Homma  Noriyasu

Zhang Xiaoyong

English

紀要類 (bulletin)departmental bulletin pape

Zhang, Xiaoyong

Homma, Noriyasu

Tohoku University Repository (TOUR) / 東北大学機関リポジトリ

Target Tracking in Medical Images UsingTemplate Matching著者 Zhang  Xiaoyong, Homma  Noriyasujournal orpublication title東北大学医学部保健学科紀要volume 23number 1page range 9-15year 2014-01-31URL http://hdl.handle.net/10097/571479????Target Tracking in Medical Images Using Template Matching???????????23?1? : 9?15?2014Review ArticleTarget Tracking in Medical Images Using Template MatchingXiaoyong Zhang and Noriyasu hommaDepartment of Radiological Imaging and Informatics, Tohoku University Graduate School of Medicine(E-mail : xiaoyong@ieee.org)????????????????????????? ? ? ??? ? ? ???????????????????????Key words :  Visual tracking, template matching, mean squared error, correlation coefficient, correlation ratio, mutual information, radiation therapy, fluoroscopic image??Tracking or recognizing an object in medical image is one of the most critical tasks in many medical image-related applications, such as image-guided radiation therapy (IGRT), computer-aided diagnosis (CAD), etc.???Template matching, as one of the common-used techniques in computer vision, has  widely been applied to these applications due to its simplicity and flexibility.?The goal of this note is to introduce the principles of the tem-plate matching technique, explain several similarity matrices used in the template matching, and give an exam-ple of the template matching for tracking a tumor target in fluoroscopic image sequence for IGRT.?In addition, we will also give some experimental results to evaluate the performance of the template matching based on dif-ferent similarity in terms of the accuracy and computation time.1.?Introduction?With the development of medical imaging technol-ogy, medical image processing has been involved in many clinical applications, ranging from diagnosis, treatment to patient follow-up.?In these applica-tions, automatic tracking or recognizing an object in the medical images is an important task.?For ex-ample, in image-guided radiation therapy (IGRT), a tumor tracking system, which is capable of tracking the respiration-induced tumor motion, allows clini-cian to deliver high-dose treatment beam to a mov-ing target for improving the treatment efficiency and reducing the risk to healthy tissues around the tu-mor [1, 2].??As one of the common-used techniques, template matching has widely been applied to various applica-tions due to its simplicity and flexibility. Generally, the template matching is a technique in digital image processing for finding small parts of an observed im-age which match a template image [3].?In this note, we will introduce the principles of the template matching technique, explain different similarity metrics used in the template matching, and give an example of the template matching for tracking a tumor target in fluoroscopic image se-quence for IGRT.?We will evaluate the performance of the template matching based on different similari-10????Xiaoyong Zhang?Noriyasu hommaty metrics in terms of the accuracy and computation cost.?2.?Template Matching?Let I(x, y) be an observed image of size M?N, where x=0,1,. . . , M?1 and y=0, 1, . . . , N?1 are the coordinates, and I denotes the image intensity at the coordinates of (x, y), and w(x, y) be a template (target) of size m?n.?In general, the size of the template is less that that of the observed image.??As an example, figures 1(a) and 1(b) show a fluo-roscopic image as the observed image I(x, y) and a pre-defined tumor target w(x, y) as the template, respectively.?The template matching is to find a sub-image in I(x, y) which is similar to the template.?Figure 1(c) illustrates the mechanism of the tem-plate matching in which a template whose center is at an arbitrary location (x, y).?The border around I(x, y) is a padding necessary to provide for the situ-ation when the center of w(x, y) is on the border of I(x, y).?As usual, we consider that the templates are of odd size for notational convenience.?We shift the template from the origin of image I(x, y) pixel by pixel, and compute a pre-defined measure of match between the template and a sub-image (target candi-date) overlapped by the template.?The measure of match is considered to be a metric that indicates the degree of similarity or dissimilarity between the tar-get and the target candidate.?After a full scanning, a matching measure map of size (M+m, N+n) is ob-tained, and we crop it to the size of the image I(x, y).?The template is said to be a match at a particular po-sition in the observed image if a distinct peak in the measure of match is found at that position.?A number of measures of match have been pro-posed in the fields of the medical image and comput-er vision technologies.?There is no best measures of match but a set of measures that are appropriated for particular applications.?In this note, we will in-troduce several typical measures of match used in template matching.2.1?Intensity Difference Measures?The intensity difference is the simplest measure that is based on the pixel-by-pixel intensity differ-ences between the target and target candidates.?Typical intensity difference measures include the mean squared error (MSE), sum of absolute differ-ence (SAD), to name a few.?The lower value of in-tensity difference indicates the higher similarity, while the higher value of intensity difference indi-Fig. 1.? An example of the template matching for tracking a tumor in fluoroscopic image.?(a) A fluoroscopic im-age as an observed image I(x, y).?(b) A pre-defined tumor target w(x, y) as the template.?(c) Mecha-nism of the template matching.11????Target Tracking in Medical Images Using Template Matchingcates the less similarity.??The MSE is a common measure of mismatch be-tween a template w(x, y) and the candidates in I(x, y), given byMSE , , ,x y mn I x s y t w s t1t bbs aa2= + + -== --^ ^ ^h h h6 @!! (1)where a=(m?1)/2 and b=(n?1)/2 are the padding size described previously.?Similarly, the SAD is de-fined as , , ,x y I x s y t w s tSADt bbs aa= + + -=-=-^ ^ ^h h h!!  (2)?Figure 2 shows an MSE map between the tem-plate and the observed image as shown in Figs. 1(a) and 1(b).?The match position is located at the coor-dinates (164,170) where the MSE reaches its mini-mum.   The intensity difference measures can be considered as the distance between two intensities vectors representing the the target and the target candidate.?Therefore, these measures are sensi-tive to the image intensity variation and geometrical deformation, such as luminance shift, contrast changing, scaling, and so on.?An additional reading on MSE may be found in [6].2.2?Correlation Coefficient (CC)?The correlation coefficient (also called the nor-malized cross-correlation)  of two images is a simi-larity measure of two images.?For the template matching, the CC map between the template and the observed image is computed byCC ,, ,, ,x yw s t w I x s y t Iw s t w I x s y t I, ,,s t s t xys t xy2 2=+ ++ +! !!- -- -r rr r^^ ^^ ^hh hh h6 66 6@ @@ @ (3)where w¯ is the average intensity of the template, and I?xy is the average intensity of image in the region where I and w overlap.?The value of CC(x, y) rang-es from ?1 to 1.?A high value for CC(x, y) indi-cates a good match between the template and the image, when the template is centered at the coordi-nates (x, y).?Figure 3 shows a CC map between the template and the observed image as shown in Figs. 1(a) and 1(b).?The match position is located at the coordi-nates (164,170) where the CC reaches its maximum.?A geometric interpretation of correlation coefficient is that the correlation coefficient can be viewed as the cosine of an angle between two vectors that rep-resent the intensities of two images [7].?Therefore, the CC is robust against the image intensity varia-Fig. 2.? Template matching based on mean squared er-ror (MSE).Fig. 3.? Template matching based on correlation coeffi-cient (CC).12????Xiaoyong Zhang?Noriyasu hommation.?However, the CC is also sensitive to the geo-metrical deformation.? 2.3?Correlation Ratio (CR)?In probability theory, correlation ratio measures the functional dependence between two random variables [9].?Given two images A and B, the cor-relation ratio of A and B is defined as (4)where A2v  and B2v  are the intensity variances of im-age A and B, respectively, and A B2v ,  is the total vari-ance of images A and B.?The CR takes on values between 0 and 1 that indicate the dissimilarity and similarity, respectively.?For the template matching, a similarity map based on the CR is computed by   (5)where C(?) denotes the CR defined by Eq. (4).?Figure 4 shows a CR map between the template and the observed image as shown in Figs. 1(a) and 1(b).?The match position is located at the coordinates (164,170) where the CR reaches its maximum.2.4?Mutual Information (MI)?In probability theory and information theory, the ,C A B2 A BA B22 2=vv v+,^ hCR , , , ,x y C I x s y t w s tt bbs aa= + +== --^ ^ ^h h h6 @!!mutual information (MI) of two random variables is a measure of the mutual dependence of the two ran-dom variables.?The MI has been one of the most popular similarity measures for multi-modal image registration, such as registration of CT and MR im-ages [10].??Given two images A and B, the MI of the two im-ages is defined as (6)where i and j are intensities of images A and B (For example, i, j=0, 1, . . . , 255 if A and B are 8-bit im-ages), P(i, j) is the normalized two-dimensional (2-D) histogram (also called joint probability density function) of A and B, PA(i) and PB(j) are the normal-ized 1-D histograms (marginal probability density functions) of A and B, respectively.?The MI mea-sures the similarity between A and B, i.e., a high value of MI indicates high similarity, while low value of intensity difference indicates dissimilarity.?The detail about the 1-D and 2-D histograms can be found in [8, 10].? ?Given an observed image and a template, the sim-ilarity map based on the MI is computed by (7), ,,logM A B P i jP i P jP i j, A Bi j2=^ ^ ^ ^^h h h hh!MI , , , ,x y M I x s y t w s tt bbs aa= + +== --^ ^ ^h h h6 @!!Fig. 4.? Template matching based on correlation ratio (CR).Fig. 5.? Template matching based on mutual information (MI).13????Target Tracking in Medical Images Using Template Matchingwhere M(?) denotes the MI defined by Eq. (6).?Figure 5 shows an MI map between the template and the observed image as shown in Figs. 1(a) and 1(b).?The match position is located at the coordi-nates (164,170) at where a distinct peak is located.?3.?Tracking Tumor Motion for IGRT?In this section, we will present an example of template matching used for tracking tumor target in fluoroscopic image sequence.?In radiation therapy, as we known, respiration-in-duced tumor motion limits the efficiency of radiation delivery, especially for abdominal and thoracic tumor.?One of the solution for improving the efficiency of radiation delivery is to utilizes a fluoroscopic imag-ing system to monitor the tumor motion during the treatment.?On the base of the imaging system, a tumor tracking system, which is capable of automati-cally tracking the tumor motion, allows the treat-ment device to deliver the treatment beam to a mov-ing tumor target.?Figure 6 shows a fluoroscopic imaging system mounted on a radiation therapy de-vice and a template matching-based tracking system for tracking the tumor in the fluoroscopic image se-quence.?Here, we present several experimental results of the tumor tracking by using different similarity metrics.?Experimental data is a fluoroscopic image sequence which consists of 100 frames of size 300?300 pixels obtained by an On-Board Imaging (OBI) system (Varian Medical Systems, Palo Alto, CA).?A tumor target is delineated by a rectangle of size 81?81  pixels in the first frame.?For the subsequent frames, we utilize the template matching based on four similarity metrics (MSE, CC, CR, and MI) to lo-cate the tumor position in each frame.?Figures 1(b) and 1(a) show the first frame of the image sequence and the template used for the template tracking, respectively.?The tracking algorithms are imple-mented by using MATLAB on an Intel Core i7 3.3 GHz computer with Windows 7 OS.??Figures 7(a)-7(d) shows the tumor tracking re-sults along the superior-inferior (SI) and left-right (LR) directions.?In these figures, we also plot the ground truths of the tumor motion that are generat-ed by manual localization.?Table 1 summaries the root of mean squared errors (RMSEs) (mm) be-tween the tracking results and the ground truths.?In this table, we also list the computational times (s/frame) of each tracking method.?From this table, we can see that the accuracy of the CC-based tem-plate matching is higher than those of MSE-, CR-, and MI-based methods.?On the other hand, the computational times show that the lowest computa-tional cost is the MSE-based method.??In the experiments, the template matching is per-formed by using an exhaustive searching strategy (full scan).?In practice, some efficient search strat-egies, such as coarse-to-fine template matching, can be used to reduce the computational cost to meet Fig. 6.? Tracking tumor motion in fluoroscopic image sequence for IGRT.14????Xiaoyong Zhang?Noriyasu hommathe requirement of real-time tracking.?Further reading about the efficient search strategies can be found in [11, 12].4.?Conclusion?In this note, we present the fundamental of tem-plate matching technique and introduced four com-mon-used similarity metrics used for the template matching : MSE, CC, CR, and MI.?By using an ex-periment of tumor tracking, we also evaluated the performances of these similarity metrics in terms of the accuracy and computational cost.?In computer vision technology, the template matching is only one of the object tracking methods.?Extensive surveys of object tracking methods can be found in [4, 5].Table 1.?Root of mean squared errors (RMSEs) (mm) in tumor motion estimationMSE-based CC-based CR-based MI-basedRMSE (mm) 1.10 1.05 8.40 20.73Computation time (s/frame) 1.2 2.2 2.6 5.8Fig. 7.? Experimental results of template matching based on different similarity metrics.?(a) Mean squared error (MSE).?(b) Correlation coefficient (CC).?(c) Correlation ratio (CR).?(d) Mutual information (MI).15????Target Tracking in Medical Images Using Template MatchingReferences[ 1 ]? Xing, L., Thorndyke, B., Schreibmann, E., Yang, Y., Li, T., Kim, G., Luxton, G., Koong, A. : Overview of Im-age-Guided Radiation Therapy, Medical Dosimetry, 31(2), 99-112, 2005[ 2 ]? Dawson, L.A., Jaffray, D.A. : Advances in Image-Guid-ed Radiation Therapy, Journal of Clinical Oncology, 25(8), 838-946, 2007[ 3 ]? Brunelli, R. : Template Matching Techniques in Com-puter Vision : Theory and Practice, Wiley, 2009[ 4 ]? Yilmaz, A., et al. : Object Tracking : A Survey, ACM Computing Surveys, 38(4), 1-45, 2006[ 5 ]? Trucco, E., Plaks, K. : Video Tracking : A Concise Survey, IEEE Journal of Oceanic Engineering, 31(2), 520-529, 2006[ 6 ]? Zhou, W., et al. : Mean squared error : Love it or leave it ??A new look at Signal Fidelity Measures, IEEE Signal Processing Magazine, 26(1), 98-117, 2009[ 7 ]? Rodgers, J.L., Nicewander, W.A. : Thirteen Ways to Look at the Correlation Coefficient, The American Statistician, 42(1), 59-66, 1988[ 8 ]? Gonzalez, R.C., Woods, R.E. : Digital Image Process-ing, Prentice Hall Press, 2002[ 9 ]?Roche, A., et al. : The correlation ratio as a new simi-larity measure for multimodal image registration, MIC-CAI, 98, 1115-1124, 1998[10]? Maes, F., et al. : Multimodality Image Registration by Maximization of Mutual Information, IEEE Transac-tions on Medical Imaging, 16(2), 187-198, 1997[11]? Vanderbrug, G.J., Rosenfeld, A. : Two-stage template matching, IEEE Transactions on Computers, 26, 384-393, 1977[12]? Goshtasby, A., et al. : A two-stage cross correlation approach to template matching, IEEE Transactions on PAMI, 6, 374-378, 1984

Target Tracking in Medical Images Using Template Matching

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