Přepis řeči - A LEARNING-BASED APPROACH TO EXPLOSIVES DETECTION USING MULTI-ENERGY X-RAY COMPUTED TOMOGRAPHY

0:00:15	a lower everyone and one car oh i'm from boston university a be talking about our work uh on uh
0:00:20	multi energy x-ray computed tomography for explosives detection
0:00:23	this is work of my student are our student will more you're uh in our collaborators and how do home
0:00:28	or P N from M G H and percussion ish for my call from boston
0:00:32	first
0:00:34	so a quick overview um
0:00:37	in finding explosive materials like at the airport i'm sure we've all experienced having our bags skin
0:00:42	uh
0:00:43	you can discriminate materials uh using multi energy three
0:00:46	computed tomography the X ray buys you the ability to look inside things without impacting packing them
0:00:51	our focus is on uh
0:00:54	a so called attenuation versus energy curves of materials i describe those in a bit
0:00:58	and our interest is in take you learning based perspective seen what the data tells us about this problem
0:01:04	uh will study the dimensionality in the span of the set of curves that the fine materials
0:01:08	and we'll look at what happens when we go classifiers using different choices of features
0:01:13	what i hope to convince you is that there's the potential for improvement over existing methods in uh in these
0:01:18	techniques by taking a learned based perspective
0:01:20	and uh i hope to show that uh using different choices of features and the conventional sh choice
0:01:26	tension by you something and using a more features than the conventional uh choice of two features can potentially by
0:01:32	something
0:01:33	so a little bit of overview of explosive detection by multi energy uh x-ray ct
0:01:38	so uh
0:01:40	unit demography let's you look inside things without opening the bags and taking everything out so C T by Z
0:01:45	the ability to
0:01:45	penetrate at rate materials
0:01:47	multi energy ct by you the ability to discriminate different material types
0:01:52	uh so you can kind of think of it as a spectrographic type of an now
0:01:56	a focus of this work all talk about the day is what the fundamental information available in these kinds of
0:02:01	measurements is
0:02:02	and again to try to take a learning based perspective try to see what data
0:02:05	or measurements of this type uh has to say about our ability to discriminate materials
0:02:10	and to try to focus a bit on what the best choice of features is if you know you wanna
0:02:14	do material discrimination not just make picture
0:02:17	so here i have
0:02:18	uh uh uh a colour coded X ray picture give V the idea here's the kind of thing see in
0:02:23	the airport
0:02:24	and this is the kind of thing that is typically done now where there's two features that are extracted and
0:02:28	you try to cluster materials
0:02:29	this two dimensional features
0:02:32	okay a little bit of physics so we understand where the information is
0:02:36	so X rays well any time you do X very ct of course the modalities X rate based and so
0:02:41	the interaction of X rays
0:02:42	uh with materials is where the information gonna come from
0:02:46	uh the key a a quantity for us as what's called the linear attenuation coefficient or the L A C
0:02:52	oh which is denoted by the symbol new of the up here
0:02:55	uh basically new V tells you about the uh uh the number of photons that are lost uh as they
0:03:01	propagate through material
0:03:02	a and that comes through physics from beers law which is down here
0:03:06	if you put a number of photons i zero into a homogeneous material of length L
0:03:11	there is the L
0:03:13	a the number of photons a uh the come out
0:03:16	a follows this law i zero E to the minus you we of L
0:03:19	and
0:03:20	the number of photons lost is given by this uh parameters
0:03:24	slash function you of the
0:03:26	uh the thing to note is that that you of V depends on the photon energy so if you put
0:03:30	in photons of different energy here
0:03:32	the attenuation will be different depending on the energy of those vote so this you of V the a curve
0:03:38	a a new in this axis your somebody's curves over here you in this axis energy or you on this
0:03:43	axis
0:03:44	which defines the attenuation as a function of energy so you can see that for most materials
0:03:48	lower energy
0:03:49	photons are absorbed at a higher rate than high energy
0:03:54	so we material has a curve of this sort so here's the curve that you'd see for lead
0:03:58	here's the curve you'd see for say water and there's another curve for hunting
0:04:02	and so when you do X ray based uh interrogation materials what you're really are getting in at is the
0:04:07	differences in these curves that's that that's how the materials in pack
0:04:11	a a a a a the measurement
0:04:13	and you can see there's some interesting features somebody's curves at discontinuities called K edges that occur at different locations
0:04:19	and so the basic ideas from measurements uh X ray measurements what we wanna do with associate the extra measurements
0:04:25	what this L A C these per and with the L A C we can associate with material so that's
0:04:30	kind of the that picture where we're gonna go
0:04:34	okay now what's typically done in in uh
0:04:37	X ray based multi energy x-ray imaging is that the uh a linear uh attenuation coefficient is assumed separable and
0:04:43	space an energy
0:04:45	and so these news uh these functions are a function of both space and energy
0:04:50	uh and we do some sometime of uh of decomposition where we split what out the energy of part from
0:04:55	the spatial part
0:04:56	so the spatial part is the volumetric thing that tells you the distribution of materials
0:05:01	uh we decide on some energy functions that describe the space of these curves
0:05:05	and then the goal is from the X measurements to find these coefficients a K
0:05:10	so here's sort of a notional diagram of that
0:05:12	the you E the the energy curve
0:05:15	as is decomposed in this picture in the two different functions
0:05:18	this is
0:05:18	a a a common standard choice of functions using the photo like so called photo electric function the comp function
0:05:24	and so you write the overall attenuation per
0:05:27	as some coefficient times this curve
0:05:29	plus a different coefficient times this curve
0:05:32	uh and you try to find these coefficients at an A C
0:05:35	some more generally you get the pick these functions
0:05:37	and you try to find his coefficients so overall all again the picture i having your head is that at
0:05:42	the end of the day you try to find school fashion
0:05:44	say a vector of coefficients and those vector of coefficients to find a material
0:05:51	okay now
0:05:52	historically the medical world sort of drove this kind of multi energy X ray work in in the medical world
0:05:57	the kinds of things you're looking at are the body
0:05:59	biological tissues
0:06:01	and the universe of biological kind of materials is relatively small mostly we look like water make we have phone
0:06:07	and it in that domain it we shown that the the the space of materials was well represented as two
0:06:12	dimensional
0:06:13	and uh the particular two-dimensional dimensional functions that were originally proposed where the photo electric and the constant functions
0:06:19	and so the the world kind of evolve along on this
0:06:22	two dimensional point
0:06:24	uh a and the choice of basis being you the focused on for electric and compton basis functions
0:06:28	and sometimes people choose another two basis functions that are based on their application in the medical world up P
0:06:34	sort of extreme of things like soft if you and bound
0:06:37	but the space is generally a two dimensional space and since they know that the functional space
0:06:41	uh the spinning space as dimensional
0:06:43	that leads to skinner's that
0:06:45	uh
0:06:45	only exploit a to energy spectra in the skinning so you sort of take measurements at two energies
0:06:51	you try to extract these coefficients for these two functions at that and a two dimensional space
0:06:56	this is propagated of the security don't where it's nominated by a dual energy uh machines trying to extract two
0:07:03	dimensional features and displaying them in a two dimensional space and trying to be cluster
0:07:07	but you think about the security domain main the space of uh materials is much greater than and the biological
0:07:12	space i mean it since S since anything you can think about putting into a suitcase
0:07:15	and so you have much less control about what goes into
0:07:18	the scanner
0:07:19	and that the universe materials as much greater
0:07:22	so perhaps it shouldn't be surprising that
0:07:24	you might expect that that them
0:07:26	a dimensionality space might increase
0:07:28	okay so what
0:07:30	so this is a what our hypothesis is is that we might wanna be interesting
0:07:34	a higher dimensional features a higher dimensional uh spanning space
0:07:38	and a perhaps different features than this photo electric and compton expansion set or the corresponding call
0:07:47	now there's an additional piece here and that's that rather than imaging the medical world is always focused on imaging
0:07:51	is in a
0:07:53	explosives detection were interested more in discrimination
0:07:56	it's not so much making the picture it's it's more or less saying look you have something that's gonna explode
0:08:00	in the bag
0:08:01	and so for that we're trying to get these features that we're gonna be using to do classification
0:08:06	now let me go back for a minute to the x-ray sensing so there's this process where the material bag
0:08:12	the body whatever is in the scanner
0:08:14	you're gonna take a bunch of these projection measurements and from that at the end of the day you're gonna
0:08:18	try to estimate these coefficients these a K and the expansion
0:08:22	uh expansion function
0:08:23	so at a high level we can kind of you the left hand side as the measurements projection from
0:08:28	and there's some nonlinear perhaps messy
0:08:31	why roll tomographic kind of measurement
0:08:33	and so there's some on linear transformation of the thing that you want these coefficients that define the material perhaps
0:08:39	spatially distributed across the line
0:08:42	so for our purposes where we're gonna take this abstract view of the tomographic problem you get measurements and from
0:08:47	those you're gonna try to extract the a case
0:08:50	yeah case or would fundamentally defined find material
0:08:53	okay through this equation where you this expansion
0:08:56	uh so if you change the basis expansion
0:08:59	when you try to estimate these a case you're changing the feature space
0:09:02	so the the viewpoint point we have is this is that choosing these basis is really the choice of the
0:09:07	classification space
0:09:09	in the work that we're gonna do we're gonna suppress the worry about demography we're gonna focus on the basis
0:09:14	choice
0:09:14	okay so that's this were
0:09:16	so here again no only a kind of describe that is yours a bunch of explosive materials class one
0:09:21	there's a bunch of non explosive potential confuse or is class zero
0:09:24	each of these explosive materials has some L A C associated with that an an explosive ones have some L
0:09:29	A C so there's a universe of L A C over here
0:09:32	a different universe of L A Cs over here
0:09:34	and what we're gonna wanna do is choose these expansion things uh a um
0:09:38	basis functions so that the coefficients
0:09:40	which are features help us to doing discrimination between the two classes
0:09:45	okay now the approach that we've take initially
0:09:47	is just to take a a a uh
0:09:49	a universe of the
0:09:51	uh we take a bunch of uh labeled samples some explosive some non explosive we discrete eyes them
0:09:57	and we stick them as columns in double major so we have the T N T yell A see the
0:10:01	honey L a C all the way up to the R X L A C so we have material one
0:10:05	this access
0:10:06	we have the uh uh the values of the curves of different energies coming down you along each column
0:10:11	and then we apply singular value decomposition analysis
0:10:14	what we're gonna do was look at these functions the singular value functions and different combinations of them as different
0:10:20	choices of a a uh is that we can extract features from
0:10:24	or we're gonna look at the singular values to tell us about the relative importance of these different feature
0:10:29	okay okay
0:10:32	so i
0:10:33	a experiments so experiment number one is
0:10:35	is
0:10:36	trying to make a move towards understanding the space of explosive materials both the dimensionality and sort of what it
0:10:41	might look like
0:10:42	so the first thing you can do well first let me take the experiment we took a for explosives fourteen
0:10:46	non explosive
0:10:48	we discrete eyes them do a hundred forty one energy level so each L A C is essentially now hundred
0:10:53	hundred forty one dimensional vector
0:10:54	and we stack them up in this matrix and we do S V D well i forgot to add we
0:10:58	we discrete tries them over the essentially the diagnostic range from ten K V up to a hundred fifty K
0:11:03	T V
0:11:04	that's typically the range the gets measured in an uh
0:11:07	ct T machine
0:11:08	uh and we apply the svd so over here i have the singular values i ordered as a function of
0:11:13	index
0:11:14	and again i go back to remember the conventional approach says that that's space materials is is well uh characterised
0:11:20	as a two dimensional subspace case so you should only need
0:11:24	two functions to span it
0:11:26	so if that was try to the svd analysis should show on them too large singular values and the rash
0:11:31	be insignificant
0:11:32	but as you can see there is one up here there's two three four five six seven you can see
0:11:37	that this thing isn't one or two and then dropping down to zero
0:11:40	it actually rolls off relatively slowly and it looks like based on this analysis they're significantly more than two
0:11:46	uh the to the feature space of at least explosive materials these are biological anymore more
0:11:51	so this was our first interesting result
0:11:53	that says that uh hmmm maybe we wanna use a larger than a two-dimensional space
0:11:57	the other thing is if if you think okay maybe a a well approximated by the first two singular value
0:12:02	those first to uh uh a a single functions corresponding to these first two singular values are shown here
0:12:07	and just for reference like put the the standard two functions the photo content functions down here
0:12:13	notice these are very smooth
0:12:14	to smooth functions to represent materials
0:12:17	the first two singular functions are not very smooth they have these discontinuities
0:12:21	but remember a lot of these materials can have things like these K had just discontinuity so this was a
0:12:25	another interesting observation
0:12:27	yeah i you might say is okay two functions to functions they look different but maybe they span the same
0:12:32	space but even that's not true
0:12:34	if you look at the angle between the subspace spanned by the first two singular functions and the subspace in
0:12:39	by the for constant functions
0:12:41	the between them sixty eight degree so it's not like they're the same functions
0:12:45	okay so there's a lot of difference here
0:12:49	or second experiment was to look at the effect of a feature dimensionality on classification for four
0:12:55	so we have the same setup as before the same a universe of explosives and non explosive the same discrete
0:13:00	as a nation the same stacking in the S P D
0:13:03	okay
0:13:03	and what we did here was we look you know order at a singular or uh values and the singular
0:13:08	vectors
0:13:09	we divided the data randomly into an eighty percent take training twenty percent test set
0:13:13	and then for a different numbers of features going in order uh according to the S P D
0:13:19	we trained a classifier and then tested the performance
0:13:21	a classifier so we only picks say one feature the first single or of uh function
0:13:26	use that
0:13:27	and we used one in two then we use one two one three one two three and four
0:13:31	and and re repeated this for different numbers of features and then we look at what happens to the classification
0:13:36	performance
0:13:37	as you increase the dimensionality of the space in which you represent B
0:13:41	okay okay
0:13:42	so you can see what happens here we and we did cross validation on that
0:13:45	so if you start with a one your performance is down here one into your performance down here as you
0:13:49	go to three an improve
0:13:51	or five six to jumps up and when you get to seven or eight it
0:13:53	it jumps up and then it seems to local law
0:13:56	so that this access is about sixty five percent correct classification here at eighty five percent correct classification
0:14:02	so this seems to suggest that there's some dramatic room for improvement by increasing the dimensionality of the feature space
0:14:09	that you represent materials in at we at least for explosives tech
0:14:12	in this is sort of counter the conventional wisdom which is always been focused on a two dimensional feature space
0:14:18	centered around for electric in comp
0:14:22	okay K third experiment so so those speeches were chosen in order so when we chose a a um two
0:14:27	features we chose the largest us to singular value
0:14:30	what we did next was we fixed the number of features i E the dimensionality of the space to be
0:14:34	to the same as the photo compton choice
0:14:36	but now we looked at different combinations of S uh a single or function
0:14:40	we tried to see what happened as we went through all the different pairs you could imagine so essentially we're
0:14:44	comparing different choices of two dimensional feature space
0:14:47	so the dimensionality is fix but we're looking over the different sub-spaces
0:14:52	okay so the same set same explosive saying non explosives same cross validation eighty twenty split i'll
0:14:58	so here are the choices that we may so this is singular functions one into one and three one and
0:15:03	four two one three two one four three and four
0:15:06	over here to the right is the performance of the photo compton choice this particular conventional two dimensional feature space
0:15:12	and we can see that the conventional two-dimensional a photocopy in choice of the two dimensional feature space gives you
0:15:18	about
0:15:18	sixty six percent correct classification
0:15:21	as you go through these different
0:15:22	pair choice lots of them are very similar but this one one and four seems to perform much better
0:15:27	so this seems to suggest that again even if you want to limit
0:15:31	yourself to a two dimensional feature space
0:15:33	that the conventional choice of photo comp and may not be the best and that there might be room and
0:15:37	a classification context
0:15:39	the optimize this choice to get a better classification of a particular
0:15:43	a folk it's classes of materials then a uh a has been carried over a traditionally from the matter
0:15:50	okay so our conclusions here in this initial work
0:15:53	is that well we study this problem of material classification from X ray based L C feature
0:15:59	okay
0:15:59	we took a learning based approach we used uh a actual curves of materials and we said what is the
0:16:04	data tell us about this we kind of took a first principles approach look at the dimensionality of the space
0:16:10	look at the choice of the space and tried to see whether there was room for improvement
0:16:14	our initial results seem to suggest that there's the per potential for improvement
0:16:17	both in terms of increasing the dimensionality
0:16:20	and then optimising the choice for any given dimension
0:16:23	so this was an initial work
0:16:25	we limited ourselves to svd analysis what we've been working on since the time we did this
0:16:29	is trying to break out of that S P D paradigm "'cause" there's nothing that says that the S D
0:16:34	uh um
0:16:35	svd based singular functions are the right functions to represent things
0:16:39	and so we've been sort of trying to a a push this for
0:16:43	thank you
0:16:56	um
0:16:58	you talk about
0:17:00	right
0:17:00	class
0:17:01	patient
0:17:02	i would have thought that you know
0:17:05	or
0:17:06	we you false alarm
0:17:08	problem
0:17:09	section probably not of
0:17:10	you for
0:17:11	i mean
0:17:12	in
0:17:12	classifying something
0:17:14	close
0:17:15	is probably not
0:17:17	a missing
0:17:19	yeah there's lots of choices you can do a and and the
0:17:22	working up some of that stuff i mean we've done some additional work in doing things
0:17:27	a a so so this pick some particular classifier an svm based when your for kernel classifier and then looks
0:17:33	at correct classification for that class of part we've also done work
0:17:36	and just basically what's the uh
0:17:38	the choice of things that sort of a
0:17:40	as the most information
0:17:42	so one way you can measure that is
0:17:43	for example a area under the roc
0:17:45	oh the things you can do or you can fix false alarm rates and look at P B we've been
0:17:49	plane with all of that so you i mean you're right i agree with you
0:17:53	is just the plumbing
0:18:01	it's the second to last Y
0:18:04	and the one that know the that yeah yeah the but one no one for seems to work a lot
0:18:09	better than the others
0:18:10	yeah is the fact that that's that an outlier is that in into the result three
0:18:14	not at all
0:18:15	i the
0:18:16	first of all the the svd features
0:18:18	you you know the single functions you get are are are physically but
0:18:22	so there's nothing i mean we've looked at them there you use all the first two there's nothing the jumps
0:18:26	out that says these look like
0:18:27	certain materials for example
0:18:29	so no i would say nothing into about that result
0:18:32	to me
0:18:34	yeah
0:18:40	composition position on
0:18:43	exponential decaying function
0:18:45	am i correct
0:18:46	the the
0:18:48	on on the functions they're not necessarily exponentially okay
0:18:51	yeah but but the yeah the non to have generally have the proper okay
0:18:55	if you thought of utilizing other functions because some of the ones you showed have these we use an this
0:19:00	got do it is that not well express
0:19:03	in that that function
0:19:05	yeah maybe a misunderstanding your question i mean the the those curves are what they are for materials what we
0:19:10	did was we stack them up and did in S P D so the singular functions of that universe or
0:19:14	just gonna be what they are they're not parametric be
0:19:16	they are not being parametrically represented a i thought that i thought you were a but a metric known no
0:19:21	we present a there it's a discrete eyes world so they just turn out to be what they are we
0:19:25	we
0:19:26	well i i don't where i'm running a i'm i'm pass can time we'll we'll talk of

A LEARNING-BASED APPROACH TO EXPLOSIVES DETECTION USING MULTI-ENERGY X-RAY COMPUTED TOMOGRAPHY

Machine Learning Methods and Applications

Přednášející: William Clem Karl, Autoři: Limor Eger, Boston University, United States; Synho Do, Massachusetts General Hospital, United States; Prakash Ishwar, William Clem Karl, Boston University, United States; Homer Pien, Massachusetts General Hospital, United States