0:00:13that's one
0:00:15um i um is and the
0:00:16a pair of uh
0:00:19but subject to
0:00:25the some
0:00:29uh the more
0:00:35maybe some things about
0:00:37uh the uh
0:00:38modeling issues
0:00:45start i want to go through a very quickly through the enjoyment you have an image
0:00:50by which the what we call excel
0:00:53uh they stay
0:00:55on a
0:00:58is it two
0:00:59a is
0:01:00and do can excel as that was sent there's
0:01:04that time was you see you know
0:01:07or noted the U are
0:01:09a so are
0:01:11such as
0:01:13and our goal is to
0:01:15uh are present the contour of
0:01:17a each
0:01:18you go by image it has but use
0:01:20for while
0:01:23and that the ones are
0:01:25for that foreground this zero a the debate
0:01:29the court would stay in between the for foreground and background
0:01:33if by to be contained in the foreground the cells
0:01:36not to you want to be three
0:01:38for you see there
0:01:40for mean required for
0:01:41binary image
0:01:43they have the property that uh
0:01:46they have an a part which is on the big
0:01:48so a the so from the
0:01:50for a each has an they work on them
0:01:52the ground
0:01:53would be a don't to the core
0:01:57the the a being counted he you know
0:01:59for one it
0:02:01so what we can see that the
0:02:03a binary in each and the contour for are
0:02:07we in the same information they can be a
0:02:10no one one mapping whatever you have one we can
0:02:13you i the other as well
0:02:15so called or more in a binary image is you to call or modeling a whole
0:02:28yeah going to a first of one for the sequence of big sense you one N
0:02:33each chi a a a it's so for an A the would be given
0:02:38like T
0:02:40a property P of this change of excess would be that to
0:02:44uh and and pair can see that you the it sense would be connected in eight
0:02:50or are for the creation
0:02:52uh which you have been
0:02:55that is that
0:02:56and the court it's of the next uh
0:02:59so in the for it's of the last but i G placement
0:03:02which are a a lot of be in as one
0:03:06except they uh
0:03:08but zero zero so we
0:03:10don't allow here
0:03:13to state
0:03:14a things
0:03:15we have always move
0:03:17a but i right all the directions
0:03:19right and north
0:03:21so it that that are not R
0:03:24no you if we look at all these past what three uh
0:03:28movements months on one
0:03:31we can see that a uh we can buy eyes
0:03:34very is you by a number you
0:03:36which has a they use from zero to seven
0:03:39and the equation
0:03:41to get
0:03:43the court it i G from
0:03:45uh you think about a phrase
0:03:46a number of you
0:03:48would be
0:03:49but i mean
0:03:50the course
0:03:51i i times
0:03:52that that five
0:03:53or four times
0:03:55and the same uh that for sinus
0:03:57you of the or the G
0:03:59and you we have that dog
0:04:01so now we make all these uh
0:04:03a was a kid eva
0:04:05mark was of five or for
0:04:07they are going to get the allowed
0:04:09oh zero would be
0:04:11for for
0:04:12well be back don't
0:04:14down works
0:04:16uh then two
0:04:17but what or and so on so all of these are allowed
0:04:24but and this a ah a prioritisation uh
0:04:27it does uh introduced in that
0:04:29this segment is the
0:04:30a few it can be cheap
0:04:32which uh uh
0:04:34so that the
0:04:35we have a part their
0:04:39that's zero seven
0:04:41uh our final change own would be a sequence of
0:04:44those that but
0:04:47don't numbers
0:04:48can be a uniquely defined by
0:04:51is you quality so if we take a job you got uh
0:04:54one issues of the pixels
0:04:56that's lot
0:04:57i T
0:04:58we get the
0:04:59i i to me
0:05:00at time
0:05:02a a a a that is a very simple because uh fashion
0:05:06to get the job but you presentation based on that
0:05:09uh on there
0:05:11a now we can component that
0:05:14we have
0:05:15a but of the point by
0:05:18the first position of the
0:05:21say i'm core
0:05:23and then a sequence of a
0:05:25the change
0:05:26sequence is now be in this set zero you know seven
0:05:29and that would be
0:05:30no one one correspondence to the gym you can
0:05:33sequence of excess P
0:05:34you want to P M
0:05:37no i was observed that the
0:05:39uh uh this uh uh a few might quotes are would be to D dot then and it's much more
0:05:45a efficient two
0:05:46introduce a new variable called the bit at T
0:05:50might as well
0:05:51the and cold
0:05:53but actually D uh a my
0:05:56simple so we have
0:05:57but minds
0:05:58the might as well
0:05:59that would be
0:06:00we that is like we take a is operation
0:06:03uh we
0:06:04but as the model at uh
0:06:07and they they the non-negative in
0:06:12is a uh
0:06:13now we see that uh
0:06:15these new numbers be tough
0:06:16uh are also connected to the positions
0:06:19because of each other
0:06:20but your are uh called binary T
0:06:23and in fact is that there is a very simple and nice the passion for getting the positions of pieces
0:06:29the second point
0:06:30you the position of the peaks the previous time
0:06:33and the
0:06:34next to used in the box
0:06:36and are
0:06:38new i'm then be thirty
0:06:39which is the partition
0:06:40you you might change
0:06:42where these metrics is that methods similar
0:06:45so now i mean that a a second uh it really representation of V C of pixels
0:06:50that the position of the first six and what addition of the second um
0:06:54and then we have that
0:06:55uh a chain code
0:06:56you can be numbers in this
0:06:58said the
0:07:00okay and it's in being model they we have a number this at zero one up seven
0:07:08yeah is um
0:07:11to code we you discuss a now it would
0:07:14you a are you to be seven that was that B
0:07:17where you have to move
0:07:19as you see they are a
0:07:21a when T V D so we move sometimes that all
0:07:24like here
0:07:26because sometimes
0:07:27okay that but
0:07:28it is what
0:07:30well as uh
0:07:32it's so wise
0:07:33i Y way to represent the binary make
0:07:36but there is also a lot and i think we how to
0:07:39we presented
0:07:39the the by
0:07:42and S
0:07:43got that P which are
0:07:46packages are is are to those
0:07:48so they are got three
0:07:51the back is these be uh that this is of those at
0:07:55so we can uh uh also discuss about the chain codes are representations or water
0:08:00just like it is that is
0:08:02to now we have been in the this that this points you want to and so on
0:08:06if we translate
0:08:07the that is by a step
0:08:10vertically and horizontally we are going to get a like things and
0:08:13we can discuss about change "'cause" when this describe that
0:08:18but is interesting is that now we have to move just in for what a T V so this uh
0:08:23but this is
0:08:24i mean to provide a something in for it but
0:08:27and the um
0:08:28we see that the uh
0:08:31of the joint code here would be
0:08:33use a number member and we went much longer than the change a the peaks
0:08:38do have just seven except the J
0:08:40you would have sixteen
0:08:42now the question is
0:08:44which would be the best presentation which one
0:08:46should be used for encoding
0:08:49uh the same P and and T which is the one of the age
0:08:52that it is and exactly the same information so
0:08:55we have to use
0:08:56uh which are better
0:08:57use the best is result
0:09:01a discussing about was so uh but that uh
0:09:04a chain codes
0:09:06we can do to this exactly as before
0:09:11chain code in the uh what if D V D for
0:09:14where you have a
0:09:15a very similar to the definition as a for now this numbers almost
0:09:20a a in this a zero one two three
0:09:22that just for values for grammar
0:09:24and uh our
0:09:26what the image you would be no if we want and
0:09:29uh two D set the initial that X
0:09:31plus the
0:09:32yeah my one uh points from the
0:09:35uh a change words on the task with that
0:09:38we can two also of attention
0:09:40uh codes by introducing these difference between galactic that one runs on
0:09:44that would believe that it is gonna before
0:09:47that is
0:09:47for this is that uh uh it is that is that is not just think that
0:09:52i whole
0:09:53which is quite a few O T
0:09:56are introduced there
0:09:57later than
0:09:58well yeah that's
0:09:59is is that to the fast at the
0:10:02uh you uh of you well
0:10:05but not it's not
0:10:06as we had before
0:10:09for for that
0:10:10a definition my
0:10:11code we had
0:10:13the difference between two uh
0:10:15you my quotes
0:10:18and you had that
0:10:19second order
0:10:20then memory
0:10:21now we don't have any more a second order memory more in fact we have a model with the
0:10:25uh you put a very long memory
0:10:28uh because now introduce to state variables
0:10:31which i we to tell if
0:10:33the sense of
0:10:34a movement or along the horizontal vertical direction
0:10:38i get or not so he's are state that
0:10:41that would be to state tiger was
0:10:43and the code itself would be defined as
0:10:46uh is you know in that is no change direction
0:10:48why if there is a change that but but you that
0:10:51well sense
0:10:52whatever whatever moved that direction
0:10:54and the call to would be one you change point detection and the sense
0:10:58no that direction
0:11:01so this would be a very uh
0:11:03lot of memory of the nation and i for now we had a have to say but
0:11:08and what of be
0:11:09chain code then what is the next
0:11:11that that's in the chain of and
0:11:13sequence of
0:11:14your these
0:11:17yeah a representation for is very simple going to with that we have the corporate along that the they sounds
0:11:26thirty seven cents
0:11:27and the colours are in the set that zero one to
0:11:30up to seven
0:11:31and and you have also the called uh
0:11:34a i the got yeah images
0:11:37you see this sequence of uh
0:11:41simple in the
0:11:42a a T a but as you one and two
0:11:45uh we have a much more C press of that this is a you T all of them
0:11:49combat to thirty seven
0:11:52and that may say that probably this is less efficient cool
0:11:55but is not
0:11:57and right as in is that uh
0:11:59we have a few force what but they are just zero one and two
0:12:03but a more uh uh what is more interesting is that the simple to
0:12:07we you know
0:12:08direction and sense
0:12:11but you is that we sell them in the scene
0:12:13so basically they we we have
0:12:16to see then it to see what it should get most of the time
0:12:19and uh
0:12:22this would be a
0:12:23but it should be able
0:12:27what would be to for uh why we are to see this this the compression problem
0:12:32uh uh because the
0:12:35you may want think one by reading is and then would be important
0:12:40but may also can here
0:12:42a very good statistical models
0:12:45we can
0:12:45call this
0:12:48for a a recognition
0:12:50and main wants to know what is the minimum description length for
0:12:54this models
0:12:55so for that reason
0:12:56we are interested in the most that's compression of the contours and that's who the study with need in this
0:13:01the they
0:13:03well so there is not but um which is but yeah well what did but is not identical is that
0:13:09contours in image segmentation and image segmentation also
0:13:12a very important the uh a region and you do we need other
0:13:20what is the state of that the of corporation of four chain codes
0:13:24uh how how a codes have been used to the twenty years ago um
0:13:28they are a fixed
0:13:31defining a simple was for the for a the extensions for who but that was uh used the five years
0:13:38a a able to variable able uh coding run it's building that
0:13:41also use
0:13:43uh a what was used in a very nice paper in two thousand six but the recognition was uh a
0:13:48or text these for
0:13:50this code
0:13:51you might
0:13:53and that was used for map uh
0:13:55what of mess
0:13:57they have a C are they are they specific or
0:14:02uh a lot of this i i think of it to um
0:14:06conflicting here
0:14:08a results
0:14:09not i is this is it telling you should use this uh uh them a the back pages follow
0:14:15like to publish and you what
0:14:16the best these definition
0:14:18if a code
0:14:20the conclusion in this paper would be that
0:14:22this is not the best is second best but the the best but would be in that a a three
0:14:26T which
0:14:27is more
0:14:28that's one reason why it was not start it so well not
0:14:33so the question would be what is the best
0:14:35the should should more than four
0:14:37or the modeling
0:14:39we that was something in important this type
0:14:41conditional probabilities what would be that the probability of
0:14:45the key even all that D
0:14:47the previous moment
0:14:49and we have the same for big so and here for but
0:14:52so our goal is to a which of these is that
0:14:55better suited for our
0:14:57one want to
0:15:01uh i our um
0:15:03first for the second are model we we have just introduced at these few my codes and iteration not well
0:15:09but in our paper but we are we can get
0:15:12also a a higher order models
0:15:13what you combine these first order and second order models
0:15:17uh in
0:15:19my model so
0:15:22a which use a fixed but next memory
0:15:25or or you models where the memory of the model depends on a
0:15:32so we have a or or just uh compressing a the point two
0:15:36for is the
0:15:38that's pretty
0:15:39oh time series is then
0:15:40we product working
0:15:41to you should use in the decoding and have a
0:15:46this is a um
0:15:48need to um is that three where we have a
0:15:50on the route
0:15:51or one on the
0:15:53the nodes
0:15:54we have
0:15:57we have to an estimate notes that was a channel
0:15:59uh they can either or distribution
0:16:02that was which are thirteen
0:16:03they are used
0:16:05when whenever code so we joined the distribution quality
0:16:08these note
0:16:10when it would coding
0:16:11in a lot of this court
0:16:13so this kind of a a context you recorded data
0:16:16we context the
0:16:18i i assume is not uh
0:16:20what did you are but they do find and you that of the digital
0:16:23uh a a a a base the T but uh
0:16:26not is pulling
0:16:28it was
0:16:29less uh
0:16:30uh uh use how they it the the the coding is that paper mission
0:16:34by a a over and the from
0:16:36used for depression
0:16:41a a big problem of be how to optimize the point T structure and we have but
0:16:45class of that i a problem uh
0:16:49for choosing this uh
0:16:51structure of the T that's
0:16:54one context you
0:16:55which is four
0:16:57symbols in the previous positions in the G
0:17:02we put that the statistics of of of of the counts we do i'd made in here so
0:17:07well the time we collect at the T V what would the code lengths at time T
0:17:12but the index
0:17:14but that's in that's
0:17:16and uh
0:17:17we are it mostly in the find a a a a a get to the and the
0:17:23the the sequence
0:17:24get that
0:17:27and uh uh are study after we get to the at least i be at each node what we
0:17:31what is the balance between coding
0:17:34coding to the choose
0:17:36we just at the codes of the children or back to the bottom
0:17:40you for be a a part and is uh
0:17:43next year is that than the children last
0:17:46a T
0:17:47because you have to encode the structure of this uh
0:17:50a those relations
0:17:51and whenever a this happens uh we you this you know as and that you node otherwise
0:17:58it would be a as a uh
0:18:02and we provide like data
0:18:03five or or for this next uh
0:18:08these calls
0:18:09that is that i think that um
0:18:12that and program
0:18:13a way to
0:18:14optimized the quantity structure
0:18:16now we've the putting we have a a bit more
0:18:18did you got or more more thinks to
0:18:21study we um
0:18:23like the statistics not only that the
0:18:26note to and time T
0:18:28well so we take all the possible groupings of E
0:18:32a second no
0:18:33and and a complete the
0:18:35such a a a code
0:18:37oh that is
0:18:38because the same so
0:18:40choosing which two
0:18:42to use would be the uh
0:18:44a a class the lucky
0:18:46which is now
0:18:49we can do that
0:18:51structure of the three
0:18:53so that is a a set to me a a a a are adapted the
0:18:57a we encode
0:18:59first thing for the structure of the T we number that is the best the at and of our change
0:19:04and then we just we that uh chain code the with a i keep statistics but this that no no
0:19:12two show some results
0:19:14but that we have this a set of the what high by use only when B are shown here
0:19:18that a very different from you you know like to make it to you know but
0:19:23a a some images is making many holes
0:19:26uh i think you're
0:19:29we can
0:19:30everything think there which uh
0:19:32would be equivalent to a won't the full binary
0:19:35one example is this uh a set in each
0:19:38and you can see what is that the optimal structure of the P
0:19:42for a
0:19:43uh you T change go
0:19:45and that would be to what the most structure forty uh to finish if you michael
0:19:51this uh
0:19:52uh uh if it should if you might what would have just a five song
0:19:56for i
0:19:56simple this one seven
0:19:58something to hide that
0:20:03the structure of the fee
0:20:06is you more interesting if you represent dramatically what would be a to "'cause" that these of this call
0:20:11you we have the context
0:20:12what do with the excel
0:20:15you have the context text up with a a a guy it is
0:20:18and you that the german because sectors are no longer for the crack them for the because
0:20:23although the two are
0:20:24it but and representation
0:20:26the context and this statistical on uh a it's to and S is different in the two representation
0:20:33maybe i'm going the desired
0:20:34yeah the results for the one having five we had in the that sense
0:20:39yeah a and we uh it represents in um
0:20:43or the performance of the
0:20:45and probably by a context C everything here
0:20:48we different from the a chain codes
0:20:50the that really to be as your T which is the bands
0:20:53well yeah or so that would be the zero line
0:20:56oh yeah as is that you can see a higher on top of these you don't my meaning that they
0:21:00are not as efficient as the code you want the and that happens for all the five
0:21:04the best company but is still on the uh
0:21:07yeah a is the core the
0:21:10a a month with this
0:21:13uh and
0:21:14then um
0:21:16blue um is there uh
0:21:18the best the context the on T D
0:21:21excel one
0:21:25a that that was a is i it's of a a code by grouping
0:21:31i this is that the the sure that is that that's which are published in a recent paper in uh
0:21:37just of that since the processing
0:21:39but that is as well as you can see here
0:21:42i results in the context you at what is the
0:21:45i a much better
0:21:47tens of course and
0:21:48a a better than
0:21:49then the
0:21:50this one
0:21:51uh here what they use that you just at a few or more
0:21:57and they established by a uh yeah you great again that the best legs for all the models would be
0:22:02well as we have a uh
0:22:04due to a possibility to take the longest uh one text
0:22:07and the were used other markov model
0:22:09and we you got but but a result
0:22:13or T one hundred five
0:22:14and for each individual files or
0:22:19is that a special but is day
0:22:21uh dependence of the possible and that's so be um
0:22:25and as you see uh our T models
0:22:29such a some points so at this point you may say that this they
0:22:32what they're six
0:22:33get the best performance
0:22:35uh a of the models
0:22:37so this the same that additional
0:22:38it happens us by the same or
0:22:40the same plane
0:22:43as got images
0:22:45we have many presentations ah a a of the contour data are uh we found that a statistical efficiency of
0:22:51in E papers right but
0:22:54and the uh when we have when we use uh a T context modeling for a
0:22:59uh that is a significant difference between the trees for one in which what D image
0:23:05for that we said that
0:23:06but that we use in adaptive
0:23:07but for
0:23:09uh i think of
0:23:10and what we see find it that the what we we won't and is not only
0:23:15yeah uh important point coding but is also for a find good this kid of uh
0:23:20binary images
0:23:22i you the
0:23:29i i i i have time to ask some session
0:23:32for for a i
0:23:36i ask
0:23:38i yeah about