Přepis řeči - WEBER'S LAW-BASED SIDE-INFORMED DATA HIDING

0:00:14	a work
0:00:15	a a a a a a about
0:00:16	uh present road constraints
0:00:18	a following what was little up like to sign from data hiding systems
0:00:22	this work by but a calm an on the press
0:00:24	a and i don't them could be here they
0:00:27	so while the my best to try to transfer to you
0:00:29	the the what that the uh
0:00:32	so this is the
0:00:33	a line of the presentation
0:00:35	yeah first will see
0:00:37	a
0:00:38	a brief introduction about day what long
0:00:40	for such a constraint
0:00:42	then we define all the perceptual constraints and the constraints coming from uh robustness considerations of four
0:00:48	i a side from data hiding
0:00:50	and we will uh derive
0:00:53	the
0:00:54	the equation corresponding to a a and betting that will follow
0:00:58	but a kind a generalized logarithmic the M
0:01:00	then we'll see the analysis of embedding bedding power embedding distortion power
0:01:04	and probably give the coding are or and a some result
0:01:08	or for data hiding in the in the last two years a lot of attention has been paid
0:01:12	two issues she's like a best at like to minimize the probably give the coding or or
0:01:16	but some mice and the robustness against several facts
0:01:19	a a low in the that detect but in case of this steak on a graphic a context
0:01:24	so keeping the covert channel uh uh
0:01:26	hidden
0:01:27	and also to security
0:01:29	but perceptual in
0:01:31	has been usually on the value
0:01:33	so a number of works present that
0:01:35	a dealing with perceptual impact is much lower than the move words to some four
0:01:39	any of these all issue
0:01:42	and of all the characteristics of the human visual system that you can we can think of
0:01:46	it this work is for used on what was low as law is uh a a a the rule
0:01:51	that's
0:01:52	a relates
0:01:54	the how big the money to the fussing a least
0:01:56	with
0:01:57	the money you of the distortion we can impose an that signal
0:02:00	more that to be perceptually notes
0:02:03	the intuition behind it what was lot
0:02:05	is that you with five if we have a a one kilogram one possible
0:02:09	i if we change two hundred grams
0:02:11	then this change will be noted
0:02:13	but if the pasta is fifty kilograms and that change should be hardly noticeable
0:02:17	so
0:02:18	the perceptual in
0:02:20	oh for modification
0:02:21	to a a low money to signal is not the same as the perceptual impact to that same
0:02:26	a a modification
0:02:28	to a very high my median see signal
0:02:30	so
0:02:32	what what was lost says
0:02:33	is that that modification that the signal must on the goal
0:02:37	more the to produce these smallest is not so we'll difference
0:02:39	is proportional to the magnitude of signal it's itself
0:02:42	so the higher the money do of a signal
0:02:44	the high of a modification that we can apply to that signal in order two
0:02:48	a a a half it conceals so not be perceptually not so
0:02:53	so what was is implicitly used
0:02:55	by multiplicative straight spectral methods
0:02:57	in which we have to the minute you of the watermark the do we that we are line at each
0:03:01	what with efficient
0:03:02	is proportional to the magnitude of signal what of the whole coefficient
0:03:06	in which we embedding it
0:03:07	but
0:03:08	they are outperformed by setting form data hiding scheme
0:03:12	so
0:03:12	the question that we can ask at this point is
0:03:15	can we exploit
0:03:16	the is the perceptual constraints am by was lot
0:03:19	in site form data hiding insist
0:03:21	and S is yes we can
0:03:23	and in this work
0:03:24	uh those perceptual trains
0:03:26	are
0:03:27	a
0:03:28	are are uh compared dies in the
0:03:30	use of what was a and that what was little is used
0:03:33	two
0:03:34	a derive a generalized version of a logarithmic embedding is scheme
0:03:38	of of side the of anything data hiding
0:03:41	and we will see several choices for embedding and decoding regions
0:03:45	as a function of the parameters of this
0:03:48	so first the four will the find the constraints
0:03:50	i mean from what was little and coming from a robustness constraint
0:03:54	and from signing from data hiding
0:03:55	that define the embedding equation
0:03:58	of the a spread spectrum we have to the a perceptual constraint
0:04:02	is that the man do use of the what are my each watermark efficient
0:04:05	is bounded by the i you to of the host signal
0:04:10	of of money to a host signal
0:04:12	times the money to of the spreading of the corresponding spreading sequence coefficient
0:04:15	and also this coefficient at uh that controls watermark trying
0:04:20	it will change
0:04:21	these a constraint
0:04:23	by uh
0:04:24	double bound
0:04:26	in which we with a here the that excite is possibly if for negative isn't it would be but lee
0:04:30	another those
0:04:31	and we'll but upper bound
0:04:33	a
0:04:34	the watermark coefficient by it that two times six i word that to is positive
0:04:38	and lower bounded by at the one times X i where that one
0:04:41	is negative
0:04:43	from site formant batting we get the constraint that we have to one types of of depending on the human
0:04:48	bit
0:04:49	we hear considering just a binary embedding breed would be completely and that was for any of its size
0:04:56	i'm from robustness we get to constraints
0:04:59	first that the was then these you what to be a minimum
0:05:02	if we get a uh a a a a a a given
0:05:05	a distortion power
0:05:07	then we a have to minimize the centrist density for that distortion power for their and many distortion power
0:05:13	and we have also that the total code we can be determined
0:05:16	by knowing any if its called words so if we we've we no one code work
0:05:20	for embedding a C don't then we know the whole codebook for embedding as C and also the whole code
0:05:24	look from embedding
0:05:25	a one
0:05:27	it from all these constraints
0:05:28	the embedding equation that we can derive
0:05:30	is this one
0:05:31	so this
0:05:33	a this this letting question really a some those a do the modulation we have here that
0:05:38	the vector coefficient
0:05:39	and also the embedded be it
0:05:41	but
0:05:42	it it is a in the logarithmic domain so it's a low but nick to the modulation
0:05:46	and a also these stone C here that makes seat
0:05:49	a kind of generalized slow rhythmic the em and will seen the following slides will do C means and what
0:05:55	is its function
0:05:56	all this the
0:05:57	the block diagram of the better better in which we to we take the input signal we get rid of
0:06:02	the sign
0:06:03	we
0:06:04	a a go to the logarithmic domain we have a beast and scene and we apply normal of the him
0:06:08	with either they're set a sequence the and with the input and letting sequence P
0:06:12	and then we get back to the not real domain and recall for the sign of thing but single
0:06:17	in this case the parameters C
0:06:19	defined as the shape
0:06:21	of the quantization region
0:06:23	in this case it used as colour
0:06:24	the boundaries of the quantization region
0:06:27	and C is bounded by zero and the that
0:06:29	the idea is that the either
0:06:31	and we can also be fine the quantization step then to delta i find a not real domain so the
0:06:36	equivalence
0:06:37	in the logarithmic domain would become a
0:06:39	that is the exponential of that
0:06:42	C is defined as the
0:06:44	low body from of one at that two or these so that to is the bound of we had before
0:06:48	for the
0:06:49	a a a a a a minute you've of a watermark efficient
0:06:53	and the C use and what makes this a a generalized logarithmic the M
0:06:58	we'll see that different choices of C if a different choices of the boundaries for the quantization regions
0:07:03	and
0:07:04	if we chose for example
0:07:06	a a if we define here
0:07:09	it a to the choice of that that two we determine the choice of C
0:07:12	so if we change it at two and we take it the two we close to come a minus one
0:07:16	divided by come up plus one
0:07:18	then the quantization boundaries would be a the middle of the center so i the arithmetic mean of the it
0:07:23	and this is the same codebook for multiplicative T M
0:07:26	if we chose at that to as the square root of come mine as one thing would have
0:07:30	the centroid of the geometric mean value of the quantization interval and this is equivalent to use in logarithmic the
0:07:35	M
0:07:36	and and not the choice is that the two could be able to come moments one to of a two
0:07:40	and in that case would would have the center it at the arithmetic mean value of the quantization into vol
0:07:44	all these three choices have come on that if we take the first order taylor approximation of at two
0:07:49	of it is getting of it that two
0:07:52	as a function of them uh
0:07:53	then all all three have the same first order taylor approximation
0:07:57	that means that if we are in a low distortion regime one dealt approach zero and therefore them approach just
0:08:02	one
0:08:03	then all of them are asymptotically equivalent
0:08:07	to see graphically if the
0:08:09	a a yellow
0:08:10	bars
0:08:11	we present the centroids
0:08:12	for the first choice we would have
0:08:14	but the quantization boundaries located at the middle of the
0:08:18	sent rights so what your from a to of two consecutive centroids rates
0:08:21	for the second choice we get this entry look at it at the geometric mean
0:08:25	all of the two boundaries
0:08:28	and and a chip third choice we have the center look at that the arithmetic mean
0:08:32	of the two boundaries
0:08:34	so for the coding
0:08:35	these choice of C can be taken for encoding just two
0:08:39	a a defined one quantization the embedding a one decision boundaries
0:08:43	and forty recording
0:08:44	for defining
0:08:45	B
0:08:47	skip
0:08:48	the uh the coding on that the column region boundaries
0:08:51	so the choice of C at the embedder and the choice of see that we will call C prime the
0:08:56	be colour doesn't have to be the same
0:09:00	a was you had
0:09:00	a a the choice of the embedder will be
0:09:03	drive them by the minimization of the embedding distortion power
0:09:07	and the choice of C prime at the decoder will be driving
0:09:10	by the minimization of the a the coding probability
0:09:13	yeah or four
0:09:16	so here we have a a a a a formula for the embedding distortion power as a function of the
0:09:20	host
0:09:21	a distribution
0:09:23	if we take the assumption of a little distortion dredging
0:09:26	then this the this equation gets independent of these score distribution and we get these approximation
0:09:32	and this formula is
0:09:33	a a symmetric with respect to see was to that that divided by two
0:09:38	and that L to the it but to happens to be the minimum of these
0:09:42	embedding distortion
0:09:43	then the function rows
0:09:46	yeah i to the boundaries of the domain of C
0:09:49	uh reaching the maxim at C plus zero and see posted
0:09:53	and
0:09:54	for what can be called the high distortion regime so for when that is pretty big
0:09:59	we have these approximation this not a realistic approximation of course because we will never be
0:10:03	and high distortion reading
0:10:05	but
0:10:06	a a a it serves to the propose of checking how much we can do urge from the low distortion
0:10:12	regime approximation
0:10:13	when this assumption is not really true
0:10:17	so if we put a plot the this the equations
0:10:21	and never we get this representation
0:10:22	this solid lines
0:10:24	represent
0:10:25	the
0:10:25	experimental results
0:10:28	the dashed lines represent
0:10:30	the approximation for a little distortion in here we have that that's so here this side we are in low
0:10:35	distortion volume
0:10:36	we see that the approximation is really good
0:10:38	and be sold the lines the dashed but for percent approximation for the high distortion reading
0:10:43	but is to which the experimental results tend when we are in this
0:10:47	side of the plot
0:10:48	will were present and the document to watermark ratio so it is the inverse to the embedding distortion
0:10:54	and we can see have that
0:10:56	a if we choose elements
0:10:58	points that are symmetric with respect to does that divide by two
0:11:02	for C
0:11:03	then we get exactly the same approximation you to the symmetry of the of the formula that we have seen
0:11:07	the previous slide
0:11:08	and we get the maxim a the maximum for the document watermark ratio for the choice of C paul
0:11:14	does that of to by to as predict
0:11:18	if we go for the probably of the coding of or
0:11:21	and if we take a minimum distance D colour that of course is not the
0:11:25	a optimal decoder but it serves the purpose of having
0:11:28	um an analytic expression a closed form expression for this probably four
0:11:33	then
0:11:33	in the low distortion in
0:11:35	we can come out with this approximation that depends on the choice of C at the embedder and the choice
0:11:40	of C prime of the decoder
0:11:42	yeah we see that
0:11:43	this formula is minimised
0:11:45	one C approach is that to
0:11:47	and once you prime approach is that the it by four
0:11:50	so we can see here that we have a trade-off and C
0:11:53	the choice of C at the embedder for me my sin the embedding power is not the same as the
0:11:58	choice of C
0:11:59	given for to mice in the decoding of or or but is this one so
0:12:03	one is that that a very but to and other is that
0:12:06	in any case
0:12:08	in you to the symmetry of the embedding distortion formula
0:12:12	in a if we are in low distortion writing the team of C would be in the second half of
0:12:16	the form that so
0:12:17	in between the the E to a two and that the
0:12:20	if this is not true then
0:12:22	a is no longer holds and C can be chosen at any point between zero and that that
0:12:27	a it's worth multi signals in this formula that here we have that this from less ill defined for C
0:12:33	prime ten into a zero or to does by the by two the points in which the sign
0:12:39	a a gets a all
0:12:40	so for that point approximation we would be worse
0:12:43	so we we plot the formula
0:12:45	then we get
0:12:46	uh
0:12:49	here the
0:12:50	uh a continuous lines so the theoretical approximation we get in the previous slide
0:12:54	and the dots
0:12:55	represents the a experimental results
0:12:58	we see that the board C prime
0:13:00	it was that that but it by for a we get the minimum of
0:13:03	the probability of the coding of or
0:13:05	for values symmetric
0:13:07	but a with respect
0:13:08	to that they but it by for we get exactly the same
0:13:12	uh
0:13:12	the same approximation of the previous formula
0:13:15	we see here
0:13:16	here here that these approximations not
0:13:19	it a very good at this point you to the ill definition of a formula
0:13:23	and anyway we see again that for the choices of C
0:13:27	as we increase E and we approach to that a
0:13:30	then we get a lower probably to the coding or
0:13:33	as expected
0:13:35	so checking which is the the robustness of this method against
0:13:39	a a different kinds of that's
0:13:41	and comparing it to other side in hiding methods
0:13:45	if which are we we choose uh jpeg peg attack
0:13:48	we can see
0:13:49	that a
0:13:51	if we plot the quality factor used for the jpeg attack
0:13:54	and the bit error rate that we get with that that
0:13:58	then when the attack is smile so we get a very high quality factor
0:14:02	nobody make the em performs
0:14:03	a bit worse
0:14:04	then normal of the M
0:14:06	and that's because
0:14:07	a here the probably do for or or you know what if think the M would be dominated by the
0:14:11	small magnitude coefficients
0:14:12	the top the the is centre each you four point station very close to each other
0:14:18	but for the rest
0:14:19	of the plot
0:14:20	we get here for this
0:14:21	the for this area of the of the plot
0:14:24	that for low quality factors so when when the tape a get that is a strong
0:14:28	low i think the M performs much better than
0:14:31	uh a normal the em and that's because the the robustness of the center each used for the high money
0:14:36	to coefficients is much
0:14:38	a a better
0:14:40	a you think the em than for normal the M
0:14:44	regarding the
0:14:46	another type of a tax so the awgn attack
0:14:49	we get exactly
0:14:50	the same results
0:14:52	when you're that is mine then a it make the em performs worse than the M but when the are
0:14:57	when the is a strong so we have uh a low piece a between the watermarking image and the
0:15:02	a what are marked and attacked image
0:15:04	then the performance of liberty make the M
0:15:07	it's much better than that of
0:15:09	uh uh norm of the uh
0:15:11	so to conclude
0:15:13	we have seen mean in this work that what was a can be used to derive a perceptually constraints
0:15:18	the informed watermarking systems
0:15:20	and
0:15:21	in this work a generalized version of logarithmic the M has been derived
0:15:26	and for this a generalized version a uh we have a study of the embedding distortion power and the probability
0:15:32	of decoding error
0:15:34	yeah yeah and the parameters optimize these two and few years
0:15:39	and we have seen also that peace proposed a scheme of performs the M when we consider a severe at
0:15:44	that
0:15:44	so for that's of your J P not that an awgn a text
0:15:47	how your performs a
0:15:49	norm of the M
0:15:51	that tense the
0:15:55	you
0:16:00	time of for questions you a wire are on is available
0:16:03	at once
0:16:04	i'm i'm sure that the or or or for for non the group
0:16:07	a a a a a so the which is much much better than me
0:16:11	fine
0:16:13	uh
0:16:25	which and this one
0:16:29	a yes
0:16:30	this this
0:16:31	if the uh it is fixed that um but in distortion
0:16:35	yeah and a power of the that is is for right yeah
0:16:47	yes of uh i
0:16:48	i i would have to check with them what they have exactly used
0:16:52	but of course some some measure sure of of uh distortion must be using a to to have a for
0:16:57	comparison
0:17:07	yeah
0:17:15	yeah
0:17:27	oh
0:17:27	yeah for sure but
0:17:30	in these sense using uh a a a normal perceptual you where
0:17:34	a a measure of distortion
0:17:35	then a a a a we get uh a a lower bound on the
0:17:39	difference
0:17:39	that we get
0:17:41	a with respect to lower make the em of course if we used a a a a perceptually were distortion
0:17:45	metric
0:17:46	then we would have a better results
0:17:49	that from here it is not
0:17:52	the no it's not clear that i'm have to check but i think that they have used is now
0:17:59	the perceptually to were yeah
0:18:07	yes your right
0:18:08	know bit
0:18:16	you
0:18:17	on this slide
0:18:19	i
0:18:19	thank you
0:18:20	so apparently a chose on the five lattice coefficient from bad
0:18:24	in my view point use
0:18:26	potentially introducing problems them of synchronization
0:18:30	on it seems to be that
0:18:32	scenes
0:18:33	the or is no longer reaching can of minus infinity when
0:18:38	for high quality meaning that you you no longer guarantee
0:18:41	the
0:18:42	efficiency of the scheme
0:18:44	i don't have one of the percent i'm betting efficient
0:18:47	have you looked that
0:18:49	you know which coefficient modify that time betting on
0:18:53	instead of
0:18:54	selecting a the five about this coefficient that detection you we use exactly the same quick would you have a
0:19:00	different care
0:19:01	i mean uh why this choice of the coefficient
0:19:04	well i can as and the joy but this
0:19:06	introduce the problem of synchronization i know
0:19:09	so
0:19:10	some is care is kind of
0:19:12	mergings the two problems in one here right
0:19:15	there a new modulation scheme and the uses
0:19:17	this synchronization problem
0:19:19	i you try to separate the two aspects no you here a synchronization is not consider the poll
0:19:25	so we have this completely the the
0:19:28	the synchronisation problem and of course you would be a problem you these
0:19:32	use if this truly followed
0:19:34	if we embedded in any coefficient than
0:19:36	one have those those strains
0:19:41	so i think you
0:19:42	much
0:19:43	a more thank you

WEBER'S LAW-BASED SIDE-INFORMED DATA HIDING

Watermarking and Multimedia Security

Přednášející: Juan Ramsa Troncoso Pastoriza, Autoři: Pedro Comesaña, Fernando Pérez-González, University of Vigo, Spain