficients of the pair and supplies this difference to an adder  320 , which also receives a bias value B i  from the generator  318 . The adder calculates a biased difference value p i −q i +B i  from its inputs and supplies this biased difference value to a signature generator  322 . The generator  322  determines a signature bit S i  in accordance with Table 2 and supplies the signature bit to the formatting unit  306  by way of a port  324 .  
         [0078]     If the subdivision unit  298  ( FIG. 5A ) subdivides the luminance component into tiles that are 13 samples wide and 17 samples high, a so-called 9-7 irreversible wavelet transform will result in a nine-row, six-column matrix of coefficients in the 1HL sub-band for the tile. Similarly, other sub-bands will have matrices of coefficients, but the number of rows and columns in these matrices depend upon the particular sub-band. In the present embodiment, the varying bias generator  318  assigns pseudo-random numbers to positions in pseudo-random number matrices that correspond to the coefficient matrices and selects, as the bias value B i , the pseudo-random number having the same position in the relevant pseudo-random number matrix as the coefficient q i  has in the coefficient matrix.  
         [0079]     An example is shown in  FIG. 5D , which shows a nine-row, six-column pseudo-random number matrix of numbers selected from the set {−64, −32, −16, 0, 16, 32, 64} and randomly assigned to positions in the matrix. The matrix shown in  FIG. 5D  has the same dimensions (that is, number of rows and columns) as the matrix of coefficients for a tile in the 1HL sub-band. Consequently, any location in the matrix of coefficients where the coefficient q i  is located will correspond to a position in the pseudo-random number matrix shown in  FIG. 5D . The number at the corresponding position in the pseudo-random number matrix is selected by the generator  318  as the bias value B i . The net effect is that, when the pseudo-random vector v i  is added to a coefficient p i  to determine the paired coefficient q i , the pseudo-random vector v i  also selects the bias value B i  at the same time.  
         [0080]     It is convenient, although not necessary, to use the same matrix of random numbers for all the tiles of a component (that is, luminance, red chrominance, or blue chrominance) in a given sub-band.  
         [0081]     An image decoder  326  for decoding the image that was encoded by the image encoder  286  is shown in  FIG. 5E . The encoded data image frame is supplied to the decoder  326  by a source (e.g., a storage device)  328 . A payload extractor  330  supplies the quantized-and-encoded coefficients, together with information about the quantization and entropy encoding that was used to generate them, to a luminance branch  332  and to chrominance branches  334  and  336 . The luminance branch includes a decoder  338  (which expands the entropy-encoded data), an inverse quantizer  340  (which multiplies the wavelet coefficients by the same quantization values that served as divisors when the original coefficients were quantized in the image encoder  286 ), an inverse DWT unit  342  (which generates pixel values for the tiles of the luminance component from the wavelet coefficients), and a subdivision assembly unit  344  (which stitches the tiles of the luminance component together into a total luminance image). The chrominance branches  334  and  336  are similar. The total luminance and chrominance images are supplied to a color space converter  346 , which converts the YCrCb components to an RGB image.  
         [0082]     The decoded but still-quantized wavelet coefficients from decoder  338  in the luminance branch to  332  and similar decoders in the chrominance branches are supplied to a signature verifier  348 . The signature values S i  (for each of the sub-bands that was used on the signature-generation side to generate them), information identifying the coefficients p i  that were chosen in each of the sub-bands that were used, and information about the pseudo-random numbers characterizing the vectors v i , are also retrieved from the header of the encoded image data frame by the payload extractor  330  and supplied to the signature verifier  348 . The signature verifier  348  then computes difference values p i −q i  in the restored image, adds the random bias B i  (which is determined using the same matrix of pseudo-random numbers, for each sub-band of interest, that was employed by the image encoder  286 ), and compares the biased difference values with a signature bits S i  in accordance with Table 2 to determine whether the coefficient differences in the reconstructed image are acceptable. If not, the signature verifier  348  marks areas that are judged to have been attacked when the restored image is displayed on a device  350 .  
         [0000]     Variations:  
         [0083]     It will be apparent to those killed in the art that the specific embodiments described above are susceptible to many variations and modifications, and it is therefore the intention that such variations and modifications shall fall within the meaning and range of equivalents of the appended claims. Some of these variations and modifications will be briefly noted below.  
         [0084]     Although the relationship between pairs of coefficients has been characterized herein by using the difference p i −q i , the relation can be characterized in different ways. One possibility would be to use the average, ½(p i +q i ). Numerous other possibilities, such as the average minus the difference or the difference plus a predetermined number, also exist.  
         [0085]     Although coefficients have been grouped into pairs in the embodiments described above, other groupings could be used. One possibility would be to use triplets of coefficients, p i , q i , and r i . The third coefficient r i  could be found, for example, by generating a second pseudo-random vector and adding it at the location associated with the coefficient p i . Groups of four or more coefficients might also be employed.  
         [0086]     Although the embodiments of encoders and decoders described herein employ DCT or DWT transforms, the invention is not limited thereto. Indeed, transforms need not be used at all, and the techniques described can be employed in the pixel domain.  
         [0087]     Although the embodiments described above employ watermarking units for all three branches of the image encoder and verification for all three branches of the image decoder, it is believed that acceptable results can be obtained by using only one watermarking unit and one verification unit. If a single watermarking unit and a single verification unit are used, they are preferably placed in the luminance branch. The reason is that this will permit detection of attacks even if a colored image is converted to a grayscale image prior to the attacks.  
         [0088]     Instead of being embedded in host coefficients or placed in the header of an encoded image data frame, the signature bits S i  may be stored in a separate file.  
         [0089]     Although the embodiments are described above with reference to image files, the invention is also applicable to audio-visual files and other types of files.  
         [0090]     This application claims the benefit of priority of U.S. provisional application No. 60/302,184, filed Jun. 29, 2001, the disclosure of which is incorporated herein by reference.