BAUM, Peter, Georg (Aschendorfer Str. 25, Hannover, 30539, DE)
ARNOLD, Michael (Eichendorffstr. 1b, Isernhagen, 30916, DE)
GRIES, Ulrich (Friedenauer Str. 20b, Hannover, 30419, DE)
CHEN, Xiao-Ming (Vahrenwalderstr. 101, Hannover, 30165, DE)
BAUM, Peter, Georg (Aschendorfer Str. 25, Hannover, 30539, DE)
ARNOLD, Michael (Eichendorffstr. 1b, Isernhagen, 30916, DE)
GRIES, Ulrich (Friedenauer Str. 20b, Hannover, 30419, DE)
| Claims 1. Method for detecting which one of symbols of watermark data embedded in an original signal - by modifying sec- tions of said original signal in relation to at least two different reference data sequences (REFP) - is present in a current section of a received (11) version of the wa¬ termarked original signal (RWAS) , wherein said received watermarked original signal can include noise and/or ech- oes, said method including the steps: correlating (13) in each case said current section of said received watermarked signal (RWAS) with candidates of said reference data sequences (REFP) ; based on peak values in the correlation result values for said current signal section, detecting (14) - using related values of false positive probability of detection of the kind of symbol - which one of the candidate sym¬ bols is present in said current signal section, characterised in that said false positive probability (P(M ) is calculated (21, L2, L3) in a recursive manner, wherein the total false positive probability for a given number of correlation result peak values is evaluated by using initially the false positive probabilities for a number smaller than said given of correlation result peak values, and by increasing gradually the number of consid¬ ered correlation result peak values according to the re¬ quired detection reliability. 2. Apparatus for detecting which one of symbols of watermark data embedded in an original signal - by modifying sec¬ tions of said original signal in relation to at least two different reference data sequences (REFP) - is present in a current section of a received (11) version of the wa¬ termarked original signal (RWAS) , wherein said received watermarked original signal can include noise and/or ech¬ oes, said apparatus including means being adapted for: correlating (13) in each case said current section of said received watermarked signal (RWAS) with candidates of said reference data sequences (REFP) ; based on peak values in the correlation result values for said current signal section, detecting (14) - using related values of false positive probability of detection of the kind of symbol - which one of the candidate sym¬ bols is present in said current signal section, characterised in that said false positive probability (P(M is calculated (21, L2, L3) in said symbol detec¬ tion means in a recursive manner, wherein the total false positive probability for a given number of correlation result peak values is evaluated by using initially the false positive probabilities for a number smaller than said given of correlation result peak values, and by in¬ creasing gradually the number of considered correlation result peak values according to the required detection reliability . Method according to claim 1, or apparatus according to claim 2, wherein said original signal is an audio signal or a video signal. Method according to claim 1 or 3, or apparatus according to claim 2 or 3, wherein for a first peak value and a first one of said candidate symbols said false positive probability is calculated (21), and: if the corresponding false positive probability is smaller than a predetermined threshold value (22), the current candidate symbol is assumed (24) to be the cor¬ rect symbol; if said false positive probability is not smaller than said predetermined threshold value (22), said false posi¬ tive probability for said first peak value is calculated (21) for the following one of said candidate symbols and the processing continues with step a) ; if none of the calculated false positive probability val ues is smaller than said predetermined threshold value (22), steps a) and possibly b) are continued for a fol¬ lowing one of said peak values; if none of the calculated false positive probability val ues is smaller than said predetermined threshold value (22), the candidate symbol for which the minimum false positive probability has been calculated is assumed (23, 24) to be the correct symbol. Method according to claim 4, or apparatus according to claim 4, wherein a total value of the false positive probability of multiple peaks is determined by calculat¬ ing the complementary probability in a recursive manner, and wherein the complementary probability for a given number of peaks is calculated by using representative vectors identifying each individual probability. Method according to claim 5, or apparatus according to claim 5, wherein the complementary probability for k+1 peaks is calculated recursively from the complementary probability for k peaks plus all the probabilities repre¬ sented by the representative vectors for k+1 peaks, and wherein the representative vectors for k+1 peaks are con¬ structed recursively from the representative vectors for k peaks . |
The invention relates to a method and to an apparatus for detecting which one of symbols of watermark data is embedded in a received signal, wherein following correlation with reference data sequences peak values in the correlation result are evaluated using false positive probability of wrong detection of the kind of symbol.
Background
EP 2175443 Al discloses a statistical detector that is used for detecting watermark data within an audio signal. Multiple peaks in a correlation result values sequence of length N (resulting from a correlation of a reference sequence with a corresponding section of the received audio signal) are taken into account for improving the detection reliability. The basic steps of this statistical detector are:
- Find peak values v l ≥...≥v M in the correlation result values sequence for each candidate watermark symbol, where M is the number of peaks taken into consideration.
- Calculate the false positive probability denoted as P (M) for the M peak values that the candidate watermark symbol is embedded.
- The candidate watermark symbol with the lowest probability P (M) i s selected as current watermark symbol. P (M) i s the probability of falsely accepting a candidate wa ¬ termark symbol. It describes the probability of M or more correlation result values in an unmarked case (i.e. no watermark is present in the corresponding original signal section) being greater than or equal to the actual M peak val- ues under consideration. Invention
A non-recursive statistical detector could be used for the watermark detection but this would be inefficient and lead to difficulties for a large number of correlation result peaks .
For the evaluation of the probability P (M) °f M or more val ¬ ues being greater than or equal to M peaks, all possible allocations of N correlation values are to be considered. For a small number M of peak values it is easy to manually list all possibilities, i.e. positions within the group of correlation results. However, for a larger number of M it becomes increasingly difficult to manually find all possibilities. Alternatively, instead of searching for probabilities of M or more correlation values being greater than or equal to M peak values, cases can be considered where less than M correlation values are greater than or equal to M peaks. But again, the problem is how to efficiently find all possibili- ties.
Known statistical detectors are using a fixed number of correlation peaks. However, due to the time-varying property of a received audio signal the number of peaks to be considered should be selected adaptively. That is, for a high signal- to-noise ratio SNR a small M is sufficient for the detection, whereas a greater M may be necessary for a low-SNR signal. Therefore, using a number of peaks that is adaptive to the signal quality provides computational and technical advantages.
A problem to be solved by the invention is how to recursively and effectively evaluate the probability P (M) even for a large number M of correlation result peaks. This prob- lem is solved by the method disclosed in claim 1. An apparatus that utilises this method is disclosed in claim 2. According to the invention, the total false positive probability of multiple peaks in a correlation result values sequence is evaluated by calculating the complementary probability in a recursive manner. The complementary probability for a given number of peaks in turn can be calculated by using representative vectors identifying each individual probability. The problem of recursive calculation of the complementary probabilities is solved by a recursive construction processing for the representative vectors.
The probability ( ) f° r -^+l correlation result peaks is evaluated as the P (k) f° r ^ peaks minus the probabilities P (i k+1) f° r cases identified by vectors in the repre ¬ sentative vector set for k+1 peaks:
P = P - P = I - p' -V = \ -P c m
i i
Therefore the complementary probability Ρ^ +\ f° r ^+l peaks is calculated recursively from the complementary probability P^ k) for k peaks plus all the probabilities represented by the representative vectors for k+1 peaks. In addition the representative vectors for k+1 peaks are constructed recursively from the representative vectors for k peaks.
All occurrences of less than M correlation result values being greater than or equal to M peaks can be determined recursively and, as a consequence, (M) can 1 ° e evaluated re ¬ cursively, which kind of processing yields effectiveness and adaptivity .
Advantageously, the recursive evaluation of P (M) enables a statistical detector feature in which the number M of con- sidered peaks can be increased gradually and adaptively. In addition, the recursive evaluation of P (M) minimises the computational complexity by re-using previously performed calculations . In principle, the inventive method is suited for detecting which one of symbols of watermark data embedded in an origi ¬ nal signal - by modifying sections of said original signal in relation to at least two different reference data se- quences - is present in a current section of a received ver ¬ sion of the watermarked original signal, wherein said re ¬ ceived watermarked original signal can include noise and/or echoes, said method including the steps:
correlating in each case said current section of said re- ceived watermarked signal with candidates of said reference data sequences;
based on peak values in the correlation result values for said current signal section, detecting - using related val ¬ ues of false positive probability of detection of the kind of symbol - which one of the candidate symbols is present in said current signal section,
wherein that said false positive probability is calculated in a recursive manner, and wherein the total false positive probability for a given number of correlation result peak values is evaluated by using initially the false positive probabilities for a number smaller than said given of corre ¬ lation result peak values, and by increasing gradually the number of considered correlation result peak values accord ¬ ing to the required detection reliability.
In principle the inventive apparatus is suited for detecting which one of symbols of watermark data embedded in an origi ¬ nal signal - by modifying sections of said original signal in relation to at least two different reference data se- quences - is present in a current section of a received ver ¬ sion of the watermarked original signal, wherein said re ¬ ceived watermarked original signal can include noise and/or echoes, said apparatus including means being adapted for: correlating in each case said current section of said re- ceived watermarked signal with candidates of said reference data sequences; based on peak values in the correlation result values for said current signal section, detecting - using related values of false positive probability of detection of the kind of symbol - which one of the candidate symbols is present in said current signal section,
wherein said false positive probability is calculated in said symbol detection means in a recursive manner, and wherein the total false positive probability for a given number of correlation result peak values is evaluated by us- ing initially the false positive probabilities for a number smaller than said given of correlation result peak values, and by increasing gradually the number of considered correlation result peak values according to the required detection reliability.
Advantageous additional embodiments of the invention are disclosed in the respective dependent claims.
Drawings
Exemplary embodiments of the invention are described with reference to the accompanying drawings, which show in:
Fig. 1 block diagram of the inventive detector;
Fig. 2 flow diagram of the inventive processing.
Exemplary embodiments The inventive processing evaluates the probability P (M) from its complementary probability, i.e. the probability of less than M correlation values being greater than or equal to M peaks .
For a specific correlation result peak value Vj_, the prob- ability of one correlation result value being greater than or equal to Vj_ - under the assumption that the candidate wa- termark does not exist - is denoted as pj_, which is the false positive probability in case the magnitude of value v is used as the threshold value to detect the candidate wa ¬ termark symbol.
For convenience, a vector Ά) — a ' Ίl k ,a l k _ l ,...,a ll ) with non-negative integer elements is introduced to represent an allocation of correlation result values with respect to k peaks (denoted by superscript k) . The set of all vectors belonging to k peaks is indexed by subscript i. In the sequel, such a vec ¬ tor is referred to as a representative vector. Specifically,
<¾ , /≠l indicates that there are a il correlation values in the interval [ , v l-l ~ \ r an d <¾ indicates that there are a tl correlation values greater than or equal to V]_ (in the in- terval [v ] _,+∞)) . In addition there are k-1 values greater than or equal to v^, whereas the remaining N- (k-1) correla ¬ tion values are smaller than ^. Consequently, the probabil ¬ ity for the case represented by can be evaluated as = 0 . (2)
In the sequel, Case k is used to denote the case where there are exactly k-1 values greater than or equal to k-1 peaks v k-l' ---' v l no value lies within interval i v k' v k-l^ -
Therefore, Cases 1 to f together correspond to the case that there are no more than k-1 values greater than or equal to k peaks v^, . . . , V]_ . And the complementary case for Cases 1 to f together is that there are if or more values greater than or equal to if peaks v_¾-, . . . , V]_ .
If P (k) denotes the probability for Case if, then
· That is, the total probability for k+1
peaks is just the total probability for if peaks minus an ad- ditional sum of the probabilities ^-^ i+i) · The individual i
probabilities P (i = P^ k+l) are calculated according to equation (2) using the vector ^ +1) . As an example, the following Cases 1, 2 and 3 are consid ¬ ered :
Case 1
There is no correlation value greater than or equal to V]_ . The representative vector is aj^ = (θ) .
Case 2
There is one value greater than or equal to V]_ and no value lies within interval [ 2, ]_] , represented by a vector
Case 3, with two alternatives:
(i) There are two values greater than or equal to V]_ and no value lies within interval [ 3, ]_] .
(ii) There is one value greater than or equal to V]_, one value within interval [ 2, ]_] , and no value within interval [v 3 , 2 ] .
The corresponding vectors for Case 3 are aj 3) = ( 0 , 0 , 2 ) and
&2 ) = (0,1,1) . Case 3 is disjoint to Case 2 and Case 1. More ¬ over, Case 3 corresponds to a case where there are exactly two values greater than or equal to two peaks V2' v l and no value lies within interval [V2' v 2^ ·
Cases 1, 2 and 3 together correspond to a case where there are no more than two values greater than or equal to three peaks V3, V2 and V]_ .
Given all disjoint representative vectors (indexed by i) for Case k, the probability is the summation of probabili- i
ties of the events represented by these vectors, where each event probability can be evaluated according to Equation (2) .
Then, the problem is how to recursively obtain representa ¬ tive vectors for Case k. Let S (i) denote a set of representa ¬ tive vectors and L (i) a set of lowest positions of '1' in the unit vectors (note that a unit vector has a single ' 1 ' ele ¬ ment only whereas all other elements are '0') to be added to a representative vector in S (i) . For each vector in S (i) there exists one corresponding position value in L (i) . The meaning of L (i) will become clear in the following.
A recursive construction procedure for S (i) and L (i) is carried out:
(1) Initialisation
Set the recursion step k=l , and initialise S (1) = {(0)} , L (1) = {1} .
(2) Adding unit vector and extending
For each vector in S (i) , say , add it with unit vectors (wherein denotes a unit vector of length k with value
'1' at position j±) , ^ - Ji - k , where l k) is the element in L (i) corresponding to af and the lowest possible position of the value ' 1 ' in . The resulting vectors after adding a unit vector are extended by a leading value ' 0 ' . Specifi ¬ cally, a new representative vector is obtained from a ; w following adding and extending = {,α^ + u < ^ ) ), which is included in the new vector set S (i+1) .
The leading value ' 0 ' in indicates that there is no cor- relation value in the interval v k^ > anc ^ adding a unit vector u (i) indicates that there are exactly k values greater than or equal to ν - , . . . , V]_ . The adding position corresponding to is which is included in the new posi ¬ tion set L (i+1) . (3) Update
Increase k by one: k^-k+1. If k < M, go back to step (2), otherwise the recursion is finished.
As an example, the first three steps of the recursive con- struction procedure are shown in the following:
For k=2 , a unit vector (1) is added to the vector (0) and the resulting vector (1) is extended by a leading zero, i.e. leading to vector S (2) = {(0,1)} with lowest position L (2) = {1} .
For k=3 , because L ( ' = {1} , l<jj_<2, to vector (0,1) two unit vectors (0,1) and (1,0) (with lowest positions 1 and 2) are added resulting in vectors (0,2) and (1,1) . Again, these vectors are each extended by a leading zero.
The corresponding lowest positions are still 1 and 2, re ¬ spectively. Thus, the vectors S (3) = {(0,0,2), (0,1,1)} and the lowest positions L (3) = {1,2} are obtained.
For jf=4, the adding position 1 for L (3) will result in three adding positions 1,2,3 (since l≤jj_≤3) while the adding posi ¬ tion 2 for L (3) will result in two adding positions 2,3
(since 2≤jj_≤3) .
Accordingly, S (4) = {(0,0,0,3), (0,0,1,2), (0,1,0,2), (0,0,2,1), (0,1,1,1)} and
L (4) = {1,2,3,2,3} , where the first three vectors are generated via
(0,0,2) in S (3) with adding positions 1,2,3 and the last two vectors are generated via (0,1,1) in S (3) with adding posi ¬ tions 2,3.
S , S , S and S include all representative vectors corre ¬ sponding to Cases 1, 2, 3, and 4. By means of induction it can be generally proved that the recursively constructed vector set S (i) corresponds to Case k, i.e. there are exactly k-1 values greater than or equal to k-1 peaks ν_¾-_ ] _,..., and there is no value within interval i v k' v k-l^ ·
Following each recursion step for S (i) and L (i) , the total probability P (k) can be calculated, which is the total prob ¬ ability of the previous step k-1 minus the probability
∑P(ijc) for S (i) . That is, the computational efforts for total i
probability evaluation of previous steps are recursively used in the current step. Because P {k) = P(k-v> - -^c ) anc ^ P (ik) >0,\/k , the probability P (k) will decrease from one i
step to the next. If the current total probability P (k) i- s already small enough, e.g. smaller than an application- dependent probability value for false positive detection, the recursion can be stopped.
A further speed-up of the calculation of the false positive probability can be obtained by storing the binomial coeffi- cients N~ ∑ a u
j=0 of equation (2), because the correlation length N and the vector sets can be calculated for a given number of peaks k. The only data-dependent values in equa ¬ tion (2) are the factors P k ) N ^ ^ and {Pi ~ Ρι-ι ' , which are depending on the false positive probabilities p± of the in dividual peaks . In the watermark decoder block diagram in Fig. 1, a received watermarked signal RWAS is re-sampled in a acquisition or receiving section step or stage 11, and thereafter may pass through a pre-processing step or stage 12 wherein a spectral shaping and/or whitening is carried out. In the following correlation step or stage 13 it is correlated section by section with one or more reference patterns REFP. A symbol detection or decision step or stage 14 determines, according to the inventive processing described above, whether or not a corresponding watermark symbol DSYM is present. In an op- tional downstream error correction step or stage (not depicted) the preliminarily determined watermark information bits of such symbols can be error corrected, resulting in a corrected detected watermark symbol DSYM.
At watermark encoder side, a secret key was used to generate pseudo-random phases, from which related reference pattern bit sequences (also called symbols) were generated and used for watermarking the audio signal. At watermark decoder side, these pseudo-random phases are generated in the same way in a corresponding step or stage 15, based on the same secret key. From the pseudo-random phases, related candidate reference patterns or symbols REFP are generated in a refer ¬ ence pattern generation step or stage 16 and are used in step/stage 13 for checking whether or not a related watermark symbol is present in the current signal section of the received audio signal.
In Fig. 2 the inventive processing is depicted. Within a first loop LI, for each symbol i the maximum correlation result peak value for the current signal section is deter ¬ mined, and a given number of peak values next in size - e.g. the five greatest peak values for each symbol i are deter ¬ mined, e.g. by sorting.
Loop L2 runs over the symbols i and loop L3 runs over the correlation result peaks j. In L2, the false positive prob ¬ ability P (M) f° r a current peak is calculated in step 21 as explained in detail above. In case that probability is smaller than a threshold value T m j_ n in step 22, it is as- sumed that a correct symbol was detected, that symbol is output in step 24 and the processing is finished. Otherwise the processing continues in loop L2 for the next symbol and in loop L3 for the peaks next in size.
In case none of the checked probabilities was smaller than T m j_ n , the symbol resulting in the overall minimum false positive probability is selected in step 23.
As an option, a second threshold value T max can be used in a step 25 for checking whether the minimum min ( falseProb_i ) of all false positive probability values over i is greater than the first threshold value T m j_ n but still smaller than a sec ¬ ond threshold value T max greater than T m j_ n . If true, the corresponding symbol i is output in step 24. Otherwise, no symbol is detectable.
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