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