0:00:16alright one two
0:00:18well yeah
0:00:21you got your in our studies on some
0:00:23so we can practise having shoes in
0:00:27that's an and
0:00:28more precisely about that
0:00:31and duration based what there's which are one of the most
0:00:35successful quarters during the fast decade
0:00:40uh any better based coders
0:00:42we can see containing these general steps
0:00:45yeah first by applying development transform of the input image the coefficients remit is generated
0:00:54then from these coefficients on the lower one regarding the current
0:01:00budgets and limited partners
0:01:03together with their locations will be coded
0:01:06transmitted to the decoder using these
0:01:08coded location uh locations of do what they're we'll be able to
0:01:12regenerate the remit
0:01:14to reconstruct the image by an inverse transform on the decoded quite efficient
0:01:21or is based on the conventional are separable wavelets piece to horizontal and vertical directions software from a non problem
0:01:31and the problems around the edges
0:01:34if you can see there and it's like what we have here
0:01:39independent the spanish
0:01:41uh sprays across many coefficients and this means when we have limited budgets
0:01:47some of these are significant coefficients cannot be coded and that
0:01:53reconstructed image may be some regularities around it
0:01:59our remote that yeah
0:02:01and uh then to detect the menu research has been done to overcome this limitation and all
0:02:07a wavelet transform on image edges
0:02:10uh but it's just some of them are the an isotropic dictionaries of care less control this
0:02:16she speech
0:02:18uh i have of saddam of in terms of approximation power because of the year
0:02:23a high redundancy can present is not between one of the most
0:02:27successful the application
0:02:29reported on these
0:02:32uh we also have a that that's transform which becomes optimality similarly
0:02:37uh forty presenting in it
0:02:40but the code there's based on the visual transform be the L E
0:02:44so that image geometries stones
0:02:46exactly match
0:02:47the base your geometry which is
0:02:49the case at the textures for example and to make it
0:02:53also at the cable for these case says as there are are some words that
0:02:57combines the base that's
0:02:59transform be to be a web based coders
0:03:03and finally we have that i do not apply in be let's of long those durations
0:03:08duration of a list
0:03:09uh this leads to several the schemes such as man this direction this
0:03:14many more that's decide
0:03:16just some of that
0:03:19if we only in you were taught that it off these i do not
0:03:23and for image compressed and
0:03:25using a simple model on it
0:03:27if we have right
0:03:29but along the this direction forty five degree direction
0:03:33and then and the second stage of not six to seven and all the are in the case of low
0:03:38how bad has then
0:03:40for a high pass band and no ninety degree or any other directions scenes
0:03:45yeah does happen
0:03:46dominant and direction
0:03:49uh don't don't that have process usually a uh result in using and signal it can see the in should
0:03:55off or the three are group
0:03:58for a a high frequency bands and
0:04:01uh and so on like the separable wavelets here uh no
0:04:06not not the most
0:04:08variational image and the image
0:04:11and this is of great importance for comparison purposes
0:04:16and it's uh improves the compression results
0:04:20that's in terms of psnr and
0:04:23also visual quality and
0:04:26a as you can see that the you yeah or the ringing artifacts around the H
0:04:31is the same in this up here and the results
0:04:34uh i
0:04:34yeah function list
0:04:37uh when we move into two images these
0:04:40it is a lot more than one direction
0:04:43uh we should experiment
0:04:45the image into some homogeneous partitions and
0:04:48and assign directions
0:04:51pair partition
0:04:53yeah we have a popular partitioning algorithm which is quite three
0:04:58you you
0:04:59and can see that the as a distortion in court image or images to decide between on and its construction
0:05:06i had and also or and the number of bits we need to go to
0:05:10partitioning a structure and the selected directions that quite cheap follows the query all
0:05:16uh are reducing the or not that original cost function which is a D plus them do or in an
0:05:21iterative manner
0:05:24a this means uh using or or a model of the gone first
0:05:28the but with is up a lot of the best direction and D plus them or is computed
0:05:33then it
0:05:34uh a you made use is split it into four forty to all blocks and for each of them to
0:05:38same the steps of a direction of late
0:05:42"'cause" is
0:05:43perform and uh finally be
0:05:46uh make a decision after splitting the original block if the news a lot
0:05:52totally reviews the
0:05:54define a cost function
0:05:56if we
0:05:57uh these
0:06:00for each partition
0:06:02as long as he can improve the plot them or cost
0:06:06you can see here there is also
0:06:08four levels of what she on the polygon model
0:06:12and after these
0:06:14yeah about the questions we personally during or studies pairs we want to know
0:06:19are we can analyse that
0:06:22i'm very successful direction of a list
0:06:25uh for a man
0:06:26so critical point of view
0:06:28you in image compression and also was the results of to marry
0:06:32direction and separate weightless assume basically
0:06:36as another question we want
0:06:39well actually provides an optimal partitioning for duration
0:06:45for these we
0:06:47or analysis on the don't know rate distortion framework which is treated as a comparison
0:06:53there was used and at least framework if you
0:06:57quote the impulse function if using or
0:07:00then the
0:07:02performance of the coder decoder uh pair
0:07:05on the input function a space
0:07:08is equal to the maximum distortion being mapping
0:07:12yeah to the
0:07:13that's that's true for all elements
0:07:16or man from its
0:07:18it is well to this optimal or of the distance between and
0:07:22it's reconstruction
0:07:25um we do a or analysis on a
0:07:29a classical piecewise linear
0:07:31uh yeah it just um a smooth transitions between zero
0:07:37and one regions and
0:07:39first if you can see they're just one place without any singularity we that's for increasing or
0:07:50the distortion of uh
0:07:52separately liz on these
0:07:54uh functions we can be too large or power minus three second
0:07:58which is
0:07:59very slow regarding this in a function which can
0:08:03is decoded by a few problem
0:08:06uh we then to that direction is
0:08:09be headed
0:08:11financially and
0:08:13it is very faster than the support of this
0:08:16also confirms the
0:08:18uh improvements you are seeing the reconstructed
0:08:22i mean
0:08:24uh returning to the whole class so that piecewise functions
0:08:28is obvious that the performance of separable wavelets will not change because
0:08:33okay we use the same horizontal and vertical directions for all cases
0:08:38in the case of duration of it was as we explain
0:08:43michelle partition
0:08:44and i
0:08:45if we use quad tree then be who that
0:08:50again direction and the list for rice and exponential rate of decay but is somewhat this slower than the
0:08:57one piece case by changing the Q
0:09:00a this work of top or into to the Q or or at the exponent and also
0:09:04introducing a
0:09:06six a put a four
0:09:10and what we D grace the performance of a duration of the a list because two
0:09:15oh only present a singularity below it generates many blocks
0:09:21similar direction
0:09:24a lot of those should be called a
0:09:26this you impose a large amount of overhead on the algorithm
0:09:31just a thing is an issue you want to use the idea of joining similar blocks
0:09:36and creating larger lots that
0:09:40make a locks and if we
0:09:43clara duration yeah directions per macroblock then in addition to better representing the
0:09:50image geometries
0:09:53we have your reviews the amount of over a signal we can see
0:09:59and finally
0:10:01well that's what i'm equivalently better performance art direction of the atlas will remain is added to our minus
0:10:08square root of or
0:10:09even when we have
0:10:11singularity is around it
0:10:15oh theory is and now the question is now a channel or megablocking
0:10:21id also be
0:10:23uh applicable for real cases
0:10:26yeah things change the reader sees you when a small amount of noise may cause what generates many different directions
0:10:34and these people probably
0:10:36you raise the performance of
0:10:38may be lucky and
0:10:41sort of the use problem we have to modify the directions between joint the blocks
0:10:46uh a to do these
0:10:48uh uh the point is uh a large B
0:10:52uh dominant and
0:10:54edges as you can see a if you are are the ones that we'll this affected by noise and we
0:11:01chip their directions on changed and
0:11:04uh where where and about when the loss
0:11:08a a smaller
0:11:09uh the noise can miss lead they with them to
0:11:13so like the
0:11:16or to select the wrong direction
0:11:20uh at this smooth regions because of the
0:11:23random ms nature of the noise
0:11:26would have many different direction
0:11:28active to blocks
0:11:29these uh
0:11:31or or the ones that we want to
0:11:33um on a flight
0:11:39we want to modify
0:11:40according to the you
0:11:42strong neighbours
0:11:43to get a larger
0:11:44make a blocks
0:11:46using this
0:11:48in a practical results
0:11:50these are
0:11:51steps or or
0:11:52off or a mega blocking them
0:11:55first partition image by what three of them
0:11:59give or wrong direction then
0:12:03we align these directions
0:12:06then use the top directions
0:12:09see that gradient cost function of each
0:12:12it's first
0:12:14there is a measure of the detection domain
0:12:17the base here or the difference between the
0:12:20cost of that is
0:12:21the worst
0:12:23and and the
0:12:27this indicates that
0:12:29the future direction of a
0:12:32should the most affected
0:12:35what is larger
0:12:41at the few your you can see that
0:12:43um of line directions of the polygon
0:12:48and i here is the time that's we can
0:12:52similar blocks we've
0:12:54a similar directions and create
0:12:56make a lot
0:12:58uh as the second
0:13:00as an ex
0:13:01that we
0:13:02log duration of a list
0:13:04using that
0:13:06finally record all the
0:13:09wavelet coefficients to be the
0:13:13all over this off joining but that's the macroblocks
0:13:16and also as the selected
0:13:24a couple of these um
0:13:27of uh more
0:13:28importance in two cases
0:13:31the first case is
0:13:32of its trace each year in terms of
0:13:38for a run
0:13:40they make a lucky
0:13:41improves the
0:13:43what tree based direction of the way list i one
0:13:46point point one D V
0:13:48and the J two K bye
0:13:51a point six
0:13:52db on average
0:13:56in the case of the not the mega blocking
0:13:59performs forms bits so that the what tree by one
0:14:03T V
0:14:06the second case these for the the
0:14:09and noisy images and D V
0:14:12can see there the gaussian
0:14:14watch it's is that make of looking for a phone based so that and the what tree by
0:14:19a one point
0:14:20two B
0:14:22in the case of our uh
0:14:24okay so we know why
0:14:26one point one
0:14:27db and
0:14:28points one two
0:14:31yeah as you can see
0:14:34A J two K
0:14:36shot of the noise sensitivity in terms of
0:14:43from the
0:14:44a visual quality point you it's
0:14:47obvious that the middle lucky
0:14:50is that the
0:14:51image you yeah that these
0:14:53much better
0:14:54these are the
0:14:56results all
0:14:57reconstruction from the three D J two K watch
0:15:01a with them for the noise you being on or
0:15:04point one two
0:15:06a they're X
0:15:11all i mean these
0:15:15sure that
0:15:16uh the
0:15:17the it he's also
0:15:19or that that the direction
0:15:22a better that is that
0:15:24in compressed
0:15:25and also or make of lucky
0:15:28improves the direction
0:15:30makes it more as like it
0:15:32for coding be images
0:15:35also as or
0:15:37future direction we all uh i be or that E
0:15:41and i Z
0:15:44duration as for working on