Method and apparatus for watermarking images

• US 20030147547A1
• Filed: 02/11/2003
• Published: 08/07/2003
• Est. Priority Date: 01/10/2001
• Status: Active Grant

• Current Assignee: Trustees Of Columbia University In The City Of New York (Columbia University)
• Original Assignee: Trustees Of Columbia University In The City Of New York (Columbia University)
• Inventors: Lin, Ching-Yung, Chang, Shih-Fu
• Granted Patent: US 6,879,703 B2
• Time in Patent Office: Days
• US Class Current: 382/100
• CPC Class Codes: G06T 1/0042 Fragile watermarking, e.g. so as to detect tampering
• CPC Class Codes: G06T 1/005 Robust watermarking, e.g. average attack or collusion attack resistant
• CPC Class Codes: G06T 1/0057 Compression invariant watermarking
• CPC Class Codes: G06T 2201/0052 Embedding of the watermark in the frequency domain
• CPC Class Codes: G06T 2201/0061 Embedding of the watermark in each block of the image, e.g. segmented watermarking
• CPC Class Codes: H04N 1/32165 using cosine transforms
• CPC Class Codes: H04N 1/32187 with selective or adaptive application of the additional information, e.g. in selected frequency coefficients
• CPC Class Codes: H04N 1/32277 Compression
• CPC Class Codes: H04N 1/3232 Robust embedding or watermarking
• CPC Class Codes: H04N 2201/3236 Details of authentication information generation
• CPC Class Codes: H04N 2201/327 which are undetectable to the naked eye, e.g. embedded codes

Abstract

Digital watermarks are embedded in image data (102)in order to enable authentication of the image data and/or replacement of rejected portions of the image data. Authentication codes are derived by comparing selected discrete cosine transform (DCT) (104) coefficients within DCT data (106) derived from the original, spatial-domain image data. The authentication codes thus generated are embedded in DCT coefficients (612) other than the ones which were used to derive the authentication codes. The resulting, watermarked data can be sent or made available to one or more recipients who can compress or otherwise use the watermarked data. Image data derived from the watermarked data—e.g, compressed versions of the watermarked data—can be authenticated by: extracting the embedded authentication codes, comparing DCT coefficients derived from the coefficients from which the original authentication codes were generated; and determining whether the compared DCT coefficients are consistent with the extracted authentication codes.

Claims

1. An image-processing method, comprising:

comparing a first transformed-domain image datum to a second transformed-domain image datum, for deriving a first authentication code, the first transformed-domain image datum having a first transformed-domain location, and the second transformed-domain image datum having a second transformed-domain location; and

using a replacement code to replace at least a portion of a third transformed-domain image datum, for converting the third transformed-domain image datum into a fourth transformed-domain image datum, the replacement code comprising at least one of the first authentication code, a code derived from the first authentication code, a code selected based upon at least the first authentication code, and a code selected based upon at least the code derived from the first authentication code, the fourth transformed-domain image datum having a third transformed-domain location, the first transformed-domain image datum being for deriving a fifth transformed-domain image datum having a fourth transformed-domain location, the second transformed-domain image datum being for deriving a sixth transformed-domain image datum having a fifth transformed-domain location, the fourth transformed-domain image datum being for deriving a seventh transformed-domain image datum having a sixth transformed-domain location, the fourth transformed-domain location being approximately equal to the first transformed-domain location, the fifth transformed-domain location being approximately equal to the second transformed-domain location, and the sixth transformed-domain location being approximately equal to the third transformed-domain location, wherein the fifth, sixth, and seventh transformed-domain image data are for being authenticated by an authentication procedure comprising the steps of;

using an authentication code extraction function to extract a second authentication code from the seventh transformed-domain image datum,

comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum, for deriving a first comparison result,

based on the second authentication code, selecting a set of at least one acceptable value of the first comparison result, and

if the first comparison result is not within the set of at least one acceptable value of the first comparison result, determining that at least one of the fifth, sixth, and seventh transformed-domain image data has been improperly altered.

2. A method according to claim 1, wherein the first transformed-domain image datum is included in a first set of transformed-domain image data, the second transformed-domain image datum is included in a second set of transformed-domain image data, the fifth transformed-domain image datum is included in a third set of transformed-domain image data, and the sixth transformed-domain image datum is included in a fourth set of transformed-domain image data, the method further comprising:

using a first secret mapping to form an association between the first and second sets of transformed-domain image data; and

using the association between the first and second sets of transformed-domain image data for selecting at least one of the first and second transformed-domain image data to be compared in the step of comparing the first transformed-domain image datum to the second transformed-domain image datum, wherein the authentication procedure further comprises the steps of;

using the first secret mapping to form an association between the third and fourth sets of transformed-domain image data, and

using the association between the third and fourth sets of transformed-domain image data for selecting at least one of the fifth and sixth transformed-domain image data to be compared in the step of comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum.

3. A method according to claim 2, wherein the first and second sets of transformed-domain image data are included in a fifth set of transformed-domain image data, the third transformed-domain image datum is included in a sixth set of transformed-domain image data, the third and fourth sets of transformed-domain image data are included in a seventh set of transformed-domain image data, and the seventh transformed-domain image datum is included in an eighth set of transformed-domain image data, the method further comprising:

using a second secret mapping to form an association between the fifth and sixth sets of transformed-domain image data; and

using the association between the fifth and sixth sets of transformed-domain image data for selecting the third transformed-domain image datum to be converted, in the step of using the replacement code, into the fourth transformed-domain image datum, wherein the authentication procedure further comprises the steps of;

using the second secret mapping to form an association between the seventh and eighth sets of transformed-domain image data, and

using the association between the seventh and eighth sets of transformed-domain image data for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted in the step of using the authentication code extraction function to extract the second authentication code.

4. A method according to claim 1, wherein the first and second transformed-domain image data are included in a first set of transformed-domain image data, the third transformed-domain image datum is included in a second set of transformed-domain image data, the fifth and sixth transformed-domain image data are included in a third set of transformed-domain image data, and the seventh transformed-domain image datum is included in a fourth set of transformed-domain image data, the method further comprising:

using a first secret mapping to form an association between the first and second sets of transformed-domain image data; and

using the association between the first and second sets of transformed-domain image data for selecting the third transformed-domain image datum to be converted, in the step of using the replacement code, into the fourth transformed-domain image datum, wherein the authentication procedure further comprises the steps of;

using the first secret mapping to form an association between the third and fourth sets of transformed-domain image data, and

using the association between the third and fourth sets of transformed-domain image data for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted in the step of using the authentication code extraction function to extract the second authentication code.

5. A method according to claim 1, wherein the first transformed-domain image datum is included in a first set of transformed-domain image data, the second transformed-domain image datum is included in a second set of transformed-domain image data, the fifth transformed-domain image datum is included in a third set of transformed-domain image data, and the sixth transformed-domain image datum is included in a fourth set of transformed-domain image data, the method further comprising:

using a first secret transformed-domain location selection pattern for selecting the first transformed-domain image datum to be compared in the step of comparing the first transformed-domain image datum to the second transformed-domain image datum, the first secret transformed-domain location selection pattern comprising at least a first datum selection location, the first transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the first set of transformed-domain image data; and

using the first secret transformed-domain location selection pattern for selecting the second transformed-domain image datum to be compared in the step of comparing the first transformed-domain image datum to the second transformed-domain image datum, the second transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the second set of transformed-domain image data, wherein the authentication procedure further comprises the steps of;

using the first secret transformed-domain location selection pattern for selecting the fifth transformed-domain image datum to be compared in the step of comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum, the fourth transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the third set of transformed-domain image data, and

using the first secret transformed-domain location selection pattern for selecting the sixth transformed-domain image datum to be compared in the step of comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum, the fifth transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the fourth set of transformed-domain image data.

6. A method according to claim 5, wherein the third transformed-domain image datum is included in a fifth set of transformed-domain image data, and the seventh transformed-domain image datum is included in a sixth set of transformed-domain image data, the method further comprising using a second secret transformed-domain location selection pattern for selecting the third transformed-domain image datum to be converted, in the step of using the replacement code, into the fourth transformed-domain image datum, the third transformed-domain image datum having the third transformed-domain location, the second secret transformed-domain location selection pattern comprising at least a second datum selection location, the third transformed-domain location being approximately equal to the second datum selection location in a coordinate system of the fifth set of transformed-domain image data, wherein the authentication procedure further comprises using the second secret transformed-domain location selection pattern for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted in the step of using the authentication code extraction function to extract the second authentication code, the sixth transformed-domain location being approximately equal to the second datum selection location in a coordinate system of the sixth set of transformed-domain image data.

7. A method according to claim 1, wherein the third transformed-domain image datum is included in a first set of transformed-domain image data, and the seventh transformed-domain image datum is included in a second set of transformed-domain image data, the method further comprising using a secret transformed-domain location selection pattern for selecting the third transformed-domain image datum to be converted, in the step of using the replacement code, into the fourth transformed-domain image datum, the third transformed-domain image datum having the third transformed-domain location, the secret transformed-domain location selection pattern comprising at least a datum selection location, the third transformed-domain location being approximately equal to the datum selection location in a coordinate system of the first set of transformed-domain image data, wherein the authentication procedure further comprises using the secret transformed-domain location selection pattern for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted in the step of using the authentication code extraction function to extract the second authentication code, the sixth transformed-domain location being approximately equal to the datum selection location in a coordinate system of the second set of transformed-domain image data.

8. A method according to claim 1, wherein the portion of the third transformed-domain image datum comprises a bit of the third transformed-domain image datum, and the first authentication code comprises an authentication bit, the method further comprising processing the authentication bit and a bit of a secret key by a binary operation, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

9. A method according to claim 1, wherein the portion of the third transformed-domain image datum comprises a bit of the third transformed-domain image datum, and the replacement code comprises at least one of a bit of the first authentication code and a code selected based upon the bit of the first authentication code.

10. A method according to claim 1, wherein the authentication procedure further comprises:

using the authentication code extraction function to extract a first set of authentication codes from at least one portion of a first set of transformed-domain image data, the first set of transformed-domain image data including the sixth transformed-domain image datum;

comparing at least one portion of a second set of transformed-domain image data to at least one portion of a third set of transformed-domain image data, for deriving a first set of comparison results;

based on each of the first set of authentication codes, selecting a set of at least one acceptable value of a member of the first set of comparison results associated with the each of the first set of authentication codes;

if the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes, determining that the first set of transformed-domain image data has not been improperly altered.

11. A method according to claim 10, wherein the authentication procedure further comprises:

using the authentication code extraction function to extract a second set of authentication codes from at least one portion of a fourth set of transformed-domain image data;

comparing at least one portion of a fifth set of transformed-domain image data to at least one portion of a sixth set of transformed-domain image data, for deriving a second set of comparison results, the fifth set of transformed-domain image data including the seventh transformed-domain image datum;

based on each of the second set of authentication codes, selecting a set of at least one acceptable value of a member of the second set of comparison results associated with the each of the second set of authentication codes;

if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, determining that the fifth set of transformed-domain image data has not been improperly altered.

12. A method according to claim 11, wherein the authentication procedure further comprises the step of:

if the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes, and if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, determining that a seventh set of transformed-domain image data has been improperly altered, the seventh set of transformed-domain image data including the fifth transformed-domain image datum.

13. A method according to claim 10, wherein the authentication procedure further comprises:

using the authentication code extraction function to extract a second set of authentication codes from at least one portion of a fourth set of transformed-domain image data, the fourth set of transformed-domain image data including the fifth transformed-domain image datum;

comparing at least one portion of a fifth set of transformed-domain image data to at least one portion of a sixth set of transformed-domain image data, for deriving a second set of comparison results;

based on each of the second set of authentication codes, selecting a set of at least one acceptable value of a member of the second set of comparison results associated with the each of the second set of authentication codes;

if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, determining that the fourth set of transformed-domain image data has not been improperly altered.

14. A method according to claim 13, wherein the authentication procedure further comprises the step of:

if the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes, and if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, determining that a seventh set of transformed-domain image data has been improperly altered, the seventh set of transformed-domain image data including the seventh transformed-domain image datum.

15. An image-processing method, comprising:

encoding by an encoding function a first set of transformed-domain image data, for deriving a set of image data recovery codes comprising a first image data recovery code, the first set of transformed-domain image data being included in a second set of transformed-domain image data, the second set of transformed-domain image data being derived from a first set of spatial domain image data; and

using a replacement code to replace at least a portion of a first transformed-domain image datum, for converting the first transformed-domain image datum into a second transformed-domain image datum, the first transformed-domain image datum being included in a third set of transformed-domain image data, the third set of transformed-domain image data being derived from the first set of spatial domain image data, the replacement code comprising at least one of the first image data recovery code, a code derived from the first image data recovery code, a code selected based upon at least the first image data recovery code, and a code selected based upon at least the code derived from the first image data recovery code, the second transformed-domain image datum being for deriving a third transformed-domain image datum, the first set of spatial domain image data being for deriving a fourth set of transformed-domain image data, the third transformed-domain image datum being for deriving, by a recovery procedure, an approximation data set for replacing the fourth set of transformed-domain image data, and the recovery procedure comprising the steps of;

using a recovery code extraction function to extract a second image data recovery code from the third transformed-domain image datum, the second image data recovery code being approximately equal to the first image data recovery code; and

decoding by a decoding function at least the second image data recovery code, for deriving the approximation data set, the decoding function comprising a functional inverse of the encoding function.

16. A method according to claim 15, further comprising:

averaging a second set of spatial domain image data, for deriving a first reduced image datum;

averaging a third set of spatial domain image data, for deriving a second reduced image datum, the first and second reduced image data being included in a reduced set of spatial domain image data, and the second and third sets of spatial domain image data being included in the first set of spatial domain image data;

domain-transforming the reduced set of spatial domain image data, for deriving a fifth set of transformed-domain image data; and

quantizing the fifth set of transformed-domain image data, for deriving the first set of transformed-domain image data.

17. A method according to claim 16, wherein the portion of the first transformed-domain image datum comprises a bit of the first transformed-domain image datum, and the first image data recovery code comprises a data recovery bit.

18. A method according to claim 17, further comprising processing the data recovery bit and a bit of a secret key by a binary operation, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

19. A method according to claim 15, wherein the portion of the first transformed-domain image datum comprises a bit of the first transformed-domain image datum, and the first image data recovery code comprises a data recovery bit.

20. A method according to claim 19, further comprising processing the data recovery bit and a bit of a secret key by a binary operation, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

21. A method according to claim 15, wherein the encoding function comprises an entropy encoding function.

22. A method according to claim 21, wherein the entropy encoding function comprises at least one of a Huffman encoding function and a JPEG entropy encoding function.

23. An image-processing method, comprising:

quantizing a first set of transformed-domain image data based on a first quantization step size, for deriving a second set of transformed-domain image data, the second set of transformed-domain image data including at least a first transformed-domain image datum; and

using a replacement code to replace at least a portion of the first transformed-domain image datum, for converting the first transformed-domain image datum into a second transformed-domain image datum, the second transformed-domain image datum being included in a third set of transformed-domain image data, the replacement code comprising at least one of a watermark code, a code derived from the watermark code, a code selected based on the watermark code, and a code selected based upon at least the code derived from the watermark code, wherein the third set of transformed-domain image data is for being altered by an alteration procedure for deriving a fourth set of transformed-domain image data, the alteration procedure comprising at least one of;

(1) quantizing the third set of transformed-domain image data based on a second quantization step size, the second quantization step size being no greater than the first quantization step size, (2) transforming a data encoding format of the third set of transformed-domain image data into a different data encoding format, and (3) filtering the third set of transformed domain image data, the fourth set of transformed-domain image data including at least a third transformed-domain image datum, and the third transformed-domain image datum being derived from the second transformed-domain image datum, wherein the third transformed-domain image datum is for being processed by a watermark extraction procedure for extracting the watermark code from the third transformed-domain image datum, the watermark extraction procedure comprising the steps of;

requantizing the third transformed-domain image datum based on the first quantization step size, for generating a fourth transformed-domain image datum, and

processing the fourth transformed-domain image datum by a watermark extraction function, for deriving an extracted code approximately equal to the watermark code.

24. A method according to claim 23, wherein the first set of transformed domain image data includes a fifth transformed-domain image datum, the first transformed-domain datum being derived from the fifth transformed-domain image datum, and the method further comprising deriving the watermark code based on at least one datum derived from at least a first portion of a set of spatial domain image data, the fifth transformed-domain image datum being derived from a second portion of the set of spatial domain image data.

25. A method according to claim 24, further comprising:

using a secret mapping to form an association between at least the first. transformed-domain image datum and at least the datum derived from the first portion of the set of spatial domain image data; and

using the association between the at least the first transformed-domain image datum and the at least the datum derived from the first portion of the set of spatial domain image data for selecting the first transformed-domain image datum to be converted, in the step of using the first replacement code, into the second transformed-domain image datum.

26. A method according to claim 23, wherein the first transformed-domain image datum has a secret transformed-domain location.

27. An image-processing apparatus, comprising:

a first processor for comparing a first transformed-domain image datum to a second transformed-domain image datum, for deriving a first authentication code, the first transformed-domain image datum having a first transformed-domain location, and the second transformed-domain image datum having a second transformed-domain location; and

a second processor for using a replacement code to replace at least a portion of a third transformed-domain image datum, for converting the third transformed-domain image datum into a fourth transformed-domain image datum, the replacement code comprising at least one of the first authentication code, a code derived from the first authentication code, a code selected based upon at least the first authentication code, and a code selected based upon at least the code derived from the first authentication code, the fourth transformed-domain image datum having a third transformed-domain location, the first transformed-domain image datum being for deriving a fifth transformed-domain image datum having a fourth transformed-domain location, the second transformed-domain image datum being for deriving a sixth transformed-domain image datum having a fifth transformed-domain location, the fourth transformed-domain image datum being for deriving a seventh transformed-domain image datum having a sixth transformed-domain location, the fourth transformed-domain location being approximately equal to the first transformed-domain location, the fifth transformed-domain location being approximately equal to the second transformed-domain location, and the sixth transformed-domain location being approximately equal to the third transformed-domain location, wherein the fifth, sixth, and seventh transformed-domain image data are for being authenticated by an authentication processor comprising;

a third processor for using an authentication code extraction function to extract a second authentication code from the seventh transformed-domain image datum,

a fourth processor for comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum, for deriving a first comparison result,

a fifth processor for selecting, based on the second authentication code, a set of at least one acceptable value of the first comparison result, and

a sixth processor for determining that at least one of the fifth, sixth, and seventh transformed-domain image data has been improperly altered if the first comparison result is not within the set of at least one acceptable value of the first comparison result.

28. An apparatus according to claim 27, wherein the first transformed-domain image datum is included in a first set of transformed-domain image data, the second transformed-domain image datum is included in a second set of transformed-domain image data, the fifth transformed-domain image datum is included in a third set of transformed-domain image data, and the sixth transformed-domain image datum is included in a fourth set of transformed-domain image data, the apparatus further comprising:

a seventh processor for using a first secret mapping to form an association between the first and second sets of transformed-domain image data; and

an eighth processor for using the association between the first and second sets of transformed-domain image data for selecting at least one of the first and second transformed-domain image data to be compared by the first processor, wherein the authentication processor further comprises;

a ninth processor for using the first secret mapping to form an association between the third and fourth sets of transformed-domain image data, and

a tenth processor for using the association between the third and fourth sets of transformed-domain image data for selecting at least one of the fifth and sixth transformed-domain image data to be compared by the fourth processor.

29. An apparatus according to claim 28, wherein the first and second sets of transformed-domain image data are included in a fifth set of transformed-domain image data, the third transformed-domain image datum is included in a sixth set of transformed-domain image data, the third and fourth sets of transformed-domain image data are included in a seventh set of transformed-domain image data, and the seventh transformed-domain image datum is included in an eighth set of transformed-domain image data, the apparatus further comprising:

an eleventh processor for using a second secret mapping to form an association between the fifth and sixth sets of transformed-domain image data; and

a twelfth processor for using the association between the fifth and sixth sets of transformed-domain image data for selecting the third transformed-domain image datum to be converted, by the second processor, into the fourth transformed-domain image datum, wherein the authentication processor further comprises;

a thirteenth processor for using the second secret mapping to form an association between the seventh and eighth sets of transformed-domain image data, and

a fourteenth processor for using the association between the seventh and eighth sets of transformed-domain image data for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted by the third processor.

30. An apparatus according to claim 27, wherein the first and second transformed-domain image data are included in a first set of transformed-domain image data, the third transformed-domain image datum is included in a second set of transformed-domain image data, the fifth and sixth transformed-domain image data are included in a third set of transformed-domain image data, and the seventh transformed-domain image datum is included in a fourth set of transformed-domain image data, the apparatus further comprising:

a seventh processor for using a first secret mapping to form an association between the first and second sets of transformed-domain image data; and

an eighth processor for using the association between the first and second sets of transformed-domain image data for selecting the third transformed-domain image datum to be converted, by the second processor, into the fourth transformed-domain image datum, wherein the authentication processor further comprises;

a ninth processor for using the first secret mapping to form an association between the third and fourth sets of transformed-domain image data, and

a tenth processor for using the association between the third and fourth sets of transformed-domain image data for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted by the third processor.

31. An apparatus according to claim 27, wherein the first transformed-domain image datum is included in a first set of transformed-domain image data, the second transformed-domain image datum is included in a second set of transformed-domain image data, the fifth transformed-domain image datum is included in a third set of transformed-domain image data, and the sixth transformed-domain image datum is included in a fourth set of transformed-domain image data, the apparatus further comprising:

a seventh processor for using a first secret transformed-domain location selection pattern for selecting the first transformed-domain image datum to be compared by the first processor, the first secret transformed-domain location selection pattern comprising at least a first datum selection location, the first transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the first set of transformed-domain image data; and

an eighth processor for using the first secret transformed-domain location selection pattern for selecting the second transformed-domain image datum to be compared by the first processor, the second transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the second set of transformed-domain image data, wherein the authentication processor further comprises;

a ninth processor for using the first secret transformed-domain location selection pattern for selecting the fifth transformed-domain image datum to be compared by the fourth processor, the fourth transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the third set of transformed-domain image data, and

a tenth processor for using the first secret transformed-domain location selection pattern for selecting the sixth transformed-domain image datum to be compared by the fourth processor, the fifth transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the fourth set of transformed-domain image data.

32. An apparatus according to claim 31, wherein the third transformed-domain image datum is included in a fifth set of transformed-domain image data, and the seventh transformed-domain image datum is included in a sixth set of transformed-domain image data, the apparatus further comprising an eleventh processor for using a second secret transformed-domain location selection pattern for selecting the third transformed-domain image datum to be converted, by the second processor, into the fourth transformed-domain image datum, the third transformed-domain image datum having the third transformed-domain location, the second secret transformed-domain location selection pattern comprising at least a second datum selection location, the third transformed-domain location being approximately equal to the second datum selection location in a coordinate system of the fifth set of transformed-domain image data, wherein the authentication processor further comprises a twelfth processor for using the second secret transformed-domain location selection pattern for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted by the third processor, the sixth transformed-domain location being approximately equal to the second datum selection location in a coordinate system of the sixth set of transformed-domain image data.

33. An apparatus according to claim 27, wherein the third transformed-domain image datum is included in a first set of transformed-domain image data, and the seventh transformed-domain image datum is included in a second set of transformed-domain image data, the apparatus further comprising a seventh processor for using a secret transformed-domain location selection pattern for selecting the third transformed-domain image datum to be converted, by the second processor, into the fourth transformed-domain image datum, the third transformed-domain image datum having the third transformed-domain location, the secret transformed-domain location selection pattern comprising at least a datum selection location, the third transformed-domain location being approximately equal to the datum selection location in a coordinate system of the first set of transformed-domain image data, wherein the authentication processor further comprises an eighth processor for using the secret transformed-domain location selection pattern for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted by the third processor, the sixth transformed-domain location being approximately equal to the datum selection location in a coordinate system of the second set of transformed-domain image data.

34. An apparatus according to claim 27, wherein the portion of the third transformed-domain image datum comprises a bit of the third transformed-domain image datum, and the first authentication code comprises an authentication bit, the apparatus further comprising a seventh processor for using a binary operation to process the authentication bit and a bit of a secret key, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

35. An apparatus according to claim 27, wherein the portion of the third transformed-domain image datum comprises a bit of the third transformed-domain image datum, and the replacement code comprises at least one of a bit of the first authentication code and a code selected based upon the bit of the first authentication code.

36. An apparatus according to claim 27, wherein the authentication processor further comprises:

a seventh processor for using the authentication code extraction function to extract a first set of authentication codes from at least one portion of a first set of transformed-domain image data, the first set of transformed-domain image data including the sixth transformed-domain image datum;

an eighth processor for comparing at least one portion of a second set of transformed-domain image data to at least one portion of a third set of transformed-domain image data, for deriving a first set of comparison results;

a ninth processor for selecting, based on each of the first set of authentication codes, a set of at least one acceptable value of a member of the first set of comparison results associated with the each of the first set of authentication codes;

a tenth processor for determining that the first set of transformed-domain image data has not been improperly altered if the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes.

37. An apparatus according to claim 36, wherein the authentication processor further comprises:

an eleventh processor for using the authentication code extraction function to extract a second set of authentication codes from at least one portion of a fourth set of transformed-domain image data;

a twelfth processor for comparing at least one portion of a fifth set of transformed-domain image data to at least one portion of a sixth set of transformed-domain image data, for deriving a second set of comparison results, the fifth set of transformed-domain image data including the seventh transformed-domain image datum;

a thirteenth processor for selecting, based on each of the second set of authentication codes, a set of at least one acceptable value of a member of the second set of comparison results associated with the each of the second set of authentication codes;

a fourteenth processor for determining that the fifth set of transformed-domain image data has not been improperly altered if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes.

38. An apparatus according to claim 37, wherein the authentication processor further comprises a fifteenth processor for determining that a seventh set of transformed-domain image data has been improperly altered if:

(a) the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes; and

(b) the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, the seventh set of transformed-domain image data including the fifth transformed-domain image datum.

39. An apparatus according to claim 36, wherein the authentication processor further comprises:

an eleventh processor for using the authentication code extraction function to extract a second set of authentication codes from at least one portion of a fourth set of transformed-domain image data, the fourth set of transformed-domain image data including the fifth transformed-domain image datum;

a twelfth processor for comparing at least one portion of a fifth set of transformed-domain image data to at least one portion of a sixth set of transformed-domain image data, for deriving a second set of comparison results;

a thirteenth processor for selecting, based on each of the second set of authentication codes, a set of at least one acceptable value of a member of the second set of comparison results associated with the each of the second set of authentication codes;

a fourteenth processor for determining that the fourth set of transformed-domain image data has not been improperly altered if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes.

40. An apparatus according to claim 39, wherein the authentication processor further comprises a fifteenth processor for determining that a seventh set of transformed-domain image data has been improperly altered if:

(a) the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes; and

(b) the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, the seventh set of transformed-domain image data including the seventh transformed-domain image datum.

41. An image-processing apparatus, comprising:

a first processor for using an encoding function to encode a first set of transformed-domain image data, for deriving a set of image data recovery codes comprising a first image data recovery code, the first set of transformed-domain image data being included in a second set of transformed-domain image data, the second set of transformed-domain image data being derived from a first set of spatial domain image data; and

a second processor for using a replacement code to replace at least a portion of a first transformed-domain image datum, for converting the first transformed-domain image datum into a second transformed-domain image datum, the first transformed-domain image datum being included in a third set of transformed-domain image data, the third set of transformed-domain image data being derived from the first set of spatial domain image data, the replacement code comprising at least one of the first image data recovery code, a code derived from the first image data recovery code, a code selected based upon at least the first image data recovery code, and a code selected based upon at least the code derived from the first image data recovery code, the second transformed-domain image datum being for deriving a third transformed-domain image datum, the first set of spatial domain image data being for deriving a fourth set of transformed-domain image data, the third transformed-domain image datum being for deriving, by a recovery processor, an approximation data set for replacing the fourth set of transformed-domain image data, and the recovery processor comprising;

a third processor for using a recovery code extraction function to extract a second image data recovery code from the third transformed-domain image datum, the second image data recovery code being approximately equal to the first image data recovery code; and

a fourth processor for using a decoding function to decode at least the second image data recovery code, for deriving the approximation data set, the decoding function comprising a functional inverse of the encoding function.

42. An apparatus according to claim 41, further comprising:

a fifth processor for averaging a second set of spatial domain image data, for deriving a first reduced image datum;

a sixth processor for averaging a third set of spatial domain image data, for deriving a second reduced image datum, the first and second reduced image data being included in a reduced set of spatial domain image data, and the second and third sets of spatial domain image data being included in the first set of spatial domain image data;

a seventh processor for domain-transforming the reduced set of spatial domain image data, for deriving a fifth set of transformed-domain image data; and

an eighth processor for quantizing the fifth set of transformed-domain image data, for deriving the first set of transformed-domain image data.

43. An apparatus according to claim 42, wherein the portion of the first transformed-domain image datum comprises a bit of the first transformed-domain image datum, and the first image data recovery code comprises a data recovery bit.

44. An apparatus according to claim 43, further comprising a ninth processor for using a binary operation to process the data recovery bit and a bit of a secret key, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

45. An apparatus according to claim 41, wherein the portion of the first transformed-domain image datum comprises a bit of the first transformed-domain image datum, and the first image data recovery code comprises a data recovery bit.

46. An apparatus according to claim 45, further comprising a fifth processor for using a binary operation to process the data recovery bit and a bit of a secret key, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

47. An apparatus according to claim 41, wherein the encoding function comprises an entropy encoding function.

48. An apparatus according to claim 47, wherein the entropy encoding function comprises at least one of a Huffman encoding function and a JPEG entropy encoding function.

49. An image-processing apparatus, comprising:

a first processor for quantizing a first set of transformed-domain image data based on a first quantization step size, for deriving a second set of transformed-domain image data, the second set of transformed-domain image data including at least a first transformed-domain image datum; and

a second processor for using a replacement code to replace at least a portion of the first transformed-domain image datum, for converting the first transformed-domain image datum into a second transformed-domain image datum, the second transformed-domain image datum being included in a third set of transformed-domain image data, the replacement code comprising at least one of a watermark code, a code derived from the watermark code, a code selected based on the watermark code, and a code selected based upon at least the code derived from the watermark code, wherein the third set of transformed-domain image data is for being altered by an alteration processor for deriving a fourth set of transformed-domain image data, the alteration processor comprising at least one of;

(1) a quantization processor for quantizing the third set of transformed-domain image data based on a second quantization step size, the second quantization step size being no greater than the first quantization step size, (2) a data encoding format transformation processor for transforming a data encoding format of the third set of transformed-domain image data into a different data encoding format, and (3) an image filtering processor for filtering the third set of transformed-domain image data, the fourth set of transformed-domain image data including at least a third transformed-domain image datum, and the third transformed-domain image datum being derived from the second transformed-domain image datum, wherein the third transformed-domain image datum is for being processed by a watermark extraction processor for extracting the watermark code from the third transformed-domain image datum, the watermark extraction processor comprising;

a third processor for requantizing the third transformed-domain image datum based on the first quantization step size, for generating a fourth transformed-domain image datum, and

a fourth processor for processing the fourth transformed-domain image datum by a watermark extraction function, for deriving an extracted code approximately equal to the watermark code.

50. An apparatus according to claim 49, wherein the first set of transformed-domain image data includes a fifth transformed-domain image datum, the first transformed-domain datum being derived from the fifth transformed-domain image datum, and the apparatus further comprising a fifth processor for deriving the watermark code based on at least one datum derived from at least a first portion of a set of spatial domain image data, the fifth transformed-domain image datum being derived from a second portion of the set of spatial domain image data.

51. An apparatus according to claim 50, further comprising:

a sixth processor for using a secret mapping to form an association between at least the first transformed-domain image datum and at least the datum derived from the first portion of the set of spatial domain image data; and

a seventh processor for using the association between the at least the first transformed-domain image datum and the at least the datum derived from the first portion of the set of spatial domain image data for selecting the first transformed-domain image datum to be converted, by the second processor, into the second transformed-domain image datum.

52. An apparatus according to claim 49, wherein the first transformed-domain image datum has a secret transformed-domain location.

53. A computer-readable medium having a set of instructions operable to direct a processor to perform the steps of:

comparing a first transformed-domain image datum to a second transformed-domain image datum, for deriving a first authentication code, the first transformed-domain image datum having a first transformed-domain location, and the second transformed-domain image datum having a second transformed-domain location; and

using a replacement code to replace at least a portion of a third transformed-domain image datum, for converting the third transformed-domain image datum into a fourth transformed-domain image datum, the replacement code comprising at least one of the first authentication code, a code derived from the first authentication code, a code selected based upon at least the first authentication code, and a code selected based upon at least the code derived from the first authentication code, the fourth transformed-domain image datum having a third transformed-domain location, the first transformed-domain image datum being for deriving a fifth transformed-domain image datum having a fourth transformed-domain location, the second transformed-domain image datum being for deriving a sixth transformed-domain image datum having a fifth transformed-domain location, the fourth transformed-domain image datum being for deriving a seventh transformed-domain image datum having a sixth transformed-domain location, the fourth transformed-domain location being approximately equal to the first transformed-domain location, the fifth transformed-domain location being approximately equal to the second transformed-domain location, and the sixth transformed-domain location being approximately equal to the third transformed-domain location, wherein the fifth, sixth, and seventh transformed-domain image data are for being authenticated by an authentication procedure comprising the steps of;

using an authentication code extraction function to extract a second authentication code from the seventh transformed-domain image datum,

comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum, for deriving a first comparison result,

based on the second authentication code, selecting a set of at least one acceptable value of the first comparison result, and

if the first comparison result is not within the set of at least one acceptable value of the first comparison result, determining that at least one of the fifth, sixth, and seventh transformed-domain image data has been improperly altered.

54. A computer-readable medium according to claim 53, wherein the first transformed-domain image datum is included in a first set of transformed-domain image data, the second transformed-domain image datum is included in a second set of transformed-domain image data, the fifth transformed-domain image datum is included in a third set of transformed-domain image data, the sixth transformed-domain image datum is included in a fourth set of transformed-domain image data, and the set of instructions is further operable to direct the processor to perform the steps of:

using a first secret mapping to form an association between the first and second sets of transformed-domain image data; and

using the association between the first and second sets of transformed-domain image data for selecting at least one of the first and second transformed-domain image data to be compared in the step of comparing the first transformed-domain image datum to the second transformed-domain image datum, wherein the authentication procedure further comprises the steps of;

using the first secret mapping to form an association between the third and fourth sets of transformed-domain image data, and

using the association between the third and fourth sets of transformed-domain image data for selecting at least one of the fifth and sixth transformed-domain image data to be compared in the step of comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum.

55. A computer-readable medium according to claim 54, wherein the first and second sets of transformed-domain image data are included in a fifth set of transformed-domain image data, the third transformed-domain image datum is included in a sixth set of transformed-domain image data, the third and fourth sets of transformed-domain image data are included in a seventh set of transformed-domain image data, the seventh transformed-domain image datum is included in an eighth set of transformed-domain image data, and the set of instructions is further operable to direct the processor to perform the steps of:

using a second secret mapping to form an association between the fifth and sixth sets of transformed-domain image data; and

using the association between the fifth and sixth sets of transformed-domain image data for selecting the third transformed-domain image datum to be converted, in the step of using the replacement code, into the fourth transformed-domain image datum, wherein the authentication procedure further comprises the steps of;

using the second secret mapping to form an association between the seventh and eighth sets of transformed-domain image data, and

using the association between the seventh and eighth sets of transformed-domain image data for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted in the step of using the authentication code extraction function to extract the second authentication code.

56. A computer-readable medium according to claim 53, wherein the first and second transformed-domain image data are included in a first set of transformed-domain image data, the third transformed-domain image datum is included in a second set of transformed-domain image data, the fifth and sixth transformed-domain image data are included in a third set of transformed-domain image data, the seventh transformed-domain image datum is included in a fourth set of transformed-domain image data, and the set of instructions is further operable to direct the processor to perform the steps of:

using a first secret mapping to form an association between the first and second sets of transformed-domain image data; and

using the association between the first and second sets of transformed-domain image data for selecting the third transformed-domain image datum to be converted, in the step of using the replacement code, into the fourth transformed-domain image datum, wherein the authentication procedure further comprises the steps of;

using the first secret mapping to form an association between the third and fourth sets of transformed-domain image data, and

using the association between the third and fourth sets of transformed-domain image data for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted in the step of using the authentication code extraction function to extract the second authentication code.

57. A computer-readable medium according to claim 53, wherein the first transformed-domain image datum is included in a first set of transformed-domain image data, the second transformed-domain image datum is included in a second set of transformed-domain image data, the fifth transformed-domain image datum is included in a third set of transformed-domain image data, the sixth transformed-domain image datum is included in a fourth set of transformed-domain image data, and the set of instructions is further operable to direct the processor to perform the steps of:

using a first secret transformed-domain location selection pattern for selecting the first transformed-domain image datum to be compared in the step of comparing the first transformed-domain image datum to the second transformed-domain image datum, the first secret transformed-domain location selection pattern comprising at least a first datum selection location, the first transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the first set of transformed-domain image data; and

using the first secret transformed-domain location selection pattern for selecting the second transformed-domain image datum to be compared in the step of comparing the first transformed-domain image datum to the second transformed-domain image datum, the second transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the second set of transformed-domain image data, wherein the authentication procedure further comprises the steps of;

using the first secret transformed-domain location selection pattern for selecting the fifth transformed-domain image datum to be compared in the step of comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum, the fourth transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the third set of transformed-domain image data, and

using the first secret transformed-domain location selection pattern for selecting the sixth transformed-domain image datum to be compared in the step of comparing the fifth transformed-domain image datum to the sixth transformed-domain image datum, the fifth transformed-domain location being approximately equal to the first datum selection location in a coordinate system of the fourth set of transformed-domain image data.

58. A computer-readable medium according to claim 57, wherein the third transformed-domain image datum is included in a fifth set of transformed-domain image data, the seventh transformed-domain image datum is included in a sixth set of transformed-domain image data, and the set of instructions is further operable to direct the processor to perform the step of using a second secret transformed-domain location selection pattern for selecting the third transformed-domain image datum to be converted, in the step of using the replacement code, into the fourth transformed-domain image datum, the third transformed-domain image datum having the third transformed-domain location, the second secret transformed-domain location selection pattern comprising at least a second datum selection location, the third transformed-domain location being approximately equal to the second datum selection location in a coordinate system of the fifth set of transformed-domain image data, wherein the authentication procedure further comprises using the second secret transformed-domain location selection pattern for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted in the step of using the authentication code extraction function to extract the second authentication code, the sixth transformed-domain location being approximately equal to the second datum selection location in a coordinate system of the sixth set of transformed-domain image data.

59. A computer-readable medium according to claim 53, wherein the third transformed-domain image datum is included in a first set of transformed-domain image data, the seventh transformed-domain image datum is included in a second set of transformed-domain image data, and the set of instructions is further operable to direct the processor to perform the step of using a secret transformed-domain location selection pattern for selecting the third transformed-domain image datum to be converted, in the step of using the replacement code, into the fourth transformed-domain image datum, the third transformed-domain image datum having the third transformed-domain location, the secret transformed-domain location selection pattern comprising at least a datum selection location, the third transformed-domain location being approximately equal to the datum selection location in a coordinate system of the first set of transformed-domain image data, wherein the authentication procedure further comprises using the secret transformed-domain location selection pattern for selecting the seventh transformed-domain image datum to be a datum from which the second authentication code is extracted in the step of using the authentication code extraction function to extract the second authentication code, the sixth transformed-domain location being approximately equal to the datum selection location in a coordinate system of the second set of transformed-domain image data.

60. A computer-readable medium according to claim 53, wherein the portion of the third transformed-domain image datum comprises a bit of the third transformed-domain image datum, the first authentication code comprises an authentication bit, and the set of instructions is further operable to direct the processor to perform the step of processing the authentication bit and a bit of a secret key by a binary operation, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

61. A computer-readable medium according to claim 53, wherein the portion of the third transformed-domain image datum comprises a bit of the third transformed-domain image datum, and the replacement code comprises at least one of a bit of the first authentication code and a code selected based upon the bit of the first authentication code.

62. A computer-readable medium according to claim 53, wherein the authentication procedure further comprises:

using the authentication code extraction function to extract a first set of authentication codes from at least one portion of a first set of transformed-domain image data, the first set of transformed-domain image data including the sixth transformed-domain image datum;

comparing at least one portion of a second set of transformed-domain image data to at least one portion of a third set of transformed-domain image data, for deriving a first set of comparison results;

based on each of the first set of authentication codes, selecting a set of at least one acceptable value of a member of the first set of comparison results associated with the each of the first set of authentication codes;

if the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes, determining that the first set of transformed-domain image data has not been improperly altered.

63. A computer-readable medium according to claim 62, wherein the authentication procedure further comprises:

using the authentication code extraction function to extract a second set of authentication codes from at least one portion of a fourth set of transformed-domain image data;

comparing at least one portion of a fifth set of transformed-domain image data to at least one portion of a sixth set of transformed-domain image data, for deriving a second set of comparison results, the fifth set of transformed-domain image data including the seventh transformed-domain image datum;

based on each of the second set of authentication codes, selecting a set of at least one acceptable value of a member of the second set of comparison results associated with the each of the second set of authentication codes;

if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, determining that the fifth set of transformed-domain image data has not been improperly altered.

64. A computer-readable medium according to claim 63, wherein the authentication procedure further comprises:

if the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes, and if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, determining that a seventh set of transformed-domain image data has been improperly altered, the seventh set of transformed-domain image data including the fifth transformed-domain image datum.

65. A computer-readable medium according to claim 62, wherein the authentication procedure further comprises:

using the authentication code extraction function to extract a second set of authentication codes from at least one portion of a fourth set of transformed-domain image data, the fourth set of transformed-domain image data including the fifth transformed-domain image datum;

comparing at least one portion of a fifth set of transformed-domain image data to at least one portion of a sixth set of transformed-domain image data, for deriving a second set of comparison results;

based on each of the second set of authentication codes, selecting a set of at least one acceptable value of a member of the second set of comparison results associated with the each of the second set of authentication codes;

if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, determining that the fourth set of transformed-domain image data has not been improperly altered.

66. A computer-readable medium according to claim 65, wherein the authentication procedure further comprises:

if the member of the first set of comparison results associated with the each of the first set of authentication codes is within the set of at least one acceptable value of the member of the first set of comparison results associated with the each of the first set of authentication codes, and if the member of the second set of comparison results associated with the each of the second set of authentication codes is within the set of at least one acceptable value of the member of the second set of comparison results associated with the each of the second set of authentication codes, determining that a seventh set of transformed-domain image data has been improperly altered, the seventh set of transformed-domain image data including the seventh transformed-domain image datum.

67. A computer-readable medium having a set of instructions operable to direct a processor to perform the steps of:

encoding by an encoding function a first set of transformed-domain image data, for deriving a set of image data recovery codes comprising a first image data recovery code, the first set of transformed-domain image data being included in a second set of transformed-domain image data, the second set of transformed-domain image data being derived from a first set of spatial domain image data; and

using a replacement code to replace at least a portion of a first transformed-domain image datum, for converting the first transformed-domain image datum into a second transformed-domain image datum, the first transformed-domain image datum being included in a third set of transformed-domain image data, the third set of transformed-domain image data being derived from the first set of spatial domain image data, the replacement code comprising at least one of the first image data recovery code, a code derived from the first image data recovery code, a code selected based upon at least the first image data recovery code, and a code selected based upon at least the code derived from the first image data recovery code, the second transformed-domain image datum being for deriving a third transformed-domain image datum, the first set of spatial domain image data being for deriving a fourth set of transformed-domain image data, the third transformed-domain image datum being for deriving, by a recovery procedure, an approximation data set for replacing the fourth set of transformed-domain image data, and the recovery procedure comprising the steps of;

using a recovery code extraction function to extract a second image data recovery code from the third transformed-domain image datum, the second image data recovery code being approximately equal to the first image data recovery code; and

decoding by a decoding function at least the second image data recovery code, for deriving the approximation data set, the decoding function comprising a functional inverse of the encoding function.

68. A computer-readable medium according to claim 67, wherein the set of instructions is further operable to direct the processor to perform the steps of:

averaging a second set of spatial domain image data, for deriving a first reduced image datum;

averaging a third set of spatial domain image data, for deriving a second reduced image datum, the first and second reduced image data being included in a reduced set of spatial domain image data, and the second and third sets of spatial domain image data being included in the first set of spatial domain image data;

domain-transforming the reduced set of spatial domain image data, for deriving a fifth set of transformed-domain image data; and

quantizing the fifth set of transformed-domain image data, for deriving the first set of transformed-domain image data.

69. A computer-readable medium according to claim 68, wherein the portion of the first transformed-domain image datum comprises a bit of the first transformed-domain image datum, and the first image data recovery code comprises a data recovery bit.

70. A computer-readable medium according to claim 69, wherein the set of instructions is further operable to direct the processor to perform the step of processing the data recovery bit and a bit of a secret key by a binary operation, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

71. A computer-readable medium according to claim 67, wherein the portion of the first transformed-domain image datum comprises a bit of the first transformed-domain image datum, and the first image data recovery code comprises a data recovery bit.

72. A computer-readable medium according to claim 71, wherein the set of instructions is further operable to direct the processor to perform the step of processing the data recovery bit and a bit of a secret key by a binary operation, for deriving an encrypted bit, the replacement code comprising at least one of the encrypted bit, a code derived from the encrypted bit, and a code selected based upon the encrypted bit.

73. A computer-readable medium according to claim 67, wherein the encoding function comprises an entropy encoding function.

74. A computer-readable medium according to claim 73, wherein the entropy encoding function comprises at least one of a Huffman encoding function and a JPEG entropy encoding function.

75. A computer-readable medium having a set of instructions operable to direct a processor to perform the steps of:

quantizing a first set of transformed-domain image data based on a first quantization step size, for deriving a second set of transformed-domain image data, the second set of transformed-domain image data including at least a first transformed-domain image datum; and

using a replacement code to replace at least a portion of the first transformed-domain image datum, for converting the first transformed-domain image datum into a second transformed-domain image datum, the second transformed-domain image datum being included in a third set of transformed-domain image data, the replacement code comprising at least one of a watermark code, a code derived from the watermark code, a code selected based on the watermark code, and a code selected based upon at least the code derived from the watermark code, wherein the third set of transformed-domain image data is for being altered by an alteration procedure for deriving a fourth set of transformed-domain image data, the alteration procedure comprising at least one of;

(1) quantizing the third set of transformed-domain image data based on a second quantization step size, the second quantization step size being no greater than the first quantization step size, (2) transforming a data encoding format of the third set of transformed-domain image data into a different data encoding format, and (3) filtering the third set of transformed-domain image data, the fourth set of transformed-domain image data including at least a third transformed-domain image datum, and the third transformed-domain image datum being derived from the second transformed-domain image datum, wherein the third transformed-domain image datum is for being processed by a watermark extraction procedure for extracting the watermark code from the third transformed-domain image datum, the watermark extraction procedure comprising the steps of;

requantizing the third transformed-domain image datum based on the first quantization step size, for generating a fourth transformed-domain image datum, and

processing the fourth transformed-domain image datum by a watermark extraction function, for deriving an extracted code approximately equal to the watermark code.

76. A computer-readable medium according to claim 75, wherein the first set of transformed-domain image data includes a fifth transformed-domain image datum, the first transformed-domain datum is derived from the fifth transformed-domain image datum, and the set of instructions is further operable to direct the processor to perform the the step of deriving the watermark code based on at least one datum derived from at least a first portion of a set of spatial domain image data, the fifth transformed-domain image datum being derived from a second portion of the set of spatial domain image data.

77. A computer-readable medium according to claim 76, wherein the set of instructions is further operable to direct the processor to perform the steps of:

using a secret mapping to form an association between at least the first transformed-domain image datum and at least the datum derived from the first portion of the set of spatial domain image data; and

using the association between the at least the first transformed-domain image datum and the at least the datum derived from the first portion of the set of spatial domain image data for selecting the first transformed-domain image datum to be converted, in the step of using the first replacement code, into the second transformed-domain image datum.

78. A computer-readable medium according to claim 75, wherein the first transformed-domain image datum has a secret transformed-domain location.