a lower everyone and one car oh i'm from boston university a be talking about our work uh on uh multi energy x-ray computed tomography for explosives detection this is work of my student are our student will more you're uh in our collaborators and how do home or P N from M G H and percussion ish for my call from boston first so a quick overview um in finding explosive materials like at the airport i'm sure we've all experienced having our bags skin uh you can discriminate materials uh using multi energy three computed tomography the X ray buys you the ability to look inside things without impacting packing them our focus is on uh a so called attenuation versus energy curves of materials i describe those in a bit and our interest is in take you learning based perspective seen what the data tells us about this problem uh will study the dimensionality in the span of the set of curves that the fine materials and we'll look at what happens when we go classifiers using different choices of features what i hope to convince you is that there's the potential for improvement over existing methods in uh in these techniques by taking a learned based perspective and uh i hope to show that uh using different choices of features and the conventional sh choice tension by you something and using a more features than the conventional uh choice of two features can potentially by something so a little bit of overview of explosive detection by multi energy uh x-ray ct so uh unit demography let's you look inside things without opening the bags and taking everything out so C T by Z the ability to penetrate at rate materials multi energy ct by you the ability to discriminate different material types uh so you can kind of think of it as a spectrographic type of an now a focus of this work all talk about the day is what the fundamental information available in these kinds of measurements is and again to try to take a learning based perspective try to see what data or measurements of this type uh has to say about our ability to discriminate materials and to try to focus a bit on what the best choice of features is if you know you wanna do material discrimination not just make picture so here i have uh uh uh a colour coded X ray picture give V the idea here's the kind of thing see in the airport and this is the kind of thing that is typically done now where there's two features that are extracted and you try to cluster materials this two dimensional features okay a little bit of physics so we understand where the information is so X rays well any time you do X very ct of course the modalities X rate based and so the interaction of X rays uh with materials is where the information gonna come from uh the key a a quantity for us as what's called the linear attenuation coefficient or the L A C oh which is denoted by the symbol new of the up here uh basically new V tells you about the uh uh the number of photons that are lost uh as they propagate through material a and that comes through physics from beers law which is down here if you put a number of photons i zero into a homogeneous material of length L there is the L a the number of photons a uh the come out a follows this law i zero E to the minus you we of L and the number of photons lost is given by this uh parameters slash function you of the uh the thing to note is that that you of V depends on the photon energy so if you put in photons of different energy here the attenuation will be different depending on the energy of those vote so this you of V the a curve a a new in this axis your somebody's curves over here you in this axis energy or you on this axis which defines the attenuation as a function of energy so you can see that for most materials lower energy photons are absorbed at a higher rate than high energy so we material has a curve of this sort so here's the curve that you'd see for lead here's the curve you'd see for say water and there's another curve for hunting and so when you do X ray based uh interrogation materials what you're really are getting in at is the differences in these curves that's that that's how the materials in pack a a a a a the measurement and you can see there's some interesting features somebody's curves at discontinuities called K edges that occur at different locations and so the basic ideas from measurements uh X ray measurements what we wanna do with associate the extra measurements what this L A C these per and with the L A C we can associate with material so that's kind of the that picture where we're gonna go okay now what's typically done in in uh X ray based multi energy x-ray imaging is that the uh a linear uh attenuation coefficient is assumed separable and space an energy and so these news uh these functions are a function of both space and energy uh and we do some sometime of uh of decomposition where we split what out the energy of part from the spatial part so the spatial part is the volumetric thing that tells you the distribution of materials uh we decide on some energy functions that describe the space of these curves and then the goal is from the X measurements to find these coefficients a K so here's sort of a notional diagram of that the you E the the energy curve as is decomposed in this picture in the two different functions this is a a a common standard choice of functions using the photo like so called photo electric function the comp function and so you write the overall attenuation per as some coefficient times this curve plus a different coefficient times this curve uh and you try to find these coefficients at an A C some more generally you get the pick these functions and you try to find his coefficients so overall all again the picture i having your head is that at the end of the day you try to find school fashion say a vector of coefficients and those vector of coefficients to find a material okay now historically the medical world sort of drove this kind of multi energy X ray work in in the medical world the kinds of things you're looking at are the body biological tissues and the universe of biological kind of materials is relatively small mostly we look like water make we have phone and it in that domain it we shown that the the the space of materials was well represented as two dimensional and uh the particular two-dimensional dimensional functions that were originally proposed where the photo electric and the constant functions and so the the world kind of evolve along on this two dimensional point uh a and the choice of basis being you the focused on for electric and compton basis functions and sometimes people choose another two basis functions that are based on their application in the medical world up P sort of extreme of things like soft if you and bound but the space is generally a two dimensional space and since they know that the functional space uh the spinning space as dimensional that leads to skinner's that uh only exploit a to energy spectra in the skinning so you sort of take measurements at two energies you try to extract these coefficients for these two functions at that and a two dimensional space this is propagated of the security don't where it's nominated by a dual energy uh machines trying to extract two dimensional features and displaying them in a two dimensional space and trying to be cluster but you think about the security domain main the space of uh materials is much greater than and the biological space i mean it since S since anything you can think about putting into a suitcase and so you have much less control about what goes into the scanner and that the universe materials as much greater so perhaps it shouldn't be surprising that you might expect that that them a dimensionality space might increase okay so what so this is a what our hypothesis is is that we might wanna be interesting a higher dimensional features a higher dimensional uh spanning space and a perhaps different features than this photo electric and compton expansion set or the corresponding call now there's an additional piece here and that's that rather than imaging the medical world is always focused on imaging is in a explosives detection were interested more in discrimination it's not so much making the picture it's it's more or less saying look you have something that's gonna explode in the bag and so for that we're trying to get these features that we're gonna be using to do classification now let me go back for a minute to the x-ray sensing so there's this process where the material bag the body whatever is in the scanner you're gonna take a bunch of these projection measurements and from that at the end of the day you're gonna try to estimate these coefficients these a K and the expansion uh expansion function so at a high level we can kind of you the left hand side as the measurements projection from and there's some nonlinear perhaps messy why roll tomographic kind of measurement and so there's some on linear transformation of the thing that you want these coefficients that define the material perhaps spatially distributed across the line so for our purposes where we're gonna take this abstract view of the tomographic problem you get measurements and from those you're gonna try to extract the a case yeah case or would fundamentally defined find material okay through this equation where you this expansion uh so if you change the basis expansion when you try to estimate these a case you're changing the feature space so the the viewpoint point we have is this is that choosing these basis is really the choice of the classification space in the work that we're gonna do we're gonna suppress the worry about demography we're gonna focus on the basis choice okay so that's this were so here again no only a kind of describe that is yours a bunch of explosive materials class one there's a bunch of non explosive potential confuse or is class zero each of these explosive materials has some L A C associated with that an an explosive ones have some L A C so there's a universe of L A C over here a different universe of L A Cs over here and what we're gonna wanna do is choose these expansion things uh a um basis functions so that the coefficients which are features help us to doing discrimination between the two classes okay now the approach that we've take initially is just to take a a a uh a universe of the uh we take a bunch of uh labeled samples some explosive some non explosive we discrete eyes them and we stick them as columns in double major so we have the T N T yell A see the honey L a C all the way up to the R X L A C so we have material one this access we have the uh uh the values of the curves of different energies coming down you along each column and then we apply singular value decomposition analysis what we're gonna do was look at these functions the singular value functions and different combinations of them as different choices of a a uh is that we can extract features from or we're gonna look at the singular values to tell us about the relative importance of these different feature okay okay so i a experiments so experiment number one is is trying to make a move towards understanding the space of explosive materials both the dimensionality and sort of what it might look like so the first thing you can do well first let me take the experiment we took a for explosives fourteen non explosive we discrete eyes them do a hundred forty one energy level so each L A C is essentially now hundred hundred forty one dimensional vector and we stack them up in this matrix and we do S V D well i forgot to add we we discrete tries them over the essentially the diagnostic range from ten K V up to a hundred fifty K T V that's typically the range the gets measured in an uh ct T machine uh and we apply the svd so over here i have the singular values i ordered as a function of index and again i go back to remember the conventional approach says that that's space materials is is well uh characterised as a two dimensional subspace case so you should only need two functions to span it so if that was try to the svd analysis should show on them too large singular values and the rash be insignificant but as you can see there is one up here there's two three four five six seven you can see that this thing isn't one or two and then dropping down to zero it actually rolls off relatively slowly and it looks like based on this analysis they're significantly more than two uh the to the feature space of at least explosive materials these are biological anymore more so this was our first interesting result that says that uh hmmm maybe we wanna use a larger than a two-dimensional space the other thing is if if you think okay maybe a a well approximated by the first two singular value those first to uh uh a a single functions corresponding to these first two singular values are shown here and just for reference like put the the standard two functions the photo content functions down here notice these are very smooth to smooth functions to represent materials the first two singular functions are not very smooth they have these discontinuities but remember a lot of these materials can have things like these K had just discontinuity so this was a another interesting observation yeah i you might say is okay two functions to functions they look different but maybe they span the same space but even that's not true if you look at the angle between the subspace spanned by the first two singular functions and the subspace in by the for constant functions the between them sixty eight degree so it's not like they're the same functions okay so there's a lot of difference here or second experiment was to look at the effect of a feature dimensionality on classification for four so we have the same setup as before the same a universe of explosives and non explosive the same discrete as a nation the same stacking in the S P D okay and what we did here was we look you know order at a singular or uh values and the singular vectors we divided the data randomly into an eighty percent take training twenty percent test set and then for a different numbers of features going in order uh according to the S P D we trained a classifier and then tested the performance a classifier so we only picks say one feature the first single or of uh function use that and we used one in two then we use one two one three one two three and four and and re repeated this for different numbers of features and then we look at what happens to the classification performance as you increase the dimensionality of the space in which you represent B okay okay so you can see what happens here we and we did cross validation on that so if you start with a one your performance is down here one into your performance down here as you go to three an improve or five six to jumps up and when you get to seven or eight it it jumps up and then it seems to local law so that this access is about sixty five percent correct classification here at eighty five percent correct classification so this seems to suggest that there's some dramatic room for improvement by increasing the dimensionality of the feature space that you represent materials in at we at least for explosives tech in this is sort of counter the conventional wisdom which is always been focused on a two dimensional feature space centered around for electric in comp okay K third experiment so so those speeches were chosen in order so when we chose a a um two features we chose the largest us to singular value what we did next was we fixed the number of features i E the dimensionality of the space to be to the same as the photo compton choice but now we looked at different combinations of S uh a single or function we tried to see what happened as we went through all the different pairs you could imagine so essentially we're comparing different choices of two dimensional feature space so the dimensionality is fix but we're looking over the different sub-spaces okay so the same set same explosive saying non explosives same cross validation eighty twenty split i'll so here are the choices that we may so this is singular functions one into one and three one and four two one three two one four three and four over here to the right is the performance of the photo compton choice this particular conventional two dimensional feature space and we can see that the conventional two-dimensional a photocopy in choice of the two dimensional feature space gives you about sixty six percent correct classification as you go through these different pair choice lots of them are very similar but this one one and four seems to perform much better so this seems to suggest that again even if you want to limit yourself to a two dimensional feature space that the conventional choice of photo comp and may not be the best and that there might be room and a classification context the optimize this choice to get a better classification of a particular a folk it's classes of materials then a uh a has been carried over a traditionally from the matter okay so our conclusions here in this initial work is that well we study this problem of material classification from X ray based L C feature okay we took a learning based approach we used uh a actual curves of materials and we said what is the data tell us about this we kind of took a first principles approach look at the dimensionality of the space look at the choice of the space and tried to see whether there was room for improvement our initial results seem to suggest that there's the per potential for improvement both in terms of increasing the dimensionality and then optimising the choice for any given dimension so this was an initial work we limited ourselves to svd analysis what we've been working on since the time we did this is trying to break out of that S P D paradigm "'cause" there's nothing that says that the S D uh um svd based singular functions are the right functions to represent things and so we've been sort of trying to a a push this for thank you um you talk about right class patient i would have thought that you know or we you false alarm problem section probably not of you for i mean in classifying something close is probably not a missing yeah there's lots of choices you can do a and and the working up some of that stuff i mean we've done some additional work in doing things a a so so this pick some particular classifier an svm based when your for kernel classifier and then looks at correct classification for that class of part we've also done work and just basically what's the uh the choice of things that sort of a as the most information so one way you can measure that is for example a area under the roc oh the things you can do or you can fix false alarm rates and look at P B we've been plane with all of that so you i mean you're right i agree with you is just the plumbing it's the second to last Y and the one that know the that yeah yeah the but one no one for seems to work a lot better than the others yeah is the fact that that's that an outlier is that in into the result three not at all i the first of all the the svd features you you know the single functions you get are are are physically but so there's nothing i mean we've looked at them there you use all the first two there's nothing the jumps out that says these look like certain materials for example so no i would say nothing into about that result to me yeah composition position on exponential decaying function am i correct the the on on the functions they're not necessarily exponentially okay yeah but but the yeah the non to have generally have the proper okay if you thought of utilizing other functions because some of the ones you showed have these we use an this got do it is that not well express in that that function yeah maybe a misunderstanding your question i mean the the those curves are what they are for materials what we did was we stack them up and did in S P D so the singular functions of that universe or just gonna be what they are they're not parametric be they are not being parametrically represented a i thought that i thought you were a but a metric known no we present a there it's a discrete eyes world so they just turn out to be what they are we we well i i don't where i'm running a i'm i'm pass can time we'll we'll talk of