0:00:14you best in my on the body
0:00:17got information with the one on you but still
0:00:20speak
0:00:21also uh the company
0:00:25so i would like
0:00:26to a a kind of my to work
0:00:28so so is the
0:00:29T G minor but a
0:00:30when you can use
0:00:31yeah nice
0:00:35problem of minutes before starting to what
0:00:37yeah
0:00:38we can start five it's early but don't want that for
0:00:41start that for once one the ways people coming in
0:00:44maybe few so what a problem but minutes
0:00:46for
0:00:47but
0:00:58one one question was really useful for a single all you here are present the string
0:01:03oh the any or consider here from the or
0:01:07uh_huh but here's for marketing
0:01:10what fraction of room
0:01:17rest of five db
0:01:22well the question is that i can use the reading in terms of like S it's all of using the
0:01:27more robust tree
0:01:28but to be the mouse trying to paul
0:01:31what a things that doing is thing to think these of like guess
0:01:34there are only a you can be used
0:01:36feedback to get results way
0:01:40or
0:01:45i this base or remote start
0:01:48so
0:01:49right
0:01:50these
0:01:58i present proxy
0:01:59the method
0:02:00like in that
0:02:03i have divided my presentation
0:02:05for by
0:02:06first of it you you of hmmm you of their scope i
0:02:10i with that
0:02:11and you know
0:02:13you convex function minimize on the
0:02:16complex
0:02:17modeling right
0:02:19and of so that a
0:02:20that my
0:02:21me
0:02:22then um of different the uh
0:02:24the
0:02:25they are either with a
0:02:27one of the most competitive math
0:02:29based on
0:02:30a great for section
0:02:33and
0:02:33hmmm one on my proximity
0:02:35a technique
0:02:36based on proximity operator
0:02:38computing
0:02:39i
0:02:40project
0:02:41find a yeah present some results
0:02:44as a as the issue of of but it just i would that estimated very at
0:02:50like in uh
0:02:51the am
0:02:54so let's start with that this of the disparity
0:02:58given to uh
0:03:00to images
0:03:01the in from
0:03:02two different point
0:03:03of you
0:03:04we can see that
0:03:05the the so that that and that's is is presented by court
0:03:10why for example
0:03:12and uh uh is and the right image with
0:03:15uh
0:03:15X with different
0:03:16so we will uh not as
0:03:18by
0:03:19right
0:03:19my
0:03:21we define a is simply
0:03:23and this is between these to me
0:03:25so you will be
0:03:27uh this is a T
0:03:29and X prime
0:03:30why might white
0:03:32or or or of its
0:03:33a rectified
0:03:35so why
0:03:36Y
0:03:38but it is a is to be a
0:03:43oh problem to estimate a is is the main study
0:03:47so we ate to fine
0:03:49the corresponding pixel
0:03:51and the last
0:03:52i
0:03:54the state of the art the can find might yeah approach
0:03:59but in that we can uh can not mentioned
0:04:01feature matching approach where a with ace
0:04:04yeah
0:04:05curves
0:04:05and segments from the images
0:04:07also global methods
0:04:09as the dynamic programming and evaluation an approach where they are mean you at they minimize a global the energy
0:04:16from
0:04:17also some fines that use a of the cross or local correlation we those
0:04:22as a normalized cross-correlation correlation
0:04:27in want to follow we will a light by less a variational methods where our cost function would be uh
0:04:33and then are measure between
0:04:35the left image
0:04:36and that right image compensated by the despite its you
0:04:40and the
0:04:41we will use
0:04:42and then are or five
0:04:44that is the proper a lower semi-continuous convex function
0:04:49and the sum of the as this or will be on them
0:04:51on our limits it's the court
0:04:54but is this function is convex with respect to the disparity you
0:04:58so to avoid a non-convex optimize addition
0:05:02a problem
0:05:03we will uh suppose that the uh right image compensated by a by to you is footage
0:05:09we will consider the first taylor expansion of this not than the two
0:05:14and uh uh a uh a and fact we
0:05:17a compute this
0:05:18first or expansion
0:05:19and the first to make you but
0:05:22so i right image compensated by a but to you would be it well
0:05:27to the right image compensated by a and the of value
0:05:30you by mine is you might is to bottom to light
0:05:33by the or something to do and and of the disparity compensated right
0:05:39so to simplify the notation we will consider as D is the gradient
0:05:43R is the right image compensated by a it's paid to you bought class you bar T as the left
0:05:53so our cost function will be at most of five which is convex function
0:05:58function of the you minus R
0:06:01the some always is a on the support them at
0:06:05but
0:06:05as a with few it uh if we aim to search that's very to you that minimize i would criterion
0:06:12and this case that this problem is and it's pose problem
0:06:16because we can find uh a and and a finite in fine the sole use some of this that convex
0:06:22so we will allow uh and
0:06:24some convex constraint modeling prior knowledge and observe that that a of of our is to me
0:06:32that mean we will present our problem as a set estimating
0:06:36set theoretic estimating a problem
0:06:39that's mean we with search i would this to you
0:06:42that minimize our criterion J
0:06:44and to don't to then there's section of different constraint that we also there
0:06:51so
0:06:51what's can be these constraint
0:06:56it can be done and looks about the uh minimum and maximum amplitude of the disparity you
0:07:02or all that are also it's can be the uh uh uh you can produce an upper bound on the
0:07:08total variation of i would spend at mouth
0:07:11and this constraint to you get not does that that it's a piece there of the discontinuities and smooth some
0:07:15was it almost in is ideas
0:07:18or or can be a cost with that constraint
0:07:21we can introduce use an upper bound also on the norm and one norm of the weight of coefficient wavelet
0:07:26coefficients of our despite
0:07:34so to summarise we are minimizing a compact
0:07:37criterion J under different convex constraint
0:07:41as i said before that the sub the get projects is one method
0:07:45it's would used and uh before that two thousand and nine by me that
0:07:49and the
0:07:50uh use a fact
0:07:52two
0:07:53so this problem
0:07:54it's that convex what front
0:07:58to uh because of the algorithm that used and also they were lies to add
0:08:02convex "'cause" the convex there
0:08:05which is as far you might you box way
0:08:09so they they an is that what that the can a convex
0:08:12uh criterion
0:08:14and also they yeah uh so we use subgradient projections of the this to you on the different convex constraint
0:08:20that they can there
0:08:23this this minimizing is a on the uh number of close and are yeah
0:08:28uh
0:08:29and the two images left and right one that's mean we can that here just the peaks still that up
0:08:34here in the last
0:08:35and that i
0:08:38not though we will so our problem that is a convex function J
0:08:42and the different combat
0:08:44a that we consider
0:08:45but we are not hold lies to use just
0:08:48sickly convex quadratic function
0:08:50we have a a great flexibility and that's source
0:08:52of this criterion
0:08:54so to introduce i would want as the definition of
0:08:57that the proximity operator
0:08:59first
0:09:01if you have a points why
0:09:02that's you wanna project it on a convex set C
0:09:06uh we can find this projection
0:09:08by minimizing the come at the problem had to get a function of this constraint
0:09:13plus the uh
0:09:15quite that take distance between a
0:09:16and what
0:09:19so if we saw but this problem we can find the projection of the point why on the convex constraint
0:09:27for a place them to get a function by and that and that but three function F
0:09:32so our problem would be minimizing the function F plus the the distance between a
0:09:38and what
0:09:39this all use of this minimization problem will be the proximity operator of the function F at point point
0:09:51just to uh
0:09:53uh uh rewrite our problem and different way so we are minimizing our convex function J
0:09:59on the different convex comp constraint
0:10:01that can be modelled it it's by a line or operator and time
0:10:06the minimization is on the non on clothes and an are yeah
0:10:09and use the the error measure of five which is convex
0:10:13a function of to you minus R
0:10:16how we can solve that
0:10:17use a a to here i will present
0:10:19but are are good as a
0:10:22uh a which have especially specially will be a the P B X eight plus and yeah i go to
0:10:27them
0:10:27which i low as to minimize this context can at a complex function
0:10:32uh was some closed convex constraint C i
0:10:35uh just
0:10:36if we are able to compute the proximity operator of the criterion J
0:10:41and
0:10:42the project directory
0:10:44would what estimate on different constraints C i so our problem will be solved
0:10:49so simple
0:10:50it X a plus algorithm
0:10:52so
0:10:53we can a our algorithm was some way
0:10:57uh related to the uh convex constraint that you have
0:11:01and also go a a positive constant related to the of does zero point to the cost function that we
0:11:07have
0:11:09we initiate our our mattresses this
0:11:12and we compute the factor you which is and then G of different up a or operator that so uh
0:11:18we have a D complex cost
0:11:21as we see in that in each iteration and our there is a
0:11:25we project
0:11:26each month is on to convex
0:11:28a
0:11:30and also we compute the proximity operator of the criterion J divided by calm
0:11:37so we have our just that are i and i would this but T U
0:11:41by relaxation parameter lump
0:11:44so the most important than the side them that's we compute the proximity operator of the criterion J and we
0:11:49have
0:11:50X it's form for different convex a
0:11:53a cost function
0:11:55and the guy died projection on that the D convex a constraint that the i is not so uh so
0:12:03so to uh
0:12:05to improve the performance of this and good as a mall present some results
0:12:10the first one a corresponding to the peer what it off
0:12:13he how we present the left image and the related to going to tools
0:12:17and i present some generated disparity map using different method to can but to compare it to our method
0:12:23the first one is the block
0:12:25despite the estimation
0:12:28this a one that that i presented before using got to the what that the convex function
0:12:34based on sub granting projection
0:12:36and the our but the X a plus and go to them and we choose that of the and one
0:12:41norm
0:12:41and a a and that are much in our would cost of from
0:12:46also we compute the psnr between that is generated this to my and the ground truth
0:12:51as we see that our method gives the best result
0:12:55and some important what improvement and the disparity map that you have
0:13:02and of the results on the teddy pair
0:13:05so the last image it's and the ground the true and the generated disparity map using the same method
0:13:11oh i will have a real be the B D easy to it's of block that despite the estimation and
0:13:17the L two norm that is
0:13:19strictly convex function
0:13:21and and one norm based on the X eight but i
0:13:26as an application of the uh estimated disparity map will present
0:13:30uh that's that uh its application and stating image coding
0:13:35as we know that and uh to compare the method with an but uh that you image coding a we
0:13:40um
0:13:41codes first
0:13:42uh the last
0:13:43and the right image independently
0:13:45and here we apply the same at loss for on the left and right image using find three
0:13:50we have that like possible
0:13:54many works are done in a stereo image coding using john coding scheme
0:14:00uh based on a compensation in uh
0:14:03but
0:14:03the disparity a compensation this right image
0:14:06so
0:14:07at consist of code one image you which choose the right one
0:14:11and a residual image
0:14:13here here uh can define with the difference between the left image and the right image compensated by the despite
0:14:19its you
0:14:20and all the the the disparity was scored
0:14:25so
0:14:25we have to image to to the right
0:14:28the is it image and that is but
0:14:31and you were compared our we you method the block that
0:14:34but the if estimation that is by estimation
0:14:38using
0:14:38strictly a complex what the tick function an
0:14:40and one or based on the X eight plus and to
0:14:45the resulting wavelet coefficients are input in uh i i are encoded use it uh using a you back to
0:14:50thousand
0:14:51and also as a dense fields are and that the by applying a what be the compositions
0:14:56for the by an entropy coding with at
0:14:59point to six four
0:15:03so uh oh here we present the psnr of D reconstructed images
0:15:09left and the right one
0:15:11versus the bit error rate
0:15:13as we see that the it depends
0:15:15scheme
0:15:17uh give is of the the last P high
0:15:20and a couple states
0:15:22compensation this by the estimation
0:15:24here are give the best to all that to me in that john coding scheme uh give that uh the
0:15:29great yes and
0:15:31and you don't the L T P S and are given by our method presented by the red curve
0:15:36does this by the estimation using the and one norm and
0:15:39and then that the estimation do think this strictly convex function with it's which is whether T
0:15:44and a lot that estimation
0:15:50as i said before that our criterion J is complex
0:15:53and we have
0:15:54am a great flexibility and the choice of our i don't mess
0:15:58so we can use this so
0:16:00but
0:16:01to uh uh the case one our image images present some noise change
0:16:06that's me
0:16:08oh
0:16:09if you have a a a a for example so that paper
0:16:12oh
0:16:13the we the guide that it uh the court it or P with all that people are so we can
0:16:17use and one norm
0:16:18or or when we have a what's and noise we can use that this
0:16:21could but this that's for example
0:16:23because of when we have a a noise uh
0:16:26we we can get the prove that uh could but this does that can be used to uh
0:16:32to make a less this effect of patient
0:16:35so here we compare the at sort or to uh to D X i plus using and one or when
0:16:41we have a a so that paper
0:16:43noise changes
0:16:44and you can see that the uh and i where is all the the uh noise as the
0:16:50we don't have a is that in fact
0:16:52and that and when we have a a a noise
0:16:55the uh
0:16:56disparity map but
0:16:58present
0:16:59morse smooth are yeah and the P of this company D used for the objects that in that present in
0:17:04the uh a and the that
0:17:05disparity image
0:17:10and the some uh very numerical result using the snr and absolute you'd error measure or are given and that's
0:17:16prove that our method
0:17:18gives a uh are provide an a create that's uh map
0:17:24to conclude uh
0:17:26i would like to uh
0:17:27some right so
0:17:30we form our of our problem as a convex function
0:17:34that we are minimizing under different convex can
0:17:39and uh
0:17:40we have a uh are at that is to choose the error measure as we want
0:17:45so that we have various criteria
0:17:47and also just
0:17:48if we are able to compute the proximity operator of the criterion
0:17:53and also a make
0:17:54direct projections of the estimate on different convex constraint
0:17:58so we can run the algorithm simply
0:18:00and also i present two applications
0:18:03and the presence of noise
0:18:05uh when and the left and the right image and also on the is a uh and state you image
0:18:10coding
0:18:14a what i'm working on a this time is that to a a a uh i is then extending my
0:18:19yeah my and good as them to the case when i have a nation variation
0:18:23and also i would like to applied to a for the colour image
0:18:28that is that thank you for that then
0:18:37still have a questions
0:18:39it's really here
0:18:40but
0:18:47so that projections to compute
0:18:49or or a non be or numerically
0:18:52and the better
0:18:53remote yeah so what was that the traditional load of the scheme as compared to the mid those that are
0:18:59present
0:19:01uh competing to the of getting projection
0:19:03you have a an the other and yeah
0:19:07uh
0:19:07a fact in the lot
0:19:09by the estimation uh so
0:19:13log and the fact that based on a block disparity is so they uh compute block and the
0:19:18there are but
0:19:19in the in uh to get in projection that are obliged to compute the this again at an operator or
0:19:25or the uh
0:19:26so when we use when that use for example of the of to variation there are a like to compute
0:19:30the sub gradient
0:19:32difference of of the total variation and applied the projection the complex
0:19:36but no no method in fact so we use the
0:19:39uh a applied the projection of the operator on the comp
0:19:44or what loss in computational complexity
0:19:47how much computation how much time does it big
0:19:50run
0:19:51these different all tomatoes all comparable the
0:19:54what for
0:19:56and fact we a plot we are caught a we program this algorithm on matlab of software
0:20:01and now we are applying and do you P G P U because uh as we see that and the
0:20:06algorithm we have a the ability to light
0:20:09a a set of
0:20:10a D projection we can uh
0:20:11projected that the but and but i don't way and also the uh proximity operator can be uh computed and
0:20:17but ah
0:20:18so we are waiting the fact the results of because uh the work at the
0:20:23always the
0:20:24a that are working on
0:20:29of the questions
0:20:36you
0:20:44uh
0:20:45question uh and fact that we are going to the uh sub getting projection technique
0:20:51and it was proved that
0:20:52two thousand and nine at the best that technique get pop to the other methods
0:20:56so we are made of our uh given there is not better than the best techniques so
0:21:04oh the question
0:21:09but at let's thing we once again
0:21:12i