Int J CARSDOI 10.1007/s11548-013-0947-y

ORIGINAL ARTICLE

Deformable image registration for temporal subtraction of chestradiographs

Min Li · Edward Castillo · Hong-Yan Luo ·Xiao-Lin Zheng · Richard Castillo ·Dmitriy Meshkov · Thomas Guerrero

Received: 1 July 2013 / Accepted: 11 September 2013© CARS 2013

AbstractPurpose Temporal subtraction images constructed fromimage registration can facilitate the visualization of patho-logic changes. In this study, we propose a deformable imageregistration (DIR) framework for creating temporal subtrac-tion images of chest radiographs.Methods We developed a DIR methodology using two dif-ferent image similarity metrics, varying flow (VF) and com-pressible flow (CF). The proposed registration method con-sists of block matching, filtering, and interpolation. Specif-ically, corresponding point pairs between reference and tar-get images are initially determined by minimizing a nonlin-ear least squares formulation using grid-searching optimiza-tion. A two-step filtering process, including least median ofsquares filtering and backward matching filtering, is thenapplied to the estimated point matches in order to removeerroneous matches. Finally, moving least squares is used to

M. Li · H.-Y. Luo · X.-L. ZhengBioengineering College, Chongqing University,Chongqing 400030, China

M. Li · E. Castillo (B) · D. Meshkov · T. GuerreroDepartment of Radiation Oncology, The University of Texas MDAnderson Cancer Center, 1515 Holcombe Blvd.,Houston, TX 77030, USAe-mail: ecastillo3@mdanderson.org

E. CastilloDepartment of Computational and Applied Mathematics,Rice University, Houston, TX 77251, USA

R. CastilloDepartment of Radiation Physics, The University of Texas MDAnderson Cancer Center, Houston, TX 77030, USA

T. GuerreroThe University of Texas Graduate School of Biomedical Sciencesat Houston, Houston, TX 77030, USA

generate a full displacement field from the filtered point pairs.Results We applied the proposed DIR method to 10 pairs ofclinical chest radiographs and compared it with the demonsand B-spline algorithms using the five-point rating scoremethod. The average quality scores were 2.7 and 3 for thedemons and B-spline methods, but 3.5 and 4.1 for the VFand CF methods. In addition, subtraction images improvedthe visual perception of abnormalities in the lungs by usingthe proposed method.Conclusion The VF and CF models achieved a higher accu-racy than the demons and the B-spline methods. Furthermore,the proposed methodology demonstrated the ability to createclinically acceptable temporal subtraction chest radiographsthat enhance interval changes and can be used to detect abnor-malities such as non-small cell lung cancer.

Keywords Chest radiograph · Image registration ·Temporal subtraction · Intensity variation

Introduction

Chest radiography has been widely and frequently used todetect and diagnose lung cancer [1]. By comparing chest radi-ographs acquired at different times, radiologists can detectabnormalities and their changes [2]. One technique that mayimprove the visual assessment of chest radiographs is tempo-ral image subtraction, which enhances pathological changeby subtracting the previous image from the current image[3]. In a good temporal subtraction image, the areas with-out change appear uniformly gray and the regions indi-cating interval change stand out from this uniform back-ground [4]. However, the presence of unavoidable artifactscan obscure pathologic change in images created using direct

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temporal subtraction, thereby making diagnosis difficult.Image registration, whose goal is to establish a point-to-point correspondence between the reference image and targetimage through an accurate spatial transformation, can reducethe artifacts and improve the quality of temporal subtrac-tion images. However, the registration of chest radiographs ischallenging because of the (1) overlap of different structuresby X-ray projection, (2) dynamic nature of thoracic anatomy,and (3) variation of photographic conditions between currentand previous image acquisitions, such as various patient posi-tions and different dose-induced radiograph qualities. Thus,purely rigid methods with simple translation and rotation arenot applicable for chest radiograph registration [5]. Instead,deformable image registration (DIR) methods are increas-ingly used to establish point correspondence between chestradiographs taken on different days.

Most DIR methods have been designed for magneticresonance (MR) or computed tomography (CT) images,and many have had encouraging results. For instance, Yinet al. [6] proposed a non-rigid image registration approachin which the sum of squared intensity difference was used asthe similarity criterion; this method was successfully appliedto align CT images of the lungs. Gorbunova et al. [7] incor-porated the principle of preserving total lung mass into astandard image registration framework consisting of a globalaffine and several B-spline transformations. Castillo et al. [8]proposed a DIR method utilizing the compressible nature ofthe lungs and obtained a high spatial accuracy of lung defor-mation.

Very few publications have reported the registrationof chest radiographs. Kano et al. [9] proposed an algo-rithm based on performing local matching with the cross-correlation method to determine shift values, the distributionof which is subsequently fitted by a two-dimensional poly-nomial function; however, the ribcage edge must be detected

prior to registration. The approach has been demonstratedto produce reasonable results [10–12]. Inaba et al. [13] pre-sented a global registration method based on a rigid trans-formation that was followed by local matching. Yu et al.[1] improved this scheme by employing mutual informationfor global matching and obtained reasonable results. Loeckxet al. [3] described the deformation field using a B-splineparameterization where the spline coefficients are deter-mined by a statistical model and training data obtained frommanual alignment. Guo et al. [14] aligned the chest radi-ographs using a thin-plate spline parameterization and estab-lishing the correspondence of the ribs. However, rib move-ment is much simpler than that of soft tissues and may notbe able to represent the complicated deformation of thoracicorgans.

The purpose of this study is to construct clinically usefultemporal subtraction images using an effective DIR method.We present a block-matching framework based on robust sta-tistical filtering and two image intensity models: (i) com-pressible flow (CF), which is derived from the property ofmass conservation; (ii) varying flow (VF), which is an exten-sion of the sum of squared difference (SSD) approach [15].Because the two intensity models allow for image intensityvariation during registration, artifacts introduced by constantintensity modeling are reduced. Therefore, the resulting tem-poral subtraction images of chest radiographs derived fromour proposed approach are better suited to produce subtrac-tion images of acceptable clinical quality.

Methods

The overall framework of the registration algorithms is shownin Fig. 1. The algorithm is divided into three main steps: block

Fig. 1 The framework of the proposed registration algorithms

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matching, filtering, and interpolation. First, the referenceimage is sampled to generate a uniformly coarse image grid.Exhaustive grid searching (block matching) is then appliedto each location on the coarse grid to find the best corre-spondence within the target image according to an imageintensity model. The result is an estimated point match foreach location on the coarse reference image grid. However,these estimates are not guaranteed to be spatially accurate.Therefore, a two-step filtering scheme is applied to removeinaccurate matches. Finally, the moving least squares (MLS)method is used to interpolate filtered point matches and pro-duce a full displacement field.

Block matching

Registration is the process of mapping points in the referenceimage to corresponding positions within the target image.Because point motion can be described in terms of a displace-ment vector, registration can also be described as the processof determining optimal displacement vectors that minimizea given cost function or image similarity criterion. In thisstudy, we propose two different cost functions to minimizethe differences between temporal chest radiographs.

Compressible flow (CF) intensity model

The CF intensity model is derived from a mass conservingassumption and has been successfully applied to thoracicCT image registration [8,16,17]. Given an image density (orintensity) function ρt (x(t), t), t ∈ [0, 1] defined by a tempo-ral sequence of images, the mass conservation assumption isdefined in terms of the flow velocity v (see [8,18] for details):

ρt + ∇ρ · v + ρdiv(v) = 0. (1)

Researchers have developed several DIR methods basedon Eq. (1) [8,16,17,19,20], but typically these methodsrequire numerical approximations to the spatial and temporalderivatives of ρ. However, the approximations are prone toerrors introduced by image noise and large-magnitude defor-mation. In order to avoid image derivative approximations,we employ the integrated form of Eq. (1):

I1(x + D(x))− I0(x)e−div(D(x)) = 0, (2)

where I0(x) and I1(x) are the reference and target images,respectively, and D(x) is the displacement field. Eq. (2) canbe reformulated as an image similarity metric describing themotion of a single voxel (as derived in [16]):

mind

R(d)= 1

2

∑

xi ∈Nr (x)

[ln I1(xi +d)−ln I0(xi )+ div(d)]2,

(3)

where it can be shown that div(d) = − 1|Nr (x)|

∑xi ∈Nr (x)

[ln I1(xi + d)− ln I0(xi )] is the optimal approximation forany fixed value of displacement vector d. The voxel neigh-borhood Nr (x) is centered on x with radius r and is oftenreferred to as the “matching window.” Thus, the displace-ment vector for any point x is described as the solution to thenonlinear least squares problem (3).

Varying flow (VF) intensity model

The SSD intensity model is a simple but commonly usedtool that assumed corresponding image locations have thesame intensity value. This assumption, though effective fora wide range of image data [15] is inappropriate for the reg-istration of thoracic images where density changes neces-sarily imply intensity value variation. Instead, we propose amodified SSD formulation to accommodate varying inten-sity values by introducing a compensation variable ψ . Ourmodified SSD formulation, referred to as the VF intensitymodel, describes the motion of a single voxel as the solutionto the following nonlinear least squares problem:

mind,ψ

R(d, ψ) = 1

2

∑

xi ∈Nr (x)

[I1(xi + d)− I0(xi )+ ψ]2. (4)

However, similar to the derivation of the CF model, for anyfixed d, it can easily be shown that the optimal value of ψ isexpressed as:

ψ = − 1

|Nr (x)|∑

xi ∈Nr (x)

[I1(xi + d)− I0(xi )]. (5)

Block-matching implementation

Since Eqs. (3) and (4) are defined solely by the unknowndisplacement vector, exhaustive grid-searching optimizationcan be employed to find the optimal displacement vector.The optimal value is guaranteed to be found since the costfunction is evaluated at every gird location within a prede-fined searching window. This process is often referred to asblock matching. In order to reduce the computation cost ofthe exhaustive search, the block-matching displacements areonly computed for locations positioned on a coarse imagegrid.

Filtering the block-matching estimated displacements

For a single point in the reference image, a grid-searchingscheme is used to approximate the underlying deformationby identifying a displacement vector optimal in terms of theintensity model. However, a searching window that is notlarge enough to cover the correct displacement vector mayresult in an erroneous estimate. Even if the searching windowis large enough to capture the true displacement vector, the

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Fig. 2 Flow chart of the LMS filtering process

numerical minimizer to the intensity model does not guaran-tee to be the most spatially accurate vector. These problemsnecessitate an efficient approach for eliminating the erro-neous matches from all the block-matching generated pointpairs. To get rid of erroneous point matches, we use a two-stepfiltering strategy consisting of the least median of squares(LMS) filter defined in [16] and a backward matching filter.

LMS filter

Let xi (i = 1, 2, . . . , N ) be N point locations in the refer-ence image with corresponding estimated mapped positionyi (i = 1, 2, . . . , N ) in the target image. The LMS fit of aparameterized function f is determined by minimizing themedian of the squared residuals:

minq

mediani

‖ f (xi ,q)− yi‖, (6)

where q is the parameter vector associated with the trans-formation function f . An affine function is employed as thetransformation function for the LMS process and is definedas:

f (x; q) =[

q1 q2

q3 q4

]x +

[q5

q6

]. (7)

Although the ordinary least squares estimator is typicallyused to determine the fitting function, it is strongly influencedby outlier points. Even one corrupt point can result in anarbitrarily large estimator error. LMS regression, which isrobust for data sets containing as high as 50 % outliers, ismuch more suitable.

Once the block matches are obtained, the LMS filter isperformed as a first-step filtering procedure. The LMS filteris defined by the following forward-search iterative process(Fig. 2).

1. The affine fitting in Eq. (7) is used as the transformationfunction, and the whole data set of N point matches isused to initialize the n (n = 6) parameters q.

2. Compute residuals for all point matches. Fitting parame-ters are re-estimated using n point matches that corre-spond to the n smallest residuals.

3. Apply the new fitting function with the re-estimated para-meters to all point matches. Assign n +1 point pairs withthe smallest residuals into a new subset and use thesepoint pairs to update the fitting parameters again.

4. Repeat step 3. Each repeating procedure produces a newsubset containing one more point match than the previoussubset, an updated fitting function, and a set of residualsfor all point matches. The repeating procedures do notstop until all N point matches have been put into a finalsubset.

5. Compare the median of squares for each subset. The sub-set that has the smallest median is taken as the filteredresult.

Backward matching filter

According to the direction of point movement, image regis-tration can be (1) forward matching or (2) backward match-ing. Forward matching is used to find motion from the refer-ence image to the target image, whereas backward matchingis used to determine the deformation from target image toreference image.

Following LMS filtering, backward matching is used as asecond filter to thoroughly remove false point matches. Asshown in Fig. 3, forward matching determines a point match(A, B). Backward matching is performed to find the point inthe reference image (point C) that corresponds to point B inthe target image. If points A and C are at the same position,

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Fig. 3 Schematic of forward matching and backward matching

the point pair (A, B) is reliable. Otherwise, the match is takento be false and eliminated.

Interpolation of filtered point matches

Since the results of the two-step filtering process are assumedto be spatially accurate point matches, interpolating the fil-tered data can generate a globally defined deformation field.However, the data is not guaranteed to posses any spatialstructure after the filtering process. Thus, interpolation meth-ods dependent on structure input data, such as B-spline para-meterizations, are not appropriate. In essence, the filtereddata set of point matches represents an unstructured pointcloud. The moving least squares method [21] is an ideal strat-egy for generating a full displacement field since it has beenshown to achieve accurate function approximations withinthe context of surface reconstruction from unorganized pointcloud data [22].

Results

Data characteristics and parameter settings

The chest radiographs used in this study were from 10 ran-domly selected patients for different clinical examinations atThe University of Texas MD Anderson Cancer Center. Thesecases consisted of 5 male and 5 female individuals rangingfrom 55–86 years in age (average, 61 years). Each of thesepatients had between two and 36 chest radiographs availablewith a total of 124 original radiographs. The time intervalsbetween previous and current radiographs ranged from 11 to2,475 days (average, 116 days). The images were digitizedwith maximum image matrix of 2,022 pixels × 2,022 pixels.Each image was spatially subsampled as 512 pixels × 512pixels. The algorithm was conducted on a Linux workstationwith two Intel Xeon x5560 six-Core 2.80 GHz processorsand a single NVIDIA Tesla 2070 GPU. The programmingenvironment included MATLAB and software written in theCompute Unified Device Architecture (CUDA) C program-ming language.

To implement the algorithm, we generated the coarseimage grid by sampling the original image using a sampling

Table 1 The VF and CF block-matching GPU runtimes

Case Matchingwindowradius (pixel)

Searchingwindowradius (pixel)

Runtime (s)

VF CF

1 15 64 31.87 31.66

2 25.53 25.93

3 31.69 33.51

4 21.23 21.45

5 30.67 32.40

6 29.85 31.40

7 30.05 30.19

8 30.71 30.92

9 31.10 31.37

10 31.01 31.39

Average 29.37 23.16

interval of 3 pixels. During grid-searching process, the neigh-borhood Nr (x)was 15 pixels × 15 pixels and the predefineddisplacement ranged from −64 pixels to 64 pixels. The VFand CF block-matching GPU runtimes are shown in Table 1and demonstrate that the registration process can be com-pleted quickly using parallel computing.

Visual analysis

To evaluate the proposed methods’ performance, we comparethe subtraction images created using the CF and VF intensitymodels with those produced by the demons and B-splinealgorithms. The comparison results are shown in Fig. 4. It canbe seen that the most ribs are not aligned in the subtractionimage created by the demons method (f), but are alignedwith minor misregistration in the image created using the VFmodel (c) and the B-spline method (e), and almost completelyaligned in the entire intercostal space in the image createdusing the CF model (d).

Figure 5 shows chest radiographs of a patient with non-small cell lung cancer in the right lung before (a) and after(b) treatment as well as subtraction images created using theVF model (c), the CF model (d), the B-spline algorithm (e),and the demons algorithm (f). The subtraction image cre-ated using the B-spline algorithm has significant artifactsthat obscure the disease area. For the same case, the demonsalgorithm produces a slightly better result. However, the sub-traction images produced using the VF or CF models clearlyshow the disease area.

Quantitative evaluation

We employ the widely used, subjective, 5-point rating scoreto evaluate the quality of subtraction images created with the

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Fig. 4 a Reference image, b target image, and subtraction images, respectively, created using the VF (c), CF (d), B-spline (e), and demons (f)methods

CF or VF models [2,11,23–25]. The rating score is definedin Table 2 and an example of images with different ratings isshown in Fig. 6. A rating score equal to or greater than 3.0indicates clinically acceptable quality, whereas a rating ofless than 3.0 indicates a lack of clinically acceptable quality[2,11]. We obtained rating scores by three observers in theradiation oncology department at the University of TexasMD Anderson Cancer Center: a clinical radiologist and twomedical researchers with rich experience in medical imageprocessing. Each observer evaluated the subtraction imagequality independently and a consensus was reached for thefinal rating score.

Because poor subtraction images have high contrast andgood subtraction images have low contrast, we use the widthof the gray-scale histogram to evaluate the quality of the sub-traction images. In general, the narrower the histogram width,the better the quality of the subtraction image [2,24]. Wecalculate the histogram width for pixels located in a squareregion of interest (ROI) that includes most thoracic area. TheROI is 300 pixels×300 pixels, and the middle point of its topedge is the superior-most part of the inner plate of the cortical

bone of the third thoracic spinous process. The histogramsfor the ROIs in the subtraction images in Fig. 5 are illus-trated in Fig. 7. We can see that the preregistration histogramis wide; the histograms for the subtraction images createdusing either CF or VF are much narrower.

The rating scores and histogram widths of subtractionimages created using different methods are given in Table 3.It can be seen that the mean rating score is only 2.7 and3, respectively, for the demons and B-spline methods, asopposed to 3.5 for the VF model and 4.1 for the CF model.In addition, both the demons and B-spline methods generatea rating score as low as 2, while the proposed VF and CFmodels produce rating scores equal to or greater than a clin-ically acceptable score of 3. Both the demons and B-splinemethods create subtraction images with the mean histogramwidth over 80, whereas the images created using the VF andthe CF models have the narrower mean histogram width of79.1 and 57.3, respectively. This indicates that subtractionimages created using the CF and the VF models are of bet-ter quality than those created using the demons and B-splinemethods.

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Fig. 5 a Reference image, b target image, and subtraction images, respectively, created using the VF (c), CF (d), B-spline (e), and demons (f)methods. The abnormality is enhanced in the subtraction images created using different methods (red arrows)

Table 2 Five-point rating score definition

Rating score Indicated quality Definition

1 Very poor Most ribs not registered inthe entire intercostal space

2 Poor Most ribs not well registered inhalf of the intercostal space

3 Adequate Most ribs well registered withsome minor misregistration

4 Good Most ribs almost completelyregistered with very minormisregistration

5 Excellent All ribs perfectly registered

In order to estimate the correlation between the histogramwidth and the rating score, the Spearman’s rank correla-tion coefficient is computed for each method. The valuesare −0.87,−0.94,−0.60 and −0.92 for the VF, CF, demons,and B-spline methods, respectively, which indicate that therating score tends to increase when the histogram widthdecreases.

Discussions and conclusions

We have presented a filtered block-matching DIR algorithmand applied it to chest radiographs of 10 patients to cre-ate temporal subtraction images using two different imageintensity models. The subtraction image quality that indicatesthe registration accuracy was evaluated qualitatively based onvisual analysis and quantitatively using the five-point ratingscore and histogram width. The proposed VF and CF mod-els were also compared with the demons and B-spline DIRmethods. Results demonstrate that the subtraction imagesproduced using the proposed method are of acceptable qual-ity for clinical application and superior to those producedusing the demons and B-spline methods.

Our registration method differs from those of otherresearchers in some respects. For example, image segmen-tation, such as extraction of the chest region and detectionof the ribcage edge, which is often required prior to regis-tration [1,9,12,24], is not necessary to implement our pro-posed algorithms. Moreover, chest radiographs used in this

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Fig. 6 a Reference and b targetchest radiographs, c very poor, dpoor, e adequate, f good, and gexcellent subtraction images forthe radiographs in a and b

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Fig. 7 Histograms of the ROI in subtraction images created using dif-ferent methods

study are of practical value in routine clinical situations.The different conditions during image acquisitions result ininconsistent intensities between images and make image reg-istration difficult. Unlike registration methods that assumeconsistent intensity, our algorithm can take intensity vari-ations into account to generate subtraction images throughthe matching of temporal chest radiographs with more flexi-ble image intensity models. In addition, the two-step filteringprocedure incorporated into the algorithm eliminates as manyinaccurate point matches as possible. The LMS filter coarselydetects erroneous point matches, and the backward matchingfilter refines the registration results, thereby providing a setof trusted, block-matching generated point pairs.

Temporal subtractions are expected to facilitate the rapidinterpretation of chest radiographs [26]. The proposed DIR

algorithm is flexible in that it is driven by a block-matchingmethod that can be applied to a variety of image intensitymodels. However, this block-matching approach introducesa substantial computational workload. This issue is resolvedby adopting a parallel computing software strategy that takesadvantage of graphics processing units (GPUs).

The intensity models we proposed can eliminate the arti-facts that often occur in direct subtraction images. Using theproposed DIR method, abnormalities and their change havebeen automatically enhanced in temporal subtraction images.Consequently, our method exhibits promising performancein providing subtraction images that assist radiologists indetection of abnormalities such as non-small cell lung can-cer. Although the VF and CF models are applied to standardchest radiographs in this study, the two models could also beused to create bony or soft-tissue-based temporal subtractionimages by combining with the dual-energy imaging tech-nique, which is of great significance in disease diagnosis andtreatment.

The temporal subtraction image is a powerful way to high-light subtle change. However, misregistration artifacts maymimic or obscure pathologic change and thus cause evalua-tion errors [24]. The pathologic change is complicated dueto various diseases and it is still difficult to define a criterionfor pathology change measurement. Currently, evaluating theaccuracy of pathologic change visualization is mainly basedon the visual analysis, such as Fig. 5 in the paper. In this study,the rib registration result is taken as a factor to indicate theregistration accuracy. When two chest radiographs are wellaligned, artifacts generated by ribs would be removed by sub-traction, which also contribute to the analysis of pathologicchange. Our future work will focus on developing a highlyautomated validation method to check registration accuracyand integrating it with automated detection of pathologicchange for clinical application.

Table 3 Rating scores and histogram widths of temporal subtraction images created using VF, CF, demons, and B-spline methods

Case Histogram width Rating scale

VF CF Demons B-spline VF CF Demons B-spline

1 79 28 82 102 4 5 3 2

2 27 26 62 40 5 5 3 4

3 98 47 109 52 3 5 2 5

4 68 54 50 39 4 4 4 4

5 94 90 105 132 3 3 3 2

6 63 50 72 67 4 4 2 3

7 91 54 105 62 3 4 2 3

8 80 40 87 101 3 5 3 2

9 88 88 95 87 3 3 2 3

10 103 96 93 119 3 3 3 2

Average 79.1 57.3 86 80.1 3.5 4.1 2.7 3

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Acknowledgments We thank Dr. Samantha Aso and Justin Yu inthe Department of Radiation Oncology at the University of Texas MDAnderson Cancer Center, for providing help in subtraction image obser-vation. This work is partially funded by MD Anderson’s Cancer Cen-ter Support Grant (CA016672) and the National Institutes of Healththrough an NIH Director’s New Innovator Award (DP2OD007044), andby the grants from the National Natural Science Foundation of China(NSFC No. 60771025).

Conflict of interest The authors declare that they have no conflict ofinterest.

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