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