alright one two

like

yeah

well yeah

part

results

you got your in our studies on some

so we can practise having shoes in

image

that's an and

more precisely about that

and duration based what there's which are one of the most

successful quarters during the fast decade

uh any better based coders

we can see containing these general steps

yeah first by applying development transform of the input image the coefficients remit is generated

and

then from these coefficients on the lower one regarding the current

budgets and limited partners

together with their locations will be coded

transmitted to the decoder using these

coded location uh locations of do what they're we'll be able to

regenerate the remit

to reconstruct the image by an inverse transform on the decoded quite efficient

or is based on the conventional are separable wavelets piece to horizontal and vertical directions software from a non problem

and the problems around the edges

if you can see there and it's like what we have here

information

independent the spanish

uh sprays across many coefficients and this means when we have limited budgets

some of these are significant coefficients cannot be coded and that

reconstructed image may be some regularities around it

our remote that yeah

and uh then to detect the menu research has been done to overcome this limitation and all

a wavelet transform on image edges

uh but it's just some of them are the an isotropic dictionaries of care less control this

she speech

uh i have of saddam of in terms of approximation power because of the year

a high redundancy can present is not between one of the most

successful the application

reported on these

dictionary

uh we also have a that that's transform which becomes optimality similarly

uh forty presenting in it

but the code there's based on the visual transform be the L E

so that image geometries stones

exactly match

the base your geometry which is

the case at the textures for example and to make it

also at the cable for these case says as there are are some words that

combines the base that's

transform be to be a web based coders

and finally we have that i do not apply in be let's of long those durations

duration of a list

uh this leads to several the schemes such as man this direction this

and

many more that's decide

just some of that

uh

if we only in you were taught that it off these i do not

and for image compressed and

using a simple model on it

if we have right

but along the this direction forty five degree direction

and then and the second stage of not six to seven and all the are in the case of low

how bad has then

for a high pass band and no ninety degree or any other directions scenes

yeah does happen

dominant and direction

uh don't don't that have process usually a uh result in using and signal it can see the in should

off or the three are group

for a a high frequency bands and

uh and so on like the separable wavelets here uh no

not not the most

variational image and the image

and this is of great importance for comparison purposes

and it's uh improves the compression results

yeah

that's in terms of psnr and

also visual quality and

a as you can see that the you yeah or the ringing artifacts around the H

is the same in this up here and the results

uh i

yeah function list

uh when we move into two images these

it is a lot more than one direction

uh we should experiment

the image into some homogeneous partitions and

and assign directions

pair partition

yeah we have a popular partitioning algorithm which is quite three

you you

and can see that the as a distortion in court image or images to decide between on and its construction

i had and also or and the number of bits we need to go to

partitioning a structure and the selected directions that quite cheap follows the query all

uh are reducing the or not that original cost function which is a D plus them do or in an

iterative manner

a this means uh using or or a model of the gone first

the but with is up a lot of the best direction and D plus them or is computed

then it

uh a you made use is split it into four forty to all blocks and for each of them to

same the steps of a direction of late

a

"'cause" is

perform and uh finally be

uh make a decision after splitting the original block if the news a lot

totally reviews the

define a cost function

if we

uh these

a

for each partition

as long as he can improve the plot them or cost

you can see here there is also

four levels of what she on the polygon model

and after these

you

yeah about the questions we personally during or studies pairs we want to know

are we can analyse that

i'm very successful direction of a list

uh for a man

so critical point of view

you in image compression and also was the results of to marry

direction and separate weightless assume basically

as another question we want

now

well actually provides an optimal partitioning for duration

for these we

or analysis on the don't know rate distortion framework which is treated as a comparison

there was used and at least framework if you

quote the impulse function if using or

then the

performance of the coder decoder uh pair

on the input function a space

is equal to the maximum distortion being mapping

yeah to the

that's that's true for all elements

or man from its

it is well to this optimal or of the distance between and

it's reconstruction

um we do a or analysis on a

a classical piecewise linear

uh yeah it just um a smooth transitions between zero

and one regions and

first if you can see they're just one place without any singularity we that's for increasing or

yeah

uh

the distortion of uh

separately liz on these

uh functions we can be too large or power minus three second

which is

very slow regarding this in a function which can

is decoded by a few problem

uh we then to that direction is

be headed

financially and

it is very faster than the support of this

also confirms the

uh improvements you are seeing the reconstructed

i mean

uh returning to the whole class so that piecewise functions

is obvious that the performance of separable wavelets will not change because

okay we use the same horizontal and vertical directions for all cases

in the case of duration of it was as we explain

for

michelle partition

and i

if we use quad tree then be who that

again direction and the list for rice and exponential rate of decay but is somewhat this slower than the

one piece case by changing the Q

a this work of top or into to the Q or or at the exponent and also

introducing a

six a put a four

factor

and what we D grace the performance of a duration of the a list because two

oh only present a singularity below it generates many blocks

this

similar direction

that

a lot of those should be called a

this you impose a large amount of overhead on the algorithm

just a thing is an issue you want to use the idea of joining similar blocks

and creating larger lots that

called

make a locks and if we

clara duration yeah directions per macroblock then in addition to better representing the

image geometries

here

we have your reviews the amount of over a signal we can see

and finally

well that's what i'm equivalently better performance art direction of the atlas will remain is added to our minus

square root of or

even when we have

singularity is around it

oh theory is and now the question is now a channel or megablocking

id also be

uh applicable for real cases

yeah things change the reader sees you when a small amount of noise may cause what generates many different directions

and these people probably

you raise the performance of

may be lucky and

two

sort of the use problem we have to modify the directions between joint the blocks

uh a to do these

uh uh the point is uh a large B

uh dominant and

edges as you can see a if you are are the ones that we'll this affected by noise and we

sure

chip their directions on changed and

uh where where and about when the loss

it

a a smaller

uh the noise can miss lead they with them to

so like the

or to select the wrong direction

also

uh at this smooth regions because of the

random ms nature of the noise

B

would have many different direction

active to blocks

these uh

or or the ones that we want to

um on a flight

or

we want to modify

according to the you

uh

strong neighbours

to get a larger

make a blocks

using this

in a practical results

these are

steps or or

off or a mega blocking them

first partition image by what three of them

give or wrong direction then

we align these directions

gets

then use the top directions

by

see that gradient cost function of each

it's first

there is a measure of the detection domain

the base here or the difference between the

cost of that is

the worst

directions

and and the

second

this indicates that

the future direction of a

should the most affected

the

what is larger

and

and

using

at the few your you can see that

um of line directions of the polygon

more

and i here is the time that's we can

joint

similar blocks we've

a similar directions and create

make a lot

uh as the second

as an ex

that we

log duration of a list

using that

scheme

finally record all the

wavelet coefficients to be the

all over this off joining but that's the macroblocks

and also as the selected

duration

a couple of these um

of uh more

importance in two cases

the first case is

of its trace each year in terms of

psnr

for a run

they make a lucky

improves the

what tree based direction of the way list i one

point point one D V

and the J two K bye

a point six

db on average

also

in the case of the not the mega blocking

performs forms bits so that the what tree by one

T V

the second case these for the the

and noisy images and D V

can see there the gaussian

watch it's is that make of looking for a phone based so that and the what tree by

a one point

two B

in the case of our uh

okay so we know why

one point one

db and

points one two

yeah as you can see

A J two K

um

shot of the noise sensitivity in terms of

psnr

from the

a visual quality point you it's

obvious that the middle lucky

is that the

image you yeah that these

much better

these are the

results all

reconstruction from the three D J two K watch

i

a with them for the noise you being on or

point one two

a they're X

uh

all i mean these

you

we

sure that

uh the

the it he's also

or that that the direction

a better that is that

in compressed

and also or make of lucky

improves the direction

makes it more as like it

for coding be images

also as or

future direction we all uh i be or that E

and i Z

i

i

duration as for working on

or

data

yeah