a work a a a a a a about uh present road constraints a following what was little up like to sign from data hiding systems this work by but a calm an on the press a and i don't them could be here they so while the my best to try to transfer to you the the what that the uh so this is the a line of the presentation yeah first will see a a brief introduction about day what long for such a constraint then we define all the perceptual constraints and the constraints coming from uh robustness considerations of four i a side from data hiding and we will uh derive the the equation corresponding to a a and betting that will follow but a kind a generalized logarithmic the M then we'll see the analysis of embedding bedding power embedding distortion power and probably give the coding are or and a some result or for data hiding in the in the last two years a lot of attention has been paid two issues she's like a best at like to minimize the probably give the coding or or but some mice and the robustness against several facts a a low in the that detect but in case of this steak on a graphic a context so keeping the covert channel uh uh hidden and also to security but perceptual in has been usually on the value so a number of works present that a dealing with perceptual impact is much lower than the move words to some four any of these all issue and of all the characteristics of the human visual system that you can we can think of it this work is for used on what was low as law is uh a a a the rule that's a relates the how big the money to the fussing a least with the money you of the distortion we can impose an that signal more that to be perceptually notes the intuition behind it what was lot is that you with five if we have a a one kilogram one possible i if we change two hundred grams then this change will be noted but if the pasta is fifty kilograms and that change should be hardly noticeable so the perceptual in oh for modification to a a low money to signal is not the same as the perceptual impact to that same a a modification to a very high my median see signal so what what was lost says is that that modification that the signal must on the goal more the to produce these smallest is not so we'll difference is proportional to the magnitude of signal it's itself so the higher the money do of a signal the high of a modification that we can apply to that signal in order two a a a half it conceals so not be perceptually not so so what was is implicitly used by multiplicative straight spectral methods in which we have to the minute you of the watermark the do we that we are line at each what with efficient is proportional to the magnitude of signal what of the whole coefficient in which we embedding it but they are outperformed by setting form data hiding scheme so the question that we can ask at this point is can we exploit the is the perceptual constraints am by was lot in site form data hiding insist and S is yes we can and in this work uh those perceptual trains are a are are uh compared dies in the use of what was a and that what was little is used two a derive a generalized version of a logarithmic embedding is scheme of of side the of anything data hiding and we will see several choices for embedding and decoding regions as a function of the parameters of this so first the four will the find the constraints i mean from what was little and coming from a robustness constraint and from signing from data hiding that define the embedding equation of the a spread spectrum we have to the a perceptual constraint is that the man do use of the what are my each watermark efficient is bounded by the i you to of the host signal of of money to a host signal times the money to of the spreading of the corresponding spreading sequence coefficient and also this coefficient at uh that controls watermark trying it will change these a constraint by uh double bound in which we with a here the that excite is possibly if for negative isn't it would be but lee another those and we'll but upper bound a the watermark coefficient by it that two times six i word that to is positive and lower bounded by at the one times X i where that one is negative from site formant batting we get the constraint that we have to one types of of depending on the human bit we hear considering just a binary embedding breed would be completely and that was for any of its size i'm from robustness we get to constraints first that the was then these you what to be a minimum if we get a uh a a a a a a given a distortion power then we a have to minimize the centrist density for that distortion power for their and many distortion power and we have also that the total code we can be determined by knowing any if its called words so if we we've we no one code work for embedding a C don't then we know the whole codebook for embedding as C and also the whole code look from embedding a one it from all these constraints the embedding equation that we can derive is this one so this a this this letting question really a some those a do the modulation we have here that the vector coefficient and also the embedded be it but it it is a in the logarithmic domain so it's a low but nick to the modulation and a also these stone C here that makes seat a kind of generalized slow rhythmic the em and will seen the following slides will do C means and what is its function all this the the block diagram of the better better in which we to we take the input signal we get rid of the sign we a a go to the logarithmic domain we have a beast and scene and we apply normal of the him with either they're set a sequence the and with the input and letting sequence P and then we get back to the not real domain and recall for the sign of thing but single in this case the parameters C defined as the shape of the quantization region in this case it used as colour the boundaries of the quantization region and C is bounded by zero and the that the idea is that the either and we can also be fine the quantization step then to delta i find a not real domain so the equivalence in the logarithmic domain would become a that is the exponential of that C is defined as the low body from of one at that two or these so that to is the bound of we had before for the a a a a a a minute you've of a watermark efficient and the C use and what makes this a a generalized logarithmic the M we'll see that different choices of C if a different choices of the boundaries for the quantization regions and if we chose for example a a if we define here it a to the choice of that that two we determine the choice of C so if we change it at two and we take it the two we close to come a minus one divided by come up plus one then the quantization boundaries would be a the middle of the center so i the arithmetic mean of the it and this is the same codebook for multiplicative T M if we chose at that to as the square root of come mine as one thing would have the centroid of the geometric mean value of the quantization interval and this is equivalent to use in logarithmic the M and and not the choice is that the two could be able to come moments one to of a two and in that case would would have the center it at the arithmetic mean value of the quantization into vol all these three choices have come on that if we take the first order taylor approximation of at two of it is getting of it that two as a function of them uh then all all three have the same first order taylor approximation that means that if we are in a low distortion regime one dealt approach zero and therefore them approach just one then all of them are asymptotically equivalent to see graphically if the a a yellow bars we present the centroids for the first choice we would have but the quantization boundaries located at the middle of the sent rights so what your from a to of two consecutive centroids rates for the second choice we get this entry look at it at the geometric mean all of the two boundaries and and a chip third choice we have the center look at that the arithmetic mean of the two boundaries so for the coding these choice of C can be taken for encoding just two a a defined one quantization the embedding a one decision boundaries and forty recording for defining B skip the uh the coding on that the column region boundaries so the choice of C at the embedder and the choice of see that we will call C prime the be colour doesn't have to be the same a was you had a a the choice of the embedder will be drive them by the minimization of the embedding distortion power and the choice of C prime at the decoder will be driving by the minimization of the a the coding probability yeah or four so here we have a a a a a formula for the embedding distortion power as a function of the host a distribution if we take the assumption of a little distortion dredging then this the this equation gets independent of these score distribution and we get these approximation and this formula is a a symmetric with respect to see was to that that divided by two and that L to the it but to happens to be the minimum of these embedding distortion then the function rows yeah i to the boundaries of the domain of C uh reaching the maxim at C plus zero and see posted and for what can be called the high distortion regime so for when that is pretty big we have these approximation this not a realistic approximation of course because we will never be and high distortion reading but a a a it serves to the propose of checking how much we can do urge from the low distortion regime approximation when this assumption is not really true so if we put a plot the this the equations and never we get this representation this solid lines represent the experimental results the dashed lines represent the approximation for a little distortion in here we have that that's so here this side we are in low distortion volume we see that the approximation is really good and be sold the lines the dashed but for percent approximation for the high distortion reading but is to which the experimental results tend when we are in this side of the plot will were present and the document to watermark ratio so it is the inverse to the embedding distortion and we can see have that a if we choose elements points that are symmetric with respect to does that divide by two for C then we get exactly the same approximation you to the symmetry of the of the formula that we have seen the previous slide and we get the maxim a the maximum for the document watermark ratio for the choice of C paul does that of to by to as predict if we go for the probably of the coding of or and if we take a minimum distance D colour that of course is not the a optimal decoder but it serves the purpose of having um an analytic expression a closed form expression for this probably four then in the low distortion in we can come out with this approximation that depends on the choice of C at the embedder and the choice of C prime of the decoder yeah we see that this formula is minimised one C approach is that to and once you prime approach is that the it by four so we can see here that we have a trade-off and C the choice of C at the embedder for me my sin the embedding power is not the same as the choice of C given for to mice in the decoding of or or but is this one so one is that that a very but to and other is that in any case in you to the symmetry of the embedding distortion formula in a if we are in low distortion writing the team of C would be in the second half of the form that so in between the the E to a two and that the if this is not true then a is no longer holds and C can be chosen at any point between zero and that that a it's worth multi signals in this formula that here we have that this from less ill defined for C prime ten into a zero or to does by the by two the points in which the sign a a gets a all so for that point approximation we would be worse so we we plot the formula then we get uh here the uh a continuous lines so the theoretical approximation we get in the previous slide and the dots represents the a experimental results we see that the board C prime it was that that but it by for a we get the minimum of the probability of the coding of or for values symmetric but a with respect to that they but it by for we get exactly the same uh the same approximation of the previous formula we see here here here that these approximations not it a very good at this point you to the ill definition of a formula and anyway we see again that for the choices of C as we increase E and we approach to that a then we get a lower probably to the coding or as expected so checking which is the the robustness of this method against a a different kinds of that's and comparing it to other side in hiding methods if which are we we choose uh jpeg peg attack we can see that a if we plot the quality factor used for the jpeg attack and the bit error rate that we get with that that then when the attack is smile so we get a very high quality factor nobody make the em performs a bit worse then normal of the M and that's because a here the probably do for or or you know what if think the M would be dominated by the small magnitude coefficients the top the the is centre each you four point station very close to each other but for the rest of the plot we get here for this the for this area of the of the plot that for low quality factors so when when the tape a get that is a strong low i think the M performs much better than uh a normal the em and that's because the the robustness of the center each used for the high money to coefficients is much a a better a you think the em than for normal the M regarding the another type of a tax so the awgn attack we get exactly the same results when you're that is mine then a it make the em performs worse than the M but when the are when the is a strong so we have uh a low piece a between the watermarking image and the a what are marked and attacked image then the performance of liberty make the M it's much better than that of uh uh norm of the uh so to conclude we have seen mean in this work that what was a can be used to derive a perceptually constraints the informed watermarking systems and in this work a generalized version of logarithmic the M has been derived and for this a generalized version a uh we have a study of the embedding distortion power and the probability of decoding error yeah yeah and the parameters optimize these two and few years and we have seen also that peace proposed a scheme of performs the M when we consider a severe at that so for that's of your J P not that an awgn a text how your performs a norm of the M that tense the you time of for questions you a wire are on is available at once i'm i'm sure that the or or or for for non the group a a a a a so the which is much much better than me fine uh which and this one a yes this this if the uh it is fixed that um but in distortion yeah and a power of the that is is for right yeah yes of uh i i i would have to check with them what they have exactly used but of course some some measure sure of of uh distortion must be using a to to have a for comparison yeah yeah oh yeah for sure but in these sense using uh a a a normal perceptual you where a a measure of distortion then a a a a we get uh a a lower bound on the difference that we get a with respect to lower make the em of course if we used a a a a perceptually were distortion metric then we would have a better results that from here it is not the no it's not clear that i'm have to check but i think that they have used is now the perceptually to were yeah yes your right know bit you on this slide i thank you so apparently a chose on the five lattice coefficient from bad in my view point use potentially introducing problems them of synchronization on it seems to be that scenes the or is no longer reaching can of minus infinity when for high quality meaning that you you no longer guarantee the efficiency of the scheme i don't have one of the percent i'm betting efficient have you looked that you know which coefficient modify that time betting on instead of selecting a the five about this coefficient that detection you we use exactly the same quick would you have a different care i mean uh why this choice of the coefficient well i can as and the joy but this introduce the problem of synchronization i know so some is care is kind of mergings the two problems in one here right there a new modulation scheme and the uses this synchronization problem i you try to separate the two aspects no you here a synchronization is not consider the poll so we have this completely the the the synchronisation problem and of course you would be a problem you these use if this truly followed if we embedded in any coefficient than one have those those strains so i think you much a more thank you