Method and apparatus for digital watermarking

• US 6,704,431 B1
• Filed: 08/31/1999
• Issued: 03/09/2004
• Est. Priority Date: 09/04/1998
• Status: Expired due to Fees

• Current Assignee: Nippon Telegraph and Telephone Corporation
• Original Assignee: Nippon Telegraph and Telephone Corporation
• Inventors: Ogawa, Hiroshi, Tomioka, Atsuki, Nakamura, Takao, Takashima, Youichi
• Primary Examiner(s): Mehta, Bhavesh M.
• Assistant Examiner(s): Choobin, Barry
• Application Number:
  US09/386,993
• Time in Patent Office: 1,652 Days
• Field of Search: 382/100, 382/135, 382/250, 382/238, 382/239, 382/233, 382/173, 382/226, 380/205, 380/54, 704/270, 713/176, 348/207.99
• US Class Current: 382/100
• CPC Class Codes: G06T 1/0028 Adaptive watermarking, e.g. Human Visual System [HVS]-based watermarking
• CPC Class Codes: G06T 2201/0052 Embedding of the watermark in the frequency domain
• CPC Class Codes: G06T 2201/0083 whereby only watermarked image required at decoder, e.g. source-based, blind, oblivious
• CPC Class Codes: H04N 1/32154 Transform domain methods H04N1/32309 takes precedence
• CPC Class Codes: H04N 19/467 characterised by the embedded information being invisible, e.g. watermarking

Abstract

A method for embedding digital watermark data in digital data contents includes the steps of obtaining a frequency coefficient of block data of digital data contents, obtaining a complexity of the block data, obtaining an amount of transformation of the frequency coefficient from the complexity and the digital watermark data, and embedding the digital watermark data by transforming the frequency coefficient. In addition, a method for reading digital watermark data includes the steps of calculating a probability of reading ‘1’ or ‘0’ in a read bit sequence by using a test method on the basis of binary distribution, determining the presence or absence of digital watermark data according to the probability, and reconstituting digital watermark data. Another method includes the steps of performing soft decision in code theory by assigning weights to the digital watermark sequence with a weighting function, and reconstituting digital watermark data.

Claims

1. A method for reading digital watermark data embedded in digital data contents, said method comprising the steps of:

receiving said digital data contents;

determining threshold α

of reliability of digital watermark data which is read;

obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

calculating the number k_i of ‘

1’

or ‘

0’

included in said digital watermark sequence;

calculating a probability F(k_i) by using said binary distribution function F(x); and

reconstituting ‘

1’

or ‘

0’

from ith digital watermark data w_i if F(k_i)>

α

, reconstituting ‘

0’

or ‘

1’

from ith digital watermark data w_i if 1−

F(k_i)>

α

, and determining that there is no watermark data or the presence is unknown if both of F(k_i)>

α and

1−

F(k_i)>

α

are not satisfied.

2. The method as claimed in claim 1, further comprising the steps of:

outputting F(k_i) as reliability if said reconstituted digital watermark data w_i is ‘

1’

; and

outputting 1−

F(k_i) as the reliability if said reconstituted digital watermark data w_i is ‘

0’

.

5. The method as claimed in claim 1, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said method further comprising the steps of:

demodulating said digital watermark sequence by said pseudo-random sequence; and

reconstituting digital watermark data from said demodulated digital watermark sequence.

3. A method for reading digital watermark data embedded in digital data contents, said method comprising the steps of:

receiving said digital data contents;

determining a threshold α

of reliability of digital watermark data which is read;

obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

checking whether a probability that said digital watermark sequence is digital watermark data exceeds said threshold α

by using said binary distribution function F(x); and

reconstituting digital watermark data from said digital watermark sequence by using majority decision processing if said probability exceeds α

, and determining that there is no watermark data or the presence is unknown if said probability does not exceed α

.

4. The method as claimed in claim 3, further comprising a step of outputting said probability that said digital watermark sequence is digital watermark data.

6. A method for reading digital watermark data embedded in digital data contents, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said method comprising the steps of:

receiving said digital data contents;

determining a threshold α

of reliability of digital watermark data which is read;

obtaining a binary distribution function F(x) which represents a probability that a number of x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

demodulating said digital watermark sequence by said pseudo-random sequence;

assigning ½

to said probability q;

obtaining a maximum number x₀ which satisfies 0≦

F(x=x₀)≦

1−

α and

a minimum number x₁ which satisfies α

≦

(x=x₁)≦

1;

obtaining the number k_i of ‘

1’

or ‘

0’

included in said ith digital watermark sequence; and

reconstituting ith digital watermark data w_i as ‘

0’

or ‘

1’

if k_i≦

x₀, and reconstituting said ith digital watermark data w_i as ‘

1’

or ‘

0’

if k_i≧

x_i.

7. A method for reading digital watermark data embedded in digital data contents;

if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said method comprising the steps of;

receiving said digital data contents;

determining a threshold α

of reliability of digital watermark data which is read;

obtaining a binary distribution function F(x) which represents a probability that x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number t of embedding each bit of digital watermark data;

reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

demodulating said digital watermark sequence by said pseudo-random sequence;

assigning ½

to said probability q;

obtaining x₀ or x₁ which satisfies 0≦

F(x=x₀)≦

1−

α

or α

≦

(x=x₁)≦

1;

determining whether a value is equal to or less than x₀ or equal to or more than x₁, said value being a mean value of absolute values of a difference between the number of ‘

0’

or ‘

1’

included in said ith digital watermark sequence and a central value q×

t of a binary distribution;

reconstituting digital watermark data by performing majority decision processing for said ith digital watermark sequence if said value is equal to or less than x₀ or equal to or more than x₁; and

determining that there is no digital watermark data or the presence is unknown if said value is not equal to or less than x₀ or equal to or more than x₁.

8. The method as claimed in claim 7, further comprising the steps of:

calculating a value of said binary distribution function F(z), z being said mean value obtained from the number of ‘

0’

or ‘

1’

included in said ith digital watermark sequence and said central value q×

t; and

outputting said value of F(z) as reliability of digital watermark data.

9. An apparatus for reading digital watermark data embedded in digital data contents, said apparatus comprising;

means for receiving said digital data contents;

means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

means for calculating the number k_i of ‘

1’

or ‘

0’

included in said digital watermark sequence;

means for calculating a probability F(k_i) by using said binary distribution function F(x); and

means for reconstituting ‘

1’

or ‘

0’

from ith digital watermark data w_i if F(k_i)>

α

, reconstituting ‘

0’

or ‘

1’

from ith digital watermark data w_i if 1−

F(k_i)>

α

, and, determining that there is no watermark data or the presence is unknown if both of F(k_i)>

α and

1−

F(k_i)>

α

are not satisfied, α

being a threshold of reliability of digital watermark data which is read.

10. The apparatus as claimed in claim 9, further comprising:

means for outputting F(k_i) as reliability if said reconstituted digital watermark data w_i is ‘

1’

; and

means for outputting 1−

F(k_i) as reliability if said reconstituted digital watermark data w_i is ‘

0’

.

13. The apparatus as claimed in claim 9, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said apparatus further comprising:

means for demodulating said digital watermark sequence by said pseudo-random sequence; and

means for reconstituting digital watermark data from said demodulated digital watermark sequence.

11. An apparatus for reading digital watermark data embedded in digital data contents, said apparatus comprising:

means for receiving said digital data contents;

means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

means for checking whether a probability that said digital watermark sequence is digital watermark data exceeds said threshold α

by using said binary distribution function F(x), α

being a threshold of reliability of digital watermark data which is read; and

means for reconstituting and generating digital watermark data from said digital watermark sequence by using majority decision processing if said probability exceeds α

, and, determining that there is no watermark data or the presence is unknown if said probability does not exceed α

.

12. The apparatus as claimed in claim 11, further comprising means for outputting said probability that said digital watermark sequence is digital watermark data.

14. An apparatus for reading digital watermark data embedded in digital data contents, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said apparatus comprising:

means for receiving said digital data contents;

means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

means for demodulating said digital watermark sequence by said pseudo-random sequence;

means for assigning ½

to said probability q;

means for obtaining a maximum number x₀ which satisfies 0≦

F(x=x₀)≦

1−

α and

a minimum number x₁ which satisfies α

≦

F(x=x₁)≦

1, α

being a threshold of reliability of digital watermark data which is read;

means for obtaining the number k_i of ‘

1’

or ‘

0’

included in said ith digital watermark sequence; and

means for reconstituting ith digital watermark data w_i as ‘

0’

or ‘

1’

if k_i≦

x₀, and, reconstituting said ith digital watermark data w_i as ‘

1’

or ‘

0’

if k_i≧

x₁.

15. An apparatus for reading digital watermark data embedded in digital data contents:

, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said apparatus comprising;

means for receiving said digital data contents;

means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number t of embedding each bit of digital watermark data;

means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

means for demodulating said digital watermark sequence by said pseudo-random sequence;

means for assigning ½

to said probability q;

means for obtaining x₀ or x₁ which satisfies 0≦

F(x=x₀)≦

1−

α

or α

≦

F(x=x₁)≦

1, α

being a threshold of reliability of digital watermark data which is read;

means for determining whether a value is equal to or less than x₀ or equal to or more than x₁, said value being a mean value of absolute values of a difference between the number of ‘

0’

or ‘

1’

included in said ith digital watermark sequence and a central value q×

t of a binary distribution;

means for reconstituting digital watermark data by performing majority decision processing for said ith digital watermark sequence if said value is equal to or less than x₀ or equal to or more than x₁; and

means for determining that there is no digital watermark data or the presence is unknown if said value is not equal to or less than x₀ or equal to or more than x₁.

16. The apparatus as claimed in claim 15, further comprising:

means for calculating a value of said binary distribution function F(z), z being said mean value obtained from the number of ‘

0’

or ‘

1’

included in said ith digital watermark sequence and said central value q×

t; and

means for outputting said value of F(z) as reliability of digital watermark data.

17. An integrated circuit for reading digital watermark data embedded in digital data contents, said integrated circuit comprising:

means for receiving said digital data contents;

means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

means for calculating the number k_i of ‘

1’

or ‘

0’

included in said digital watermark sequence;

means for calculating a probability F(k_i) by using said binary distribution function F(x); and

means for reconstituting ‘

1’

or ‘

0’

from ith digital watermark data w_i if F(k_i)>

α

, reconstituting ‘

0’

or ‘

1’

from ith digital watermark data w_i if 1−

F(k_i)>

α

, and determining that there is no watermark data or the presence is unknown if both of F(k_i)>

α and

1−

F(k_i)>

α

are not satisfied, α

being a threshold of reliability of digital watermark data which is read.

18. The integrated circuit as claimed in claim 17, further comprising:

means for outputting F(k_i) as reliability if said reconstituted digital watermark data w_i is ‘

1’

; and

means for outputting 1−

F(k_i) as reliability if said reconstituted digital watermark data w_i is ‘

0’

.

21. The integrated circuit as claimed in claim 17, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said integrated circuit further comprising:

means for demodulating said digital watermark sequence by said pseudo-random sequence; and

means for reconstituting digital watermark data from said demodulated digital watermark sequence.

19. An integrated circuit for reading digital watermark data embedded in digital data contents, said integrated circuit comprising:

means for receiving said digital data contents;

means for obtaining a binary distribution function F(x) which represents a probability that a number of x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

means for checking whether a probability that said digital watermark sequence is digital watermark data exceeds said threshold a by using said binary distribution function F(x), α

being a threshold of reliability of digital watermark data which is read; and

means for reconstituting and generating digital watermark data from said digital watermark sequence by using majority decision processing if said probability exceeds α

, and, determining that there is no watermark data or the presence is unknown if said probability does not exceed α

.

20. The integrated circuit as claimed in claim 19, further comprising means for outputting said probability that said digital watermark sequence is digital watermark data.

22. An integrated circuit for reading digital watermark data embedded in digital data contents, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said integrated circuit comprising:

means for receiving said digital data contents;

means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

means for demodulating said digital watermark sequence by said pseudo-random sequence;

means for assigning ½

to said probability q;

means for obtaining a maximum number x₀ which satisfies 0≦

F(x=x₀)≦

1−

α and

a minimum number x₁ which satisfies a α

≦

F(x=x₁)≦

1, α

being a threshold of reliability of digital watermark data which is read; and

means for obtaining the number k_i of ‘

1’

or ‘

0’

included in said ith digital watermark sequence;

means for reconstituting ith digital watermark data w_i as ‘

0’

or ‘

1’

if k_i≦

x₀, and, reconstituting said ith digital watermark data w_i as ‘

1’

or ‘

0’

if k_i≦

x₁.

23. An integrated circuit for reading digital watermark data embedded in digital data contents, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said integrated circuit comprising:

means for receiving said digital data contents;

means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number t of embedding each bit of digital watermark data;

means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

means for demodulating said digital watermark sequence by said pseudo-random sequence;

means for assigning ½

to said probability q;

means for obtaining x₀ or x₁ which satisfies 0≦

F(x=x₀)≦

1−

α

or α

≦

F(x=x₁)≦

1, α

being a threshold of reliability of digital watermark data which is read;

means for determining whether a value is equal to or less than x₀ or equal to or more than x₁, said value being a mean value of absolute values of a difference between the number of ‘

0’

or ‘

1’

included in said ith digital watermark sequence and a central value q×

t of a binary distribution;

means for reconstituting digital watermark data by performing majority decision processing for said ith digital watermark sequence if said value is equal to or less than x₀ or equal to or more than x₁; and

means for determining that there is no digital watermark data or the presence is unknown if said value is not equal to or less than x₀ or equal to or more than x₁.

24. The integrated circuit as claimed in claim 23, further comprising:

means for calculating a value of said binary distribution function F(z), z being said mean value obtained from the number of ‘

0’

or ‘

1’

included in said ith digital watermark sequence and said central value q×

t; and

means for outputting said value of F(z) as reliability of digital watermark data.

25. A computer readable medium storing program code for causing a computer system to read digital watermark data embedded in digital data contents, said computer readable medium comprising:

program code means for receiving said digital data contents;

program code means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bi;

sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability a of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

program code means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

program code means for calculating the number k_i of ‘

1’

or ‘

0’

included in said digital watermark sequence; and

program code means for calculating a probability F(k_i) by using said binary distribution function F(x);

program code means for reconstituting ‘

1’

or ‘

0’

from ith digital watermark data w_i

if F(k_i)>

α

, reconstituting ‘

0’

or ‘

1’

from ith digital watermark data w_i if 1−

F(k_i)>

α

, and, determining that there is no watermark data or the presence is unknown if both of F(k_i)>

α and

1−

F(k_i)>

α

are not satisfied, α

being a threshold of reliability of digital watermark data which is read.

26. The computer readable medium as claimed in claim 25, further comprising:

program code means for outputting F(k_i) as reliability if said reconstituted digital watermark data w_i is ‘

1’

; and

program code means for outputting 1−

F(k_i) as reliability if said reconstituted digital watermark data w_i is ‘

0’

.

29. The computer readable medium as claimed in claim 25, if a data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said computer readable medium further comprising:

program code means for demodulating said digital watermark sequence by said pseudo-random sequence; and

program code means for reconstituting digital watermark data from said demodulated digital watermark sequence.

27. A computer readable medium storing program code for causing a computer system to read digital watermark data embedded in digital data contents, said computer readable medium comprising:

program code means for receiving said digital data contents;

program code means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bi;

sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability a of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

program code means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

program code means for checking whether a probability that said digital watermark sequence is digital watermark data exceeds said threshold by rising said binary distribution function F(x), α

being a threshold of reliability of digital watermark data which is read; and

program code means for reconstituting and generating digital watermark data from said digital watermark sequence by using majority decision processing if said probability exceeds α

, and determining that there is no watermark data or the presence is unknown if said probability does not exceed α

.

28. The computer readable medium as claimed in claim 27, further comprising program code means for outputting said probability that said digital watermark sequence is digital watermark data as reliability of said reconstituted digital watermark data.

30. A computer readable medium storing program code for causing a computer system to read digital watermark data embedded in digital data contents, if data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said computer readable medium comprising:

program code means for receiving said digital data contents;

program code means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number of embedding each bit of digital watermark data;

program code means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

program code means for demodulating said digital watermark sequence by said pseudo-random sequence;

program code means for assigning ½

to said probability q;

program code means for obtaining a maximum number x₀ which satisfies 0≦

F(x=x₀)≦

1−

α and

a minimum number x₁ which satisfies a α

≦

F(x=x₁)≦

1, α

being a threshold of reliability of digital watermark data which is read; and

program code means for obtaining the number k_i of ‘

1’

or ‘

0’

included in said ith digital watermark sequence;

program code means for reconstituting ith digital watermark data w_i as ‘

0’

or ‘

1’

if k_i≦

x₀, and, reconstituting said ith digital watermark data w_i as ‘

1’

or ‘

0’

if k_i≦

x₁.

31. A computer readable medium storing program code for causing a computer system to read digital watermark data embedded in digital data contents, if data sequence which is embedded as said digital watermark data is modulated by a pseudo-random sequence, said computer readable medium comprising:

program code means for receiving said digital data contents;

program code means for obtaining a binary distribution function F(x) which represents a probability that a number x of ‘

1’

bits or ‘

0’

bits are included in a bit sequence which is read at random from digital data contents, said binary distribution function F(x) being obtained by using a probability q of reading ‘

1’

or ‘

0’

in said bit sequence and a repeating number t of embedding each bit of digital watermark data;

program code means for reading an ith digital watermark sequence of said digital watermark data from a digital watermark area of said digital data contents;

program code means for demodulating said digital watermark sequence by said pseudo-random sequence;

program code means for assigning ½

to said probability q;

program code means for obtaining x₀ or x₁ which satisfies 0≦

F(x=x₀)≦

1−

α

or α

≦

F(x=x₁)≦

1, α

being a threshold of reliability of digital watermark data which is read;

program code means for determining whether a value is equal to or less than x₀ or equal to or more than x₁, said value being a mean value of absolute values of a difference between the number of ‘

0’

or ‘

1’

included in said ith digital watermark sequence and a central value q×

t of a binary distribution;

program code means for reconstituting digital watermark data by performing majority decision processing for said ith digital watermark sequence if said value is equal to or less than x₀ or equal to or more than x₁; and

program code means for determining that there is no digital watermark data or the presence is unknown if said value is not equal to or less than x₀ or equal to or more than x₁.

32. The computer readable medium as claimed in claim 31, further comprising:

program code means for calculating a value of said binary distribution function F(z), z being said mean value obtained from the number of ‘

0’

or ‘

1’

included in said ith digital watermark sequence and said central value q×

t; and

program code means for outputting said value of F(z) as reliability of digital watermark data.