i so in in from university of a company as some babble and and and present a selection a a close to a recursive and and distortion estimation for subpixel pixel motion compensated video coding is what was down a a a a batteries min an hour a let's that's it you know so what we do call there's a employee to a a temporal of the motion compensated prediction uh to exploit the temporal a redundancy and that choose where a high operating efficiency so a a if that is a when a and at uh to channel distortion like the eigen use is it are updated due to that so or or or truncation so there are many in already rescinded techniques like a multiple description uh skin what we do coding or or a need for protection extension ah are introduced to mitigate this you fight of or or propagation and the basic principle of all of them is that's really a a screen some coding efficiency for the transmission us next and so i lots and quickly you mean by on the other and it is to estimate the actual and and distortion which is that incorporating in the rate distortion a more to optimize that's done so we to use the comes all and and distortion but the formal definition of are written at the uh uh this this so the basic idea is that's say we use this i a a and super square i to denote that a a a a fixed i and frame and and this is the original and two of this pixel and and we use that high to denote know that the encoders reconstruction which is only a a a a a third of to compression and then we use to that to denote the decoders we construct a which is a subject to the packet loss and or assume and a higher a a or a tradition so that the end-to-end distortion is really you by the difference from this decoder reconstruction uh between ah a from this to this all original binary so it i that can work like that a a lossy compression of the channel and consume and what is uh that's space but the problem is oh we we do the encoder a we do the encoding process at the encoder side and this we to it is really and known to the encoder do two the fact that a a packet loss is is really a i can loss is really of anything but with respect to the encoder oh the we to optimal per pixel estimate is a a pretty well known approach to X T makes such a a and and distortion the basic idea is uh the end and distortion oh of pixel can be formulated as that's and but decomposing composing these in two or three turn we we see that is really a linear combination of some the first and second moments of we you call there's reconstruction and a trees the decoder reconstruction of each pixel as seven of arrival then recursively compute a to the second moments of the recurrence are reconstructed pixels and then in in first and second moments of the the comes of a decoder reconstruction a we i that the the expected end-to-end distortion i think of their side and which is then incorporated it into uh the we use a simple a of optimization frame more or the at the recursion explicitly accounts for a all of the operations is and like uh coding and and consume and and also the channel still cast it um a have an extension and he's whether it's these tensions have been that's that we great i in into it is a a method for we're raising coding so here are some a a update equation is not no the basic idea is that a do the first and second moments of the reference pixel we can a i was compute the first and second moments of the current pixel and which then is that the uh uh i as i expected it and and distortion so everything recent fine but there is a limitation that it the come on but i it to me computes the end-to-end distortion of each pixel that is pretty good from what a single pixel in the previously reconstructed frame but many we do a regions night of a a set it's so motion compensation but if more people reconstructed pixels in the higher for a to pretty that signal to all at such prediction usually in that are model uh in the format of like linear combination in the so called cross correlation issue and i was a quickly you real at that time that and accurate estimation of are a score nation terms will you better and are there are and square no compute and memory units where this is and where you a we use these big then to do you know the total number of pixels in for a so this is really out computation computation of such optimal and a distortion estimate a i think we're example to show calls that's "'cause" condition term you emerges in two a a our update recursion some that's consider and by near and prediction the and it is we could just the average of two a reconstructed pixel X and Y so now we need to first and second moment of the interpolated pixel for the first moment is fine mean you just a and linear combination of the first no of the of of the reconstructed pixel but for the second moment yeah the two second well most of the reconstructed a pixel there's that start uh additional term yeah of X Y which is the cross-correlation correlation and we don't have a in our for uh many higher are a is uh have in the two so a overcome these each you ah while idea is that's just a a a the this cross correlation but its maximum and which is provided by the second moment of two marginal all second moment however we can narrow yourself doing the cross condition directly we come up with a correlation coefficient as a function of the distance the the use of X Y is really the spatial distance between two pixel oh two pixels X and Y and this class conditional model as oh and this is uh exponentially decreasing with this this data oh in this work we performance an alternative or of perspective in the transform domain so we know that the means square or or it's really comes and they're the unitary transformation and that we propose a some how a spectrum coefficient vision wise optimal recursive because if that's image recall score a a to it this and distortion the two in the transformed my it provides a per transform coefficient i made of the end-to-end and distortion and things like that that's per pixel but uh and i have to we you most the recursion recursive what all computation a first and second moments of oh so some coefficients of oh we well yeah right oh as a set of a mention here that it is really a good about a can for what is a the best coding operations that are perceived in the transform domain but since were what in this work or and exclusively focusing on but and more accurate and and distortion for subpixel motion come the decoding ah but just put it but it and that's i a a basic idea or we have the original band you of the transmit coefficient vision and you know K in frame and and in there to construct a once again next hi decoder the reconstructed X a to to but uh X to there is a random variable with respect to the T encoder and the and is don't expect it and and distortion can be from as set and we C this and and not change really a you can and a first and second moments of the transform coefficient or for in time and uh the uh the is pretty much say the same is now so what would be days with probability one man P the packet that contents this transform coefficient what is that are right at the at the decoder and was a so right the decoder time a reproduced it's that this the time a reconstruction as the encoder so that's why we're using i which is in there's reconstruction and with probability P this it will be about and then the order consume and will be calm and we know that the console pixel uh sort to some coefficient stuff is really are than the right so that's why we are using X a here two uh generate a first moment of but some feature and same idea of ice two second or one the a a a main computational right is in the in uh a big recursion where T the most a reference and it's okay it's not necessarily a great in fact uh i really possible that these guys all right and i that we only have that first and second moment of transform coefficients oh we well so we really need to generate a that's why what is and were using you to oh you K but a a great i so we really need to generally first and second moments of a piece of work will i the well from those i'm great what a a that's just assume that we now the moment all this right but now the make a run our update recursion that's that's with probably he one as P we have the it which contents the we but the if you and with the residual and the motion vector so what have the rate is you which use exactly the same as the encoder but the reference is star it's and no "'cause" due to the higher or uh i can also it and or or or or or a publication and that probably be happy assume and the same thing for second moment now that's can see that how to generate this a a first and second moments of the right for a the we can go a but is a can are in general a a reference that you which is the right one which is a a a great and all the thing to do that are only but so a i'm not that of generate a for by four reference well encoder nice too reference up to my and we go to to a six kind uh i a filter you ah used for interpolation i each of sixty four so the transformation is which is typically D C is simple linear transformation there exists is a constant a set of constants that right we have a to chosen coefficients of the a green well a a a a a a a a a way and now it's really a linear combination all that was one great but and then and we have to for uh first moment you two young being a combination of a known a hundred which is exactly oh which is a tractable but that's a commandment it seems that we were getting owing to this commission you choose okay we need to generate this cross correlation which we don't know by the major advantage that what do everything the transform domain is that are the spatial transform style as already removed i i remove the correlation code uh the correlation between transform coefficient so ah specifically where tree this is a cost on the into two categories the first one a to transform coefficients a different frequency but in the same now that content i was in the same packet so that by either simultaneously or or or that the clutter so we use X that are to uh to represent the you call we the packet is received and X F E then decoder can assume in the packet is not so first moment of these a reconstruction and consume are really accurate and a tractable and it it "'cause" that cross correlation can be from the data sets with probability one month P input uh the packet right and then uh at the decoder will we produce to to constructions and that list that the P i can last because that will produce so a will generate to consume and so this is really the exact cross correlation but that's a that we do know this two a a cross correlation we seem to a a a a a a a to make this two i the product of to marginal of first form ah appealing to the are going to be an is in the transform but my and and that the second category it's for in temporal correlation so a recall the energy come a complex and the of dct with say the the uh i don't have a correlation is really dominated by that be in the P C components and which is which is that's you meant to be unity and for all other easy C coefficients which we we compute as that are uncorrelated so we note that some more re fine models are possible but our experiments show that such treatment provides firmly uh i accurate estimate for most nature of the a here's seven uh overview of the procedures of this up recursion so given first and second moments of oh we uh are transform coefficients of we well in from a my one a a condition are the packet a ride or not with then update the moments for frame and uh you frame and so a first at five where the reference block base and then a a like this first and second moments of the reference point using a linear combination of the known a moments and the we compute the a a and moments a a helping to in or inter mode so either oh holding model so here are some a a image accuracy so we first try uh in the slide in all also all where a low is known to provide the a Q more and and distortion so in this peak sure the black i one is our our a simulation where we have a or where like fifty two a hundred uh i and a packet loss or realisation issue and the point one is the and end distortion provide be by low which is known to be the optimal and the the right one which uh well be seen this is the estimate provided by score is C uh that and in the second row for pixels square really i from a practical a soon two the law which is the optimal a and the in want to the subpixel pixel siding where do this a a what we're miss some modifications to accommodate such probably nature so we use a this close these wires approximation and the pixel so model respect to generate the variance of right also or and the two blue curves are the estimated uh i estimates provided by those to my third i one is the simulation a house a mining a a and and packet loss realisation issues and the the right one is the uh and when distortion one by score i see that's score are really what war i and distortions the second off the pixel motion compensated video coding so in conclusion i we proposed a spectrum coefficient once optimal recursive as as may to estimate the end-to-end distortion the spatial transform my as as well as the correlation property of the special for as well as energy compact set a property two close and be checked the cross correlation and provides a more accurate estimate of uh and when distortion in the deciding of sub pixel and we also know that square and then be shown to sub soon within in is our original no function that yeah so we have to one question you mean of a job um as yeah a yes so this is a a question so they you is that a a a a a really person where a computational calls compared to know but the thing is this i Z this ah back here so this set of a constant coefficient which is this small i which is really a a a a a lot spatial location dependent parameter uh not all of them are you can be important usually the usual case is that but most of them that are really new vegetable able the value of them are really that yeah that the that's so so that there it's eight uh is that are like fast algorithm within two simply by these computational complexity but in this work were we focusing on there are uh optimal he okay is you and