0:00:16so uh
0:00:17this is the joint work of a
0:00:20we my phd student "'cause" to the money i come from poland something using university
0:00:27of technology uh include need to this is uh in the self of a whole
0:00:33and uh the topic of the paper is uh and it'll bit uh
0:00:39uh similar to the previous one because it is with a uh actually with convolutions
0:00:46so it's is uh about a bi lateral filter uh which is a actually
0:00:54based on the convolution so uh the outline first so i would like to say
0:01:00a few words about uh the bilateral uh filter then uh the problem of impulsive
0:01:08noise this uh this is the problem rather than interested in
0:01:14then the proposed solution
0:01:16i on modification or extension ordered normalization and some uh experimental uh results
0:01:26so uh
0:01:28the uh bilateral a filter is a
0:01:32is uh
0:01:34is uh
0:01:36very popular it was uh in the literature uh it is uh mostly people mostly
0:01:45us right that it was uh introduced by too much C and monthly G also
0:01:50be uh
0:01:55so this is this is the uh the paper which is uh actually uh very
0:02:02often cited but in fact uh it was um no before and it was described
0:02:10by us me uh in uh in and approach which is called susan and also
0:02:18uh this is this uh this uh it is available on the internet and it
0:02:24was also uh described by yellow sloughs P uh in a in about the old
0:02:30book but uh the destruction between that was so i was known uh
0:02:37more than uh ten years uh before so uh
0:02:43what is the bilateral a filter
0:02:46but actually this is a convolution
0:02:49uh we have a window which are which can be can be quite large
0:02:57uh and we assign some weights to the pixels which are uh inside uh of
0:03:05the of the filtering window would have a central pixel which is the uh the
0:03:10pixel that we would like to modify we have uh the window uh many pixels
0:03:17and we have uh some weights so we can uh call this pixel X
0:03:23and so we have a weight X uh why are the pixels uh which are
0:03:32we can say in a neighborhood relation
0:03:35so uh we uh multiply the uh intensities uh of the pixels in uh basically
0:03:44uh image for example are we the weights and then i would invite uh
0:03:51uh this uh some by the sum of the weights
0:03:56so uh the weights is a quite important a part of the bilateral filter oh
0:04:03of course we should have a tool weights because of the name of this uh
0:04:09filter one hour wait is uh
0:04:15uh expressing the distance the topological distance
0:04:21uh on the image than the main be between centre and all the pixels so
0:04:27uh we have here of a small distance and here those pixels are at large
0:04:33uh distances so this is a topological distance and so a people use uh gaussian
0:04:41like uh functions so we have a smoothing factor here
0:04:47and uh the uh second solo part uh is also a cost and like but
0:04:55uh here in the number need to we have differences in basically considers
0:05:03so if uh that topics as which are quite similar then the weight will be
0:05:08large if they are uh quite different then and the we would be small
0:05:15and those two weights are multiplied and the result is this uh weights W
0:05:25so uh yeah we have a example uh a small part of the image we
0:05:31can uh say this is the filtering window so we have uh the distances and
0:05:38we can uh make uh and that's a amount of the differences uh absolute differences
0:05:46uh between the central pixel and the neighbours for example this is to say uh
0:05:54or is a six nodes
0:05:55i six
0:05:57so this is one hundred sixteen then so we have a map of uh of
0:06:01the absolute differences so uh we just need uh to take into account this distance
0:06:09this part and the absolute differences that we basically the problem to uh and of
0:06:16course uh we have to choose uh the uh smoothing factors which are actually uh
0:06:25parameters of the bilateral filter
0:06:28so uh
0:06:30we can uh see that this bilateral filtering is quite similar to the convolution with
0:06:38a gaussian and uh
0:06:40because the gaussian kernel actually assigns weights to pixels uh um
0:06:48which are in the neighborhood relation in a large window with the central one so
0:06:53this is uh this is like in this uh bilateral filter here uh for the
0:06:59center a pixel we have a large weight and the weights are decreasing yeah so
0:07:05we can hear a noisy uh step or edge
0:07:11and then
0:07:12if we imagine that we have a pixel on this side of these edge
0:07:18then a discussion uh function is modified by the structure of the of the image
0:07:26inside of the of the filtering window and here the difference is uh in intensity
0:07:34a small so uh the structure of the gaussian uh function will be presented but
0:07:42here the differences are large and that's why the advantages of the gaussian uh function
0:07:49will be decreased so actually a instead of such a nice uh no noticeable gonna
0:07:56we have a kernel uh which is modified by the structure of the of the
0:08:03uh image of uh of the of the uh part of the image which is
0:08:09contained in the filtering window so uh
0:08:13as a result this uh this uh this uh account no will be is a
0:08:19taking uh values we've large weights from this side and small uh ways which will
0:08:27be assigned uh to this uh side and that the result will be a small
0:08:33image uh but with a result uh edges there would be no blurring of the
0:08:42and this is uh the structure of the bilateral filter they're of course um an
0:08:48extension so uh this of this kind of filtering is quite popular people are uh
0:08:55developing uh
0:08:59two lateral filters and so on and modified and that would like to present a
0:09:05modification before one or more example oh have a uh artificial uh image just uh
0:09:14of us were and say we have a point here so this is this is
0:09:20the gaussian uh like function but what defined by the by the uh like the
0:09:27structure here the differences a lot so uh they are almost zeros and if we
0:09:34and if we add some noise this uh kind of will be modified you can
0:09:40see some sports some dot sports uh this is because uh some of the pixels
0:09:47for example here or here they are quite different uh like this pixel in the
0:09:53cone so this is uh actually
0:09:57remove the that we know and perform the convolution with a with a kernel for
0:10:03which is dependent on structure of the image
0:10:07so uh now a impulsive noise
0:10:11and the colour images
0:10:13the modification um or extension of the bilateral filter to color images is uh is
0:10:21quite simple because uh the topological distance uh system defined in the same way but
0:10:28uh the difference is uh in uh intensities and can be can be huh
0:10:35change or substituted by uh distances in the colour space so uh we can we
0:10:43can easily modify uh the bilateral filter uh to the uh color uh images
0:10:51so uh color images are
0:10:54quite often uh corrupted by impulsive noise so we kind of uh here an example
0:11:02this is the land line image with uh which was uh
0:11:06uh polluted by uh artificial uh at efficiently uh modeled and noise we can see
0:11:14some pixels uh depends on the intensity of the noise which are corrupting the image
0:11:23for example uh let's cut not X the
0:11:27uh that's cover uh
0:11:30look at such a situation uh for example we have a gray scale uh image
0:11:37that's for simplicity and all the values for the here are the same so maybe
0:11:43one hundred
0:11:45and such a small part of an image is corrupted by impulsive noise so for
0:11:51example the uh white pixels
0:11:55oh we can also uh make a the colour uh example but uh that be
0:12:00easier to just to look at this is uh this one so uh this is
0:12:06the white pixel we are calculating uh the similarities and it turns out that the
0:12:13similarity between the two hundred fifty five and uh let's say one hundred uh is
0:12:19low and the similarity between uh the central pixel images corrupted and pixels which are
0:12:27in the filtering window which are also corrupted is quite large
0:12:32so in fact the weighted sum up to one which means that uh when we
0:12:38perform this uh multiplication and so on this noisy pixel will be preserved and this
0:12:45is a common drawback of the bilateral filter and also a bit for filtering designs
0:12:53like uh isotropic diffusion and many others because uh if pixels are the same uh
0:13:01in the in the filtering window uh mostly uh the corrupted pixel is of these
0:13:13we would like uh we wanted uh to improve the situation and then we show
0:13:19uh away how uh this bilateral filter can be improved a first we introduce digital
0:13:27puffs so in a result of se in eight directions for example would have a
0:13:34uh small filtering window uh is one hundred can as before the differences and we
0:13:40can we can calculate sparse
0:13:45uh joining uh the pixels for example this one this one uh free pixels the
0:13:52are depicted in this uh example
0:13:56and we can we can calculate digital buffs
0:14:00which uh have some cost
0:14:04the cost of a digital path joining us central pixel with the pixel uh in
0:14:11the filtering window used uh defined as the sum of the absolute differences between the
0:14:19successive steps
0:14:21so uh when i have uh above we've all uh what the pixels are the
0:14:29same then the cost of the power will be zero because the don't know changes
0:14:34but uh if the uh big changes then and uh the cost is high and
0:14:41for every pixel
0:14:43oh we need to find an optimal power optimal means and that the cost is
0:14:51so uh we are looking for minimum laughs
0:14:59this is uh
0:15:01this is
0:15:04uh different uh done in the uh case of bilateral filter because in the bilateral
0:15:11filter we are comparing on it on a peaks as well not looking at the
0:15:17pixels which uh between the we can say a would jump from the center the
0:15:24would be is that uh the pixels which are inside of the filtering window not
0:15:29considering uh the structure of the and here we have to consider uh the neighbourhood
0:15:36the close neighborhood of the central pixel and so on so for every pixel would
0:15:42have to find the above are so uh is a lot of intensities and these
0:15:47are these are the differences
0:15:49for the uh for finding the parts uh we are using the extra uh i'll
0:15:58go with uh which is uh quite uh quite fast
0:16:06using this uh extra et al gore of four grayscale images the cost is defined
0:16:13us uh is the sum of data from the uh intensities of successive pixels
0:16:21and we have a uh this the same structure but
0:16:28the uh weighting coefficient
0:16:31depends only on the cost
0:16:34so uh there is no actually this is not the bilateral filter this is just
0:16:40a filter which uh which uh takes into account the cost of the uh of
0:16:47uh of that pops linking the that the pixels so for every pixel there is
0:16:52the but there is a cost and we calculate that the cost and use them
0:16:58us weighting coefficients
0:17:01so for maybe just a for color images uh we substitute this uh instead of
0:17:09uh intensities uh we take uh the color uh the distance in a between color
0:17:16space for example of to be uh we made uh the uh calculations uh using
0:17:24rgb but in fact the uh
0:17:29you can use a suitable uh colour space uh we didn't check uh how it
0:17:35looks like we've other color spaces but uh even in the simplest uh rgb color
0:17:41space uh the results are promising and also we did a show uh in a
0:17:47moment so uh i will uh give uh some examples are using the three uh
0:17:54test color images and for the evaluation of the restoration quality
0:18:02oh we used the psnr which is uh which is uh
0:18:08uh using the and these word error uh for a color images we just uh
0:18:15at the differences in each channel and divided by the number of pixels and psnr
0:18:23is a good uh objective uh quality measure because it correlates the uh
0:18:32in my opinion wide world with on the objective uh coefficients are the correlation with
0:18:40subjective uh of expression is uh maybe not so uh so good but uh use
0:18:48the noise generally uh regarded as a reliable uh coefficient and some plots this is
0:18:56that this is the bilateral filter
0:18:59as you know maybe remember their uh to uh coefficients uh two parameters were required
0:19:06for the uh topological distance and for the intensity uh a lot and as you
0:19:15can see when we have a gaussian noise this is segment and sigma twenty for
0:19:21the um the choice of the part this is uh not so straightforward so uh
0:19:29mostly people uh don't write about uh choosing the parameter C yeah uh to it
0:19:38mostly uh
0:19:40set the parameters so that uh the images look nice but in fact uh choosing
0:19:47the players the parameter that is uh a little bit difficult uh with the uh
0:19:53if the images uh corrupted by a high intensity noise uh then it is easier
0:20:01and when we have uh images corrupted with guys for the gaussian noise
0:20:07and additionally uh impulsive noise is added
0:20:12then i the situation is better so that the choice of that of the optimal
0:20:17of parameters is uh
0:20:20is uh easier so um we are uh actually uh i'm interested in this case
0:20:27this is the mixed uh a gaussian and impulsive noise because it is uh quite
0:20:34quite uh quite uh difficult to uh that's uh press
0:20:39uh because uh
0:20:42it is switched to deal with impulsive noise uh they are not uh quite good
0:20:47at the gaussians and this is uh that this was proposed five by five that
0:20:53this nine by nine window uh it appears that um nine by nine five by
0:20:59five is enough so we don't need a very large uh got a kernels and
0:21:05this on some plots uh showing that our uh filter so only one parameter is
0:21:13uh needed uh it is denoted as H uses gaussian noise and this is the
0:21:19mixed noise so as you can see a we can take for example two hundred
0:21:24as a as a default value for a with the images and is uh my
0:21:32one and some results
0:21:35uh we compared it with uh some uh well no uh filters
0:21:42uh the interesting thing uh in the gaussian noise uh is that uh our filter
0:21:49was not was not matter
0:21:52than they know not a non-local means uh i don't have at the time and
0:21:58to talk about it but i didn't know local means non-local means uh is uh
0:22:03i think the best uh filter uh available one of the best maybe this is
0:22:09an anisotropic diffusion vector median filter bilateral filter by five by five modified this is
0:22:16the modification to use a five by five nine by nine
0:22:21so a non-local means uh is the wiener for the gaussian noise
0:22:27oh our uh all the filter is a has low efficiency but our filter uh
0:22:34works good uh especially for high noise intensity for the for the mixed noise case
0:22:42when you look at the examples other here so you can clearly see that uh
0:22:49this is uh obviously uh it gives much better results
0:22:55so uh usually a i think is i think is that you can you can
0:23:01see that uh that the uh the result is that looks better than me
0:23:10the uh there are no sell so many spectacles
0:23:16this is the land i image what is uh what is a disturbing thus some
0:23:22clusters of pixels which are very close uh
0:23:29uh to the center uh and we will uh result the problem uh in the
0:23:34future work so as a conclusion this is a
0:23:39and modification of the bilateral filter
0:23:42uh only one parameter uh is uh you did uh
0:23:48and then being a and uh we will uh we solve the but the problem
0:23:55of uh neighboring pixels which are uh corrupted
0:24:01so this will be a result in future work a given much for your attention
0:24:07you have any questions
0:24:25uh the computation time use a comparable uh we've the bilateral filter because uh we
0:24:34only need uh to find the parts
0:24:37we don't need to calculate the distances which is uh
0:24:43which can be uh done directly but it can be also that uh by uh
0:24:49some uh fast objects techniques
0:24:53or about actually the times are more or less uh the scene
0:24:59so i cannot say this is much faster or much slower well as the C
0:25:17uh yeah
0:25:23yeah right
0:25:36thank you