Hybrid Feature-Bad Diffeomorphic Registration for Tumor Tracking in2-D Liver Ultrasound Images Amalia Cifor*,Laurent Risr,Daniel Chung,Ewan M.Anderson,and Julia A.Schnabel,Member,IEEE
Abstract—Real-time ultrasound image acquisition is a pivotal resource in the medical community,in spite of its limited image quality.This pos challenges to image registration methods,par-ticularly to tho driven by intensity values.We address the dif-ficulties in a novel diffeomorphic registration technique for tumor tracking in ries of2-D liver ultrasound.Our method has two main characteristics:1)each voxel is described by three image features:intensity,local pha,and pha congruency;2)we com-pute a t of forces from either local information(Demons-type of forces),or spatial correspondences supplied by a block-matching scheme,from each image feature.A family of update deforma-tionfields which are defined by the forces,and inform upon the local or regional contribution of each image feature are then com-pod to form thefinal transformation.The method is diffeomor-phic,which ensures the invertibility of deformations.The quali-tative and quantitative results yielded by both synthetic and real clinical data show the suitability of our method for the application at hand.
Index Terms—Block-matching,diffeomorphic registration, tumor tracking,ultrasound.
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I.I NTRODUCTION
U LTRASOUND(US)imaging enjoys much popularity in the medical community,owing to its low cost and real-time image acquisition.Such properties are particularly desir-able in image guided interventions,and a wide range of appli-cations involving movement of organs,whether as a result of respiratory,cardiac,fetal or general patient motion.While -rial imaging of moving organs is more feasibly acquired with US than with magnetic resonance imaging(MRI)or computed
Manuscript received January29,2013;revid April25,2013;accepted April30,2013.Date of publication May07,2013;date of current version August28,2013.This publication aris from rearch funded by the Well-come/EPSRC Centre of Excellence in Medical Engineering-Personalid Healthcare(WT088877/Z/09/Z),the Cancer Rearch UK/EPSRC Oxford Cancer Imaging Centre,and the John Fell Oxford University Press(OUP) Rearch Fund.L.Risr would like to thank INSMI-CNRS for the rearch funding.Asterisk indicates corresponding author.
*A.Cifor is with the Institute of Biomedical Engineering,Department of Engineering Science,University of Oxford,OX37DQ Oxford,U.K.(e-mail: amalia.ac.uk).
L.Risr is with CNRS,Toulou Mathematics Institute,Paul Sabatier Uni-versity,31400Toulou,France(e-mail:laurent.).
D.Chung is with the Institute of Biomedical Engineering,Department of Engineering Science,University of Oxford,OX37DQ Oxford,U.K.,and also with the Department of Radiology,Churchill Hospital,OX37LE Oxford,U.K. (e-mail:daniel.chung@doctors.uk).
E.M.Anderson is with the Department of Radiology,Churchill Hospital, OX37LE Oxford,U.K.(e-mail:ewan.anderson@orh.nhs.uk).
J.A.Schnabel is with the Institute of Biomedical Engineering,Department of Engineering Science,University of Oxford,OX37DQ Oxford,U.K.(e-mail: julia.ac.uk).
Digital Object Identifier10.1109/TMI.2013.2262055tomography(CT),the output images po various challenges to the traditional intensity-bad registration methods.The main reason is that the assumptions about noi and artefacts in US are usually different from tho characteristic to MRI/CT.US images generally have a low signal-to-noi ratio and contrast. Therefore,some boundaries(of tumors in particular)may be hard to distinguish.Notable US registration techniques fall into the following categories:1)methods which u a more adequate similarity measure that takes into account the US image forma-tion and noi ,the bivariate correlation ratio(BCR) [1],[2]);2)methods which rely on identified anatom-ical ,vesls[3],liver surface[4]);3)hybri
d ap-proaches derived from combined image features like:gradient [5],vector of image attributes[6],local pha[7]–[9],pha congruency[10],etc.;4)approaches which u MRI/CT com-plementary to US ,[3],[11]).
In this paper,we address the problem of tumor tracking in time-ries of2-D US images of patients with liver cancer, aimed at a personalized US-bad targeted drug-delivery ap-plication using therapeutic US for targeted drug relea.The accurate and robust tracking of the tumors during breathing is one of the challenges that we need to address,in order to provide the clinicians with the necessary feedback to deliver therapeutic US to the tumor targets.Therefore,in addition to the above general imaging issues,the registration of US images in the application at hand needs to also tackle particular patient-specific challenges.The stem primarily from the variability of tumor location and breathing motion.The rib cage limits the acoustic window for liver US image acquisition, since the bones block the sound wave and conquently cast shadows when situated on the direct trajectory of the beam. The output images exhibit changes in intensity contrast across frames,and occluded anatomical structures.Moreover,since the liver moves due to breathing,time-ries of2-D liver US images further suffer from an aperture problem:they depict a moving3-D object using a quence of2-D images.This leads to the appearance of topological changes as the anatomical structures slide
in and out of the focus plane.The issues are noticeable for example in the two US frames in Fig.1.The outlined tumor(top)exhibits changes in intensity contrast as it moves towards the shadowed region to the left,whereas the appearance of the outlined vesl(middle-bottom)is different in the two images.
We propo a novel registration framework that handles both the US imaging challenges and the demands of our tumor tracking application.Since we do not have at our disposal optical tracking tools for the transducer[12]or breathing motion models[13],[14]to aid the tumor tracking,we need一建准考证打印时间
0278-0062©2013IEEE
Fig.1.Two US frames with overlaid gmented tumor(top)and vesl (middle-bottom)from Target(blue)and Source(yellow)images.
to rely entirely on the image data.Noting the general lack of accuracy of intensity-bad registration of US images,we characterize each voxel by a t of feature values:intensity, local pha[15]and pha congruency[16],instead of intensity alone.The pha-bad descriptors are particularly suitable for US ,[8])becau they are contrast invariant and inform upon the structural features prent in the images. Although structures may depict different topology as a result of the out-of-plane movement,we wish to match them ac-curately,without penalizing their ,by over-fitting the deformation parameters,or introducing foldings).While various deformation models can be ud to solve this problem, here we adopt a diffeomorphic one with large smoothing kernels,due to the following desirable elements of robustness: 1)diffeomorphic models yield physically plausible deforma-tions and the large smoothing kernels prevent the occurrence of additional topological changes;2)tumors are adequately registered,regardless of the vesls’change in shape due to the out-of-plane motion;and3)such models have robust properties in the prence of abrupt changes in topology.The novelty of our method lies in building a hybrid diffeomorphic transforma-tion that fus the update deformationfields obtained from a family of forces,carrying eith
er voxel-wi local information (Demons-type of forces)or regional spatial correspondences estimated with a block-matching scheme,from each feature. We propo aflexible registration paradigm that allows tofind an equilibrium between different similarity measures(SSD in Demons forces and NCC in block-matching),managing the convergence of the different updates independently,while encoding the deformations in a single stationary velocityfield. This prents a new approach in the diffeomorphic registration field.
We call this method Hybrid Feature-bad Diffeomorphic (HFD)registration.Our method is mainly inspired by the diffeomorphic Log-Demons registration framework[17],and [18].It is also similar to our earlier approach prented in[19]. However,instead of using the image features in a multi-channel Log-Demons framework as in[19]and[6]—in which the question is how to weight the derived forces—,here we u them in a complementary way by estimating updatefields from each feature independently.The updates are then compod into afinal diffeomorphic transformation.Conquently,the contribution of features is variable,and frees us from the need to explicitly weight the ,as in[19]).This makes HFD substantially different from our previous method[19]. The content of this paper is structured as follows.Wefirst give an overview of registration approaches designed in the log-do-main,and point out how our method differs from tho.Then we d
etail our method in Section II.The results are prented in Section III where we show the performance of our technique on synthetic and real datats,as well as a robustness analysis with respect to the scale parameters(Section III-C)and the conver-gence of our technique(Section III-D).We clo the paper with some concluding remarks.惠特尼休斯顿好听的歌
A.Registration Techniques in the Log-Domain Diffeomorphic registration is an esntial tool in compu-tational anatomy[17],[20],[21],[18],[22]–[24].Its interest mainly relies on the inver consistency of diffeomorphic transformations,and,for some diffeomorphic algorithms,the interesting properties of the estimated deformationflows.This can facilitate the computation of statistics from the deforma-tions,and morphometric measures that account for anatomical and functional variability in inter-or intra-subject populations. We note two major trends in modelling the diffeomorphic deformations,bad on the type of parameterization ud.One category of methods encode the deformations in time-varying velocityfi,the Large Deformation Diffeomorphic Metric Mapping(LDDMM)[25].Diffeomorphism is given by the shortestflow estimated between the input images.While such parameterization has a strong mathematical background, the integration of velocities over time has high computational demands.A cond category of methods makes u of stationary velocityfields[17],[20],[18]and requires much reduced time and memory consumption,in ge
neral,for a similar registration accuracy.We are particularly interested in the Log-Demons method[17],which is an extension of[26],where the entire spatial transformation is reprented in the log-domain through the exponential map of smooth stationary vectorfields,bad on the obrvation that the diffeomorphism forms a Lie group. Regardless of the type of parameterization ud,both LDDMM-and Demons-like techniques adopt a similar regis-tration formalism:they minimize a functional that consists of an image similarity measure and a regularization term which ensures that the solution is numerically stable.Regularization using Gaussian kernels is the common choice.We note that a global regularization of the den deformationfield does not optimally capture local characteristics of the deformation.This shortcoming can be overcome using weighting functions for a locally adapted smoothing[27],[28],that accommodate small-and large-scale structures alike.Geometrically constrained forces derived from distance measures of point ts[29],[23], [30]are other interesting solutions.
Emergent alternatives to den deformationfields are methods that estimate local affine transformations for prede-fined regions,and then globally regularize them.Such are,for instance,the fast and efficient poly-affine transforms estimated in the log-domain[31],[32].In order to register small struc-tures,Taquet et al.[31]rely on the image structure tensor to define the location of anchor points in regions of interest.A
CIFOR et al.:HYBRID FEATURE-BASED DIFFEOMORPHIC REGISTRATION FOR TUMOR TRACKING IN2-D LIVER ULTRASOUND IMAGES1649
prior matching probability estimated from a block-matching step,together with the t of best matching points are then supplied to an expectation-maximization iterative clost point optimization,over veral scales.Locally affine transforms estimated with the block-matching technique in[33],and regu-larized in the log-domain are also prented in[34]and[35]. Our work is clo in spirit to the poly-affine transforms esti-mated in the log-domain[31],[32]and tho relying on point distances within the Log-Demons framework[29],[30].The former presume a locally affine behavior of the deformation. While such an assumption is suitable for brain MRI,the nature of liver US images,the prence of pathologies and the soft tissue deformation,makes it less adequate for the application at hand.Moreover,our technique fully integrates into the dif-feomorphic framework the computation of forces,and con-quently that of spatial correspondences using block-matching. We estimate the local or regional forces at each iteration inde-pendently for each feature.This contrasts the work of Lu et al.
[30],where the block-matching step is performed a priori tofind pairs of corresponding salient points in MR volumes,which are afterwards supplied to the Log-Demons framework.
II.M ETHOD
The method consists of two main parts:feature estimation, and diffeomorphic registration bad on the features.We char-acterize each voxel by three features:intensity,local pha[15] and pha congruency[16].Then,we compute two types of forces from each feature map:1)locally estimated Demons-like forces using(3)and2)spatially estimated forces from block-matching correspondences using(11).We denote by the family of the forces obtained from the three feature maps.The forces are built and smoothed at given scales within a diffeomorphic framework.Thefinal deformation is the result of the contribution of each smooth updatefield yielded by the individual force.
A.Diffeomorphic Registration Framework
1)Variational Formulation:Our diffeomorphic registration framework is bad on a variational formulation.This formula-tion prents some similarities with the variational techniques of[36]and[37],but in a diffeomorphic context which ensures the inver consistency of the deformations.Its implementation is clo to that of the algorithms of[17]and[18]but we u a t of forces to register the images,and a different paradigm to tune the algorithm parameters.Our algorithm is also inspired by[38] as it is an iconic feature-bad ,it can explicitly u geo
metrical distances between paired blocks in addition to voxel-bad similarities to register the images.
Let be a source image registered to a target image
in the domain.Note that in the rest of this paper and are general notations for any of the image features. As in other diffeomorphic registration algorithms[17],[20], [18],we indirectly encode the displacementfields using time-dependent diffeomorphic transformations
,defined by theflow of stationary velocityfields using
,where.A key advan-tage of using stationary velocityfields,instead of time-depen-dent ones,is that they allow to efficiently compute using the scaling-and-squaring method of[39].Using diffeomorphic deformations also allows to ensure the invertibility of deforma-tions and to very easily compute their inver.In the remaining parts of the paper,we denote,the exponen-tial map of,and u to denote the transformation of toward using.Conveniently,integrating instead of allows to compute the inver transformation of. As a conquence,refers to the transformation of toward using.The deformations allow to compute the forces prented in the next ctions.
We consider the optimal velocityfield registering to as the obtained at convergence of
(1) where the are vectorfields encoding registration forces,and .refers to the convolution with a Gaussian kernel of standard deviation.Note that the velocityfield evolves according to a virtual time but we always compute its expo-nential forfixed values of,so is stationary when integrated. Equation(1)pushes toward according to the forces smoothed by.Convergence is reached when an equilib-rium is found between all the smoothed forces.Note that in each forcefield,the deformations are computed using exponen-tials of.It is therefore straightforward to make the algorithm symmetric by using the smoothed forcefields
in addition to. Note that we empirically asss the convergence of our algo-rithm in Section III-D,keeping as an open question the condi-tions which should be respected for the convergence.
成都软件培训机构2)Implementation:In this ction,we propo a strategy to solve(1).We discretize the problem using an explicitfinite differences scheme
where is the discretization step of the time and .At each time step,the velocityfield is then updated using the smoothed registration forces as follows:
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(2) After initializing the stationary velocityfield to0,the reg-istration algorithm is given by
repeat
{Compute the deformation}
Compute
shootout
{Update with the smoothed forces}
Initialize as equal to
for to do
Compute
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Smooth with
Compute
end for
Increment
until Convergence
In practice,we update at each iteration,without storing all its updated values.It is interesting to note that our algorithm prents similarities with the algorithms of[18]and[17].It is indeed clo to[17],if the demon forces of[26]and[17]are exclusively ud in,defined by the opticalflow update
(3) where controls the influence of image noi,and the spatial uncertainty.The main difference is that no diffusion regularization(smoothing the directly)is performed in our scheme.In addition,velocityfields updates are performed using the sum of vectorfields instead of the Baker–Campbell–Haus-dorff(BCH)approximation of[17].This is theoretically penalizing,as discusd in[17],but this strategy has been successfully adopted in[40].Our algorithm is more similar to [18]wherefluid regularization(smoothing the updates of) is also performed.In practice,the main differences between [17],[18]and our algorithm are that we u a t of forces instead of one derived from[25],and a different paradigm to tune the algorithm parameters.An analogy with the methods of [21],[41],[42]can also be made,as the techniques encode diffeomorphic deformations as the composition of veral dif-feomorphisms being smoothed with different Gaussian kernels. Contrary to[21],[41],[42],we encode here the deformations using a single velocityfield and the different updatefields reprent a family of forces.
3)Parameter Interpretation and Tuning:In this ction,we explain the paradigm that we u to parameterize and of our algorithm,to make their tuning intuitive or automated.This strategy is the same as the one in[21],but in the context of the registration algorithm propod in this paper.
The parameter reprents the scale at which image fea-tures are deformed,so features of a smaller scale cannot be captured and features of a larger scales might be captured with non-natural transformations due to the little regularization.If an update vectorfield contains significant contributions which are sparly distributed in space,the choice of the also al-lows to control how the contributions are interpolated.In the latter ca,using a Kriging estimator,like in[31],would also be of interest.
We tune the so that(1)each vectorfield has the same maximum amplitude at thefirst iteration of the algo-rithm,and(2)the maximum amplitude of
at thefirst iteration of the algorithm is equal to a valuefixed by the ur,typically about one voxel.This technique,also inspired by[21],ensures that the different smoothed
forces have similar contributions in the evolution of.Note that an adjustment of Fig.2.Pha-bad features estimated from Target image in Fig.1:(a)local pha;(b)pha congruency.
the may be addresd at the expen of more ur interven-tions,in order to put more or less weight on the different forces. Note also that although all have a similar influence at thefirst iteration of the algorithm,they generally converge at different speeds after each iteration.At the algorithm conver-ge
nce,some have therefore higher amplitudes than others.
B.Set of Image Features
Speckle appears as textured pattern in US images.This pat-tern tends to be correlated in successive images that depict little movement[43],which means that intensity may carry valu-able information about tissue properties.Instead of relying only on intensity values in our registration framework,we compute two additional structural features for each voxel:the local pha [15]and pha congruency[16]measures.Local pha reveals the structural features prent in the images,whereas the pha congruency is a descriptor of such features’significance.We lected them owing to their contrast invariance and for of-fering good structural localization.We note that other types of image-driven features can be equally ud with our technique, dependent on the application.We showed previously that using such a t of features produced more robust registration results, compared to using the features individually[19].Fig.2shows the local pha and pha congruency feature maps of Target image displayed in Fig.1.
We estimate the local pha using the monogenic signal[15]. The monogenic signal yields three local image properties:local pha,local energy and local orientation.It is a2-D general-ization of the
analytic signal,that us the Riesz transform in-stead of the common Hilbert transform of a1-D signal.The monogenic signal is reprented by an even and an odd compo-nent.The even one,,is obtained byfiltering the image with an isotropic bandpassfilter.We cho the log-Gaborfilter of a given scale,denoted here by
(4) We note that other kernels,such as Cauchy or difference of Gaussian,could be equally ud.
The odd component is defined by the convolution of with the Riesz transform,who kernels are[44]
(5)
(6)
CIFOR et al.:HYBRID FEATURE-BASED DIFFEOMORPHIC REGISTRATION FOR TUMOR TRACKING IN2-D LIVER ULTRASOUND IMAGES
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Fig.3.Block-matching scheme shown on intensity feature maps of a Source (left)and Target(right)image.
Finally,the local pha is the angle at point,derived from the two components
vogue是什么意思(7) and the local energy follows as:
(8) The choice of the ,wavelength of thefilter)at which structural features are lected is nontrivial.A small scale tends to characterize the speckle,whereas a scale too large may leave out important anatomical ,the vesls).The scale we considered to be a good threshold in this spectrum was chon empirically.
Pha congruency is the result of a joined contribution of local pha and local energy,derived from band-pasd images with log-Gaborfilters of scales.Kovesi[16]defines it as
(9) where
软驱英文is the pha deviation with respect to the mean pha,and is the local energy defined in(8).is a weighting factor for frequency spread,is a noi estimator,and the operator denotes the lection of positive values only.
C.Block-Matching Schemechinked out
We complement the t of image features prented above with the t of spatial correspondences established by a block-matching scheme.In this regard,the blocks are additional de-scriptors of the local information contained in them.Unlike in our previous approach[19],where the correspondences
were determined from the input vector of all three image features con-sidered simultaneously,here we estimatefields of displacement vectors from each feature independently.This has a dual signif-icance:it allows us to decouple the contribution of each feature; and facilitates the u of more robust similarity measures than the norm of all three features.
Fig.3illustrates the block-matching scheme on the intensity feature of two US images.We divide the source image feature into a t of regular blocks,large enough to capture local struc-tural information,rather than the speckle pattern.For each such block(yellow block in Source),we look for the most similar block(yellow)in,that yields the highest normalized cross correlation,compared to other candidate blocks(green)
(10) where and are the average feature values of blocks and,respectively,and and are voxels in corresponding blocks.We then define a displacement vector between the cen-tres of the matched blocks.The t of all such vectors forms a spar displacementfield that carries informa-tion about the spatial extent of the corresponding input feature. Thisfield constitutes the spatially-derived force of the respec-tive feature
(11) The block-matching scheme produces outliers that a robust ,like the least-trim
med squared regression adopted in[33])needs to handle adequately.Commowick et al.[34]weight the displacements with the amount supplied by the similarity measure,as a means to increa the confi-dence of the matching quality.We circumvent the generation of large outliers,by restricting the arch for to a small spatial neighborhood around each.Typical values for block and neighborhood sizes are[99,2020].Moreover,we threshold the feature blocks bad on their variance,such that only tho blocks containing relevant structural information (e.g.,boundaries of anatomical structures)are considered. Low variances characterize homogeneous regions,unlikely to contribute to good matches.We cho different values of the variance threshold per input ,100for intensity,300 for pha congruency,and500for local pha).The discrepan-cies introduced by mismatched correspondences are attenuated by Gaussian smoothing.
III.R ESULTS
A.Synthetic Example
We motivate the construction of our hybrid update deforma-tionfield using the synthetic example prented in Fig.4.Source (a)and Target(b)reprent two US frames from a -quence,which contain a black shadow on top,a tumor who shape changes from the darker circle in(a)to an oval in(b),and
another larger and brighter structure on the right-hand side.The registration results using the classic Log-Demons are shown in (c)and(d).Log-Demons inappropriately pushes the tumor to-wards the shadow on top.In contrast,our method,HFD,is able to adequately register all three structures in(e)using the esti-mated hybrid deformationfield(f).Since the grid size in(f) does not allow to visually asss the invertibility of the deforma-tion which is particularly sharp,we also measured the Jacobian determinant which is positive throughout.Invertible defor-mations are therefore obtained everywhere.Only the intensity values were lected as input features in this synthetic example.
