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