text: the present invention includes a method and system for embedding a signature into an original image to create a signed image . a preferred embodiment includes selecting a large number of candidate points in the original image and selecting a number of signature points from among the candidate points . the signature points are altered slightly to form the signature . the signature points are stored for later use in auditing a subject image to determine whether the subject image is derived from the signed image . the signatures are encoded in the visible domain of the image and so become part of the image and cannot be detected or removed without prior knowledge of the signature . a key point is that while the changes manifested by the signature are too slight to be visible to the human eye , they are easily and consistently recognizable by a common digital image scanner , after which the signature is extracted , interpreted and verified by a software algorithm . in contrast to prior art signature methods used on non - image data , the signatures persist through significant image transformations that preserve the visible image but may completely change the digital data . the specific transforms allowed include resizing the image larger or smaller , rotating the image , uniformly adjusting color , brightness and / or contrast , and limited cropping . significantly , the signatures persist through the process of printing the image to paper or film and rescanning it into digital form . shown in fig1 is a computer system 10 that is used to carry out an embodiment of the present invention . the computer system 10 includes a computer 12 having the usual complement of memory and logic circuits , a display monitor 14 , a keyboard 16 , and a mouse 18 or other pointing device . the computer system also includes a digital scanner 20 that is used to create a digital image representative of an original image such as a photograph or painting . typically , delicate images , such as paintings , are converted to print or film before being scanned into digital form . in one embodiment a printer 22 is connected to the computer 12 to print digital images output from the processor . in addition , digital images can be output in a data format to a storage medium 23 such as a floppy disk for displaying later at a remote site . any digital display device may be used , such a common computer printer , x - y plotter , or a display screen . an example of the output of the scanner 20 to the computer 12 is a digital image 24 shown in fig2 . more accurately , the scanner outputs data representative of the digital image and the computer causes the digital image 24 to be displayed on the display monitor 14 . as used herein “ digital image ” refers to the digital data representative of the digital image , the digital image displayed on the monitor or other display screen , and the digital image printed by the printer 22 or a remote printer . the digital image 24 is depicted using numerous pixels 24 having various pixel values . in the gray - scale image 24 the pixel values are luminance values representing a brightness level varying from black to white . in a color image the pixels have color values and luminance values , both of which being pixel values . the color values can include the values of any components in a representation of the color by a vector . fig3 shows digital image 24 a in the form of an array of pixels 26 . each pixel is associated with one or more pixel values , which in the example shown in fig3 are luminance values from 0 to 15 . the digital image 24 shown in fig2 includes thousands of pixels . the digital image 24 a represented in fig3 includes 225 pixels . the invention preferably is used for images having pixels numbering in the millions . therefore , the description herein is necessarily a simplistic discussion of the utility of the invention . according to a preferred embodiment of the invention numerous candidate points are located within the original image . signature points are selected from among the candidate points and are altered to form a signature . the signature is a pattern of any number of signature points . in a preferred embodiment , the signature is a binary number between 16 and 32 bits in length . the signature points may be anywhere within an image , but are preferably chosen to be as inconspicuous as possible . preferably , the number of signature points is much greater than the number of bits in a signature . this allows the signature to be redundantly encoded in the image . using a 16 to 32 bit signature , 50 - 200 signature points are preferable to obtain multiple signatures for the image . a preferred embodiment of the invention locates candidate points by finding relative maxima and minima , collectively referred to as extrema , in the image . the extrema represent local extremes of luminance or color . fig4 shows what is meant by relative extrema . fig4 is a graphical representation of the pixel values of a small portion of a digital image . the vertical axis of the graph shows pixel values while the horizontal axis shows pixel positions along a single line of the digital image . small undulations in pixel values , indicated at 32 , represent portions of the digital image where only small changes in luminance or color occur between pixels . a relative maximum 34 represents a pixel that has the highest pixel value for a given area of the image . similarly , a relative minimum 36 represents a pixel that has the lowest pixel value for a given area of the image . relative extrema are preferred signature points for two major reasons . first , they are easily located by simple , well known processing . second , they allow signature points to be encoded very inconspicuously . one of the simplest methods to determine relative extrema is to use a “ difference of averages ” technique . this technique employs predetermined neighborhoods around each pixel 26 ; a small neighborhood 28 and a large neighborhood 30 , as shown in fig2 and 3 . in the present example the neighborhoods are square for simplicity , but a preferred embodiment employs circular neighborhoods . the technique determines the difference between the average pixel value in the small neighborhood and the average pixel value of the large neighborhood . if the difference is large compared to the difference for surrounding pixels then the first pixel value is a relative maxima or minima . using the image of fig3 as an example , the difference of averages for the pixel 26 a is determines as follows . the pixel values within the 3 . times . 3 pixel small neighborhood 28 a add up to 69 ; dividing by 9 pixels gives an average of 7 . 67 . the pixel values within the 5 . times . 5 pixel large neighborhood 30 a add up to 219 ; dividing by 25 pixels gives an average of 8 . 76 and a difference of averages of − 1 . 09 . similarly , the average in small neighborhood 28 g is 10 . 0 ; the average in large neighborhood 30 g is 9 . 8 ; the difference of averages for pixel 26 g is therefore 0 . 2 . similar computations on pixels 26 b - 26 f produce the following table : 26a 26b 26c 26d 26e 26f 26g small neighborhood 7 . 67 10 . 56 12 . 89 14 . 11 13 . 11 11 . 56 10 . 0 large neighborhood 8 . 76 10 . 56 12 . 0 12 . 52 12 . 52 11 . 36 9 . 8 difference of − 1 . 09 0 . 0 0 . 89 1 . 59 0 . 59 0 . 2 0 . 2 averages based on pixels 26 a - 26 g , there may be a relative maximum at pixel 26 d , whose difference of averages of 1 . 59 is greater than the difference of averages for the other examined pixels in the row . to determine whether pixel 26 d is a relative maximum rather than merely a small undulation , its difference of averages must be compared with the difference of averages for the pixels surrounding it in a larger area . preferably , extrema within 10 % of the image size of any side are not used as signature points . this protects against loss of signature points caused by the practice of cropping the border area of an image . it is also preferable that relative extrema that are randomly and widely spaced are used rather than those that appear in regular patterns . using the difference of averages technique or other known techniques , a large number of extrema are obtained , the number depending on the pixel density and contrast of the image . of the total number of extrema found , a preferred embodiment chooses 50 to 200 signature points . this may be done manually by a user choosing with the keyboard 16 , mouse 18 , or other pointing device each signature point from among the extrema displayed on the display monitor 14 . the extrema may be displayed as a digital image with each point chosen by using the mouse or other pointing device to point to a pixel or they may be displayed as a list of coordinates which are chosen by keyboard , mouse , or other pointing device . alternatively , the computer 12 can be programmed to choose signature points randomly or according to a preprogrammed pattern . one bit of binary data is encoded in each signature point in the image by adjusting the pixel values at and surrounding the point . the image is modified by making a small , preferably 2 %- 10 % positive or negative adjustment in the pixel value at the exact signature point , to represent a binary zero or one . the pixels surrounding each signature point , in approximately a 5 . times . 5 to 10 . times . 10 grid , are preferably adjusted proportionally to ensure a continuous transition to the new value at the signature point . a number of bits are encoded in the signature points to form a pattern which is the signature for the image . in a preferred embodiment , the signature is a pattern of all of the signature points . when auditing a subject image , if a statistically significant number of potential signature points in the subject image match corresponding signature points in the signed image , then the subject image is deemed to be derived from the signed image . a statistically significant number is somewhat less than 100 %, but enough to be reasonably confident that the subject image was derived from the signed image . in an alternate embodiment , the signature is encoded using a redundant pattern that distributes it among the signature points in a manner that can be reliably retrieved using only a subset of the points . one embodiment simply encodes a predetermined number of exact duplicates of the signature . other redundant representation methods , such as an error - correcting code , may also be used . in order to allow future auditing of images to determine whether they match the signed image , the signature is stored in a database in which it is associated with the original image . the signature can be stored by associating the bit value of each signature point together with x - y coordinates of the signature point . the signature may be stored separately or as part of the signed image . the signed image is then distributed in digital form . as discussed above , the signed image may be transformed and manipulated to form a derived image . the derived image is derived from the signed image by various transformations , such as resizing , rotating , adjusting color , brightness and / or contrast , cropping and converting to print or film . the derivation may take place in multiple steps or processes or may simply be the copying of the signed image directly . it is assumed that derivations of these images that an owner wishes to track include only applications which substantially preserve the resolution and general quality of the image . while a size reduction by 90 %, a significant color alteration or distinct - pixel - value reduction may destroy the signature , they also reduce the image &# 39 ; s significance and value such that no auditing is desired . in order to audit a subject image according to a preferred embodiment , a user identifies the original image of which the subject image is suspected of being a duplicate . for a print or film image , the subject image is scanned to create a digital image file . for a digital image , no scanning is necessary . the subject digital image is normalized using techniques as described below to the same size , and same overall brightness , contrast and color profile as the unmodified original image . the subject image is analyzed by the method described below to extract the signature , if present , and compare it to any signatures stored for that image . the normalization process involves a sequence of steps to undo transformations previously made to the subject image , to return it as close as possible to the resolution and appearance of the original image . it is assumed that the subject image has been manipulated and transformed as described above . to align the subject image with the original image , a preferred embodiment chooses three or more points from the subject image which correspond to points in the original image . the three or more points of the subject image are aligned with the corresponding points in the original image . the points of the subject image not selected are rotated and resized as necessary to accommodate the alignment of the points selected . for example , fig5 shows a digital subject image 38 that is smaller than the original image 24 shown in fig2 . to resize the subject image , a user points to three points such as the mouth 40 b , ear 42 b and eye 44 b of the subject image using the mouse 18 or other pointer . since it is usually difficult to accurately point to a single pixel , the computer selects the nearest extrema to the pixel pointed to by the user . the user points to the mouth 40 a , ear 42 a , and eye 44 a of the original image . the computer 12 resizes and rotates the subject image as necessary to ensure that points 40 b , 42 b , and 44 b are positioned with respect to each other in the same way that points 40 a , 42 a , and 44 a are positioned with respect to each other in the original image . the remaining pixels are repositioned in proportion to the repositioning of points 40 b , 42 b and 44 b . by aligning three points the entire subject image is aligned with the original image without having to align each pixel independently . after the subject image is aligned , the next step is to normalize the brightness , contrast and / or color of the subject image . normalizing involves adjusting pixel values of the subject image to match the value - distribution profile of the original image . this is accomplished by a technique analogous to that used to align the subject image . a subset of the pixels in the subject image are adjusted to equal corresponding pixels in the original image . the pixels not in the subset are adjusted in proportion to the adjustments made to the pixels in the subset . the pixels of the subject image corresponding to the signature points should not be among the pixels in the subset . otherwise any signature points in the subject image will be hidden from detection when they are adjusted to equal corresponding pixels in the original image . in a preferred embodiment , the subset includes the brightest and darkest pixels of the subject image . these pixels are adjusted to have luminance values equal to the luminance values of corresponding pixels in the original image . to ensure that any signature points can be detected , no signature points should be selected during the signature embedding process described above that are among the brightest and darkest pixels of the original image . for example , one could use pixels among the brightest and darkest 3 % for the adjusting subset , after selecting signature points among less than the brightest and darkest 5 % to ensure that there is no overlap . when the subject image is fully normalized , it is preferably compared to the original image . one way to compare images is to subtract one image from the other . the result of the subtraction is a digital image that includes any signature points that were present in the subject image . these signature points , if any , are compared to the stored signature points for the signed image . if the signature points do not match , then the subject image is not an image derived from the signed image , unless the subject image was changed substantially from the signed image . in an alternative embodiment , the normalized subject image is compared directly with the signed image instead of subtracting the subject image from the original image . this comparison involves subtracting the subject image from the signed image . if there is little or no image resulting from the subtraction , then the subject image equals to the signed image , and therefore has been derived from the signed image . in another alternate embodiment , instead of normalizing the entire subject image , only a section of the subject image surrounding each potential signature point is normalized to be of the same general resolution and appearance as a corresponding section of the original image . this is accomplished by selecting each potential signature point of the subject image and selecting sections surrounding each potential signature point . the normalization of each selected section proceeds according to methods similar to those disclosed above for normalizing the entire subject image . normalizing each selected section individually allows each potential signature point of the subject image to be compared directly with a corresponding signature point of the signed image . preferably , an average is computed for each potential signature point by averaging the pixel value of the potential signature point with the pixel values of a plurality of pixels surrounding the potential signature point . the average computed for each signature is compared directly with a corresponding signature point of the signed image . while the methods of normalizing and extracting a signature from a subject image as described above are directed to luminance values , similar methods may be used for color values . instead of or in addition to normalizing by altering luminance values , the color values of the subject image can also be adjusted to equal corresponding color values in an original color image . however , it is not necessary to adjust color values in order to encode a signature in or extract a signature from a color image . color images use pixels having pixel values that include luminance values and color values . a digital signature can be encoded in any pixel values regardless of whether the pixel values are luminance values , color values , or any other type of pixel values . luminance values are preferred because alterations may be made more easily to luminance values without the alterations being visible to the human eye . from the foregoing it will be appreciated that , although specific embodiments of the invention have been described herein for purposes of illustration , various modifications may be made without deviating from the spirit and scope of the invention . accordingly , the invention is not limited except as by the appended claims .