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Lymph node segmentation from CT images using fast marching method
Computerized Medical Imaging and Graphics 28 (2004) 33–38 www.elsevier.com/locate/compmedimag
Lymph node segmentation from CT images using fast marching method Jiayong Yana, Tian-ge Zhuanga,*, Binsheng Zhaob, Lawrence H. Schwartzc a
Department of Biomedical Engineering, Shanghai Jiao tong University, 1954 Huashan Road, Shanghai 200030, China b Departments of Medical Physics and Radiology at Memorial Sloan-Kettering Cancer Center, New York, NY, USA c Department of Radiology at Radiology at Memorial Sloan-Kettering Cancer Center, New York, NY, USA Received 9 May 2003; accepted 19 September 2003
Abstract Accurate lymph node size analysis is important medically. This paper presents an improved fast marching method to perform semiautomatic segmentation for lymph node from CT images. In this work, we have incorporated the gray scale information of the target region into the fast marching speed term and have given a hard constraint for the stop criteria, instead of only using the spatial image gradient, to remedy the ‘boundary leaking’ problem of the traditional fast marching method. Various experimental results are provided to demonstrate the effectiveness of the proposed method. q 2004 Elsevier Ltd. All rights reserved. Keywords: Lymph node; Image segmentation; CT images; Fast marching
1. Introduction Lymph node size analysis is extremely important in a number of medical settings [1]. Node size can be an indicator of tumor activity, and enlarged nodes are generally targeted for further evaluation or treatment. A particularly important measure of the lymph node is its change in size over time. This change is used to determine if a treatment is successful or if a patient is getting worse [2]. On CT images, lymph nodes typically are intermediate in signal intensity; generally brighter than surrounding fat, but lower than contrast enhanced vessels. Often a portion of the node boundary is obscured in the image, either due to partial volume effects or sharing a boundary with other tissues of similar signal intensities. This may make it very difficult to segment the lymph node automatically with traditional segmentation techniques such as thresholding, region growing, or edge detection and linking. Until now, the measurement technique used most often in clinical practice is to estimate the lymph node size based on the boundary delineated manually by radiologists in several image slices. However, this is laborious, time-consuming and prone to human error. Honea et al. [2,3] have attempted to * Corresponding author. Tel.: þ 86-21-52540226. E-mail address: [email protected] (T. Zhuang). 0895-6111/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compmedimag.2003.09.003
semi-automatically segment lymph node with active contours and active surface methods. Their evaluation was mostly on phantom images, and many problems remain to be solved. The initial contour required was near to the target boundary. Directly using the resulted contour as the initial contour of next adjacent slice needs the interval between neighboring slices very small. Otherwise, it will be very difficult to obtain any desirable results. This paper attempts to improve the traditional fast marching method [4,5] to semi-automatically segment lymph nodes from CT images. Section 2 describes the traditional fast marching method in general. In Section 3, we describe how the technique has been improved and implemented for use on lymph node segmentation in CT images. Section 4 gives some of the experimental results. Finally, our conclusions are drawn in Section 5.
2. Fast marching method While deformable models have been widely used in medical imaging applications [6,7], they have severe limitations: they are unable to handle complex geometry and change topology without additional machinery. To overcome these difficulties, the level set method has been proposed [8,9]. In this approach, a 2D curve Cis represented
34
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
Fig. 1. Level set signed distance function.
by a marching closed hyper-curve CðtÞ : ½0; 1Þ ! R2 : Let F ~ then we have be the speed in the normal direction N;
›C ~ ¼ F N: ›t
ð1Þ
The essential idea of level set is to embed the marching front as the zero set of a 3D function fðs; tÞ ¼ ^d; where s [ R2 and d denotes the signed distance from position s to CðtÞ (Fig. 1). By embedding the interface as the zero level set of a higher dimensional function, the signed distant function remains continuous and at the same time corresponds to the propagating interface, which may change the topology. This is an important advantage. On the other hand, it has the disadvantage of a heavy computation requirement. In order to solve this problem, Sethian [4] proposed the fast marching method for monotonically advancing fronts. In this method, the speed term F is restricted to a one-way speed term at all time on every point, and the level set formulation is simplified to l7TlF ¼ 1:
ð2Þ
where T is the time at which the front crosses the given point. For a 2D problem, we are looking for a solution to the following equation: 2y 2 þx 2 2 ½maxðD2x i;j T; 0Þ þ maxðDi;j T; 0Þ þ maxðDi;j T; 0Þ 2 1=2 þ maxðDþy ¼ 1=Fi;j : i;j T; 0Þ
ð3Þ
where D2 and Dþ are backward and forward difference operators respectively. Given Iðx; yÞ; ðx; yÞ [ R2 for a 2D image, the objective is to detect the boundary of a shape in image Iðx; yÞ. Generally, fast marching method for boundary detection starts from a ‘seed point’, which is given manually or estimated from the other detected boundaries, and grows the trial front from this point. The front propagates in the normal direction with a special image-based speed Fðx; yÞ; which is often defined as a decreasing function [10] based on the image local gradient l7Iðx; yÞl: Up to now the main forms of Fðx; yÞ are
written as: Fðx; yÞ ¼ e2al7Iðx;yÞl ;
a.0
ð4Þ
and Fðx; yÞ ¼
1 ; 1 þ al7Iðx; yÞl
a.0
ð5Þ
where a is a constant. For more details of the traditional algorithm of fast marching to find the boundary of a shape, see Ref. [5]. Sethian [4,5] have proved that this algorithm is extremely fast even for 3D segmentation. Its time complexity is OðN log NÞ per time step while that of the original level set and the narrow band level set are OðN 3 Þ and OðN 2 Þ; respectively, where N is the number of points in each coordinate direction.
3. Improving fast marching method for lymph node segmentation Fast marching method has been widely applied to medical image segmentation [9] in recent years. However, due to intrinsic properties of lymph node images, such as low contrast and sharing partial boundary with other tissues of similar intensities, the boundary feature of the lymph node is usually not distinct enough and the image gradient information is generally weak. This causes the ‘boundary leaking’ problem when we directly apply the traditional fast marching method to detect the lymph node boundary. In order to solve this problem, we have improved the traditional fast marching method for the segmentation of lymph nodes in CT images in the following two aspects: (1) the speed term F; and (2) the stop criteria. 3.1. The speed term As is well known, the speed term F in the traditional fast marching method is mainly based on the local image gradient, as shown in Eqs. (4) and (5). However, the image gradient information of lymph node in CT images is
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
very weak. So it must incorporate with other image features. Motivated by the region-based strategy for image segmentation, we introduced the region information into the speed term of the traditional fast marching method. First, we developed a discrimination method to obtain the intensity likelihood between the target region and every pixel point in the image as ! 1 ðIðx; yÞ 2 mI Þ2 Lðx; yÞ ¼ pffiffiffiffi exp 2 ð6Þ 2s2I 2psI where Iðx; yÞ is the intensity of point ðx; yÞ; mI and sI are the mean intensity and standard deviation of the target region. mI and sI can be estimated from the intensity of a window centered at the seed point or the region already segmented. This function is then incorporated into the speed term in the traditional fast marching method, and a new speed function is therefore formed: Fnew ðx; yÞ ¼ Fðx; yÞLðx; yÞ
ð7Þ
Now the new speed term Fnew is not only based on the local image gradient, but also the target region intensity feature. This can better ensure that the advancing front moves from the seed point within the target region.
3.2. The stop criteria Stop criteria is another challenge associated with the fast marching method There are some stop criteria of the traditional fast marching method for the advancing front stopping on the boundary. However, they are valid only for some ideal situations and can hardly be used for clinical applications. As of yet, there are no properly designed stop criteria for noisy situations such as lymph node and other soft tissue segmentation on CT images. In this work, in order to reduce the likelihood of ‘boundary leaking’ as much as possible, a hard constraint is given to stop the front advancing. For a 2D image, when we manually select the seed point, we will also provide a circle with the seed point as its center. The circle encompasses the entire target, i.e. the lymph node. What is also of paramount importance, is that at least some part of the circumference should be very close (almost tangential) to the desired boundary (Fig. 2). This can be done easily with the computer mouse. When the front arrives at the circumference, it will stop advancing. For sequential 2D images, we attempted to set a stop constraint based on the boundary extracted from the neighboring slice and the intensity of the target region. Considering that the shape and the intensity of a lymph node do not vary substantially between the neighboring slices, we used the intensity within the segmented lymph node to estimate the mean intensity and deviation of the lymph node in the neighboring slice. Then we uniformly expanded the extracted boundary towards its outside with a certain distance
35
Fig. 2. The seed point and the initialized circle.
and used it to constrain the searching region in the neighboring image instead of the circle constraint given on the initial slice (Fig. 3). The seed point of the next slice can also be estimated from the segmented lymph node on the previous slice. For example, the geometric center was used in this paper. 3.3. Smooth the final advancing front Due to the disturbance of image noise and other surrounding soft tissues, the lymph node boundary detected with the proposed fast marching method may not be smooth enough The detected results should be adjusted interactively in some poor images although this is not often required. We selected a cubic B-spline function to smooth the segmentation results as the cubic B-spline can be easily adjusted locally without affecting the rest part of the detected boundary [11,12]. This is exactly what we need since only few part of final advancing front that deviates from the target boundary. The steps to smooth and adjust the results obtained by the presented method are as follows: 1. Sample the detected boundary, which is implicitly represented by the zero level set. 2. Drag the sampled points deviated from the target boundary to the desired position. 3. Using cubic B-spline function to interpolate the final boundary instead of the linear interpolation.
Fig. 3. The uniformly expanded boundary (outside one) used for the constraint of the next slice.
36
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
Fig. 4. The results obtained with different seed points and initial circles: (a) original image; (b) –(d) seed points and initial circles; (e) manual result; (f)– (h) results corresponding to (b)– (d).
4. Experimental results In this section, some examples are given to illustrate the efficiency and robustness of the proposed method for the segmentation of lymph nodes in approximately 400 CT images. First, we applied the method to 2D images with different seed points and initial circles. Some of the results are shown in Figs. 4 –6. The corresponding lymph node boundaries delineated manually by a radiologist are also shown for
comparison. In these examples, all of the parameters are identical, i.e. a ¼ 0:2; mI and sI are calculated from intensities of a 11 £ 11 window centered at the seed point From these results, we can see that although the image quality is quite poor, the proposed approach successfully and robustly detects most of the desired lymph node boundaries. In our experiments, most of the final advancing fronts did not need to be adjusted. Few final advancing fronts requested adjustment, but only one or two sampled points on them had such a need.
Fig. 5. The results obtained with different seed points and initial circles: (a) original image; (b) –(d) seed points and initial circles; (e) manual result; (f)– (h) results corresponding to (b)– (d).
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
37
Fig. 6. The results obtained with different seed points and initial circles: (a) original image; (b) –(d) seed points and initial circles; (e) manual result; (f)–(h) results corresponding to (b)–(d).
The proposed approach was then applied to sequential images containing lymph node tissue. One of these results is shown in Fig. 7. In this example, the parameter a is 0.2. mI and sI are calculated from the intensities of the lymph node region segmented in the neighboring slices. The seed point is estimated from the geometric center of the boundary obtained in the neighboring slice. Fig. 7c – f show that the proposed method obtains the desired lymph node boundaries. From these experiments, we can also see that
using the information between neighboring slices can effectively enhance the likelihood of automation for the sequential image segmentation.
5. Conclusions Based on the analysis of the existing problems in applying the traditional fast marching method to lymph
Fig. 7. The results of a sequential images: (a) the seed point and initial circle for the first image; (b) the result obtained from (a); (c) –(f) results obtained with sequential stop criteria proposed in this paper.
38
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
node segmentation on CT images, the information of target region is incorporated into its speed term. This can better ensure that the advancing front moves from the seed point within the target region The proposed hard constraint for the stop criteria can effectively stop the advancing front near the target lymph node boundary. All of the experiments and comparisons show that the proposed approach allows for a fast and effective detection of lymph node boundary in CT images.
References [1] Grossman SA, Burch PA. Quantitation of tumor response to antineoplastic therapy. Semin Oncol 1988;15:441 –54. [2] Honea DM, Yaorong Ge, Snyder WE, Henler PF, Vining DJ. Lymphnode segmentation using active contours. SPIE 1997;3034:265 –73. [3] Honea DM, Snyder WE. Three-dimensional active surface approach to lymph node segmentation. SPIE 1999;3661:1003–11. [4] Sethian JA. A fast marching level set method for monotonically advancing fronts. Proc Natl Acad Sci USA 1996;93:1591 –5. [5] Sethian JA. Level set methods and fast marching methods. Cambridge: Cambridge University Press; 1996. [6] Kass M, Witkin A, Terzopoulos D. Snakes: active contour models. Int J Comput Vision 1987;1(4):321–31. [7] Mclnemey T, Terzopoulos D. Deformable models in medical image analysis: a survey. Med Image Anal 1996;1(2):91 –108. [8] Osher S, Sethian JA. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys 1988;79(1):12–49. [9] Malladi R, Sethian JA, Vemuri BC. Shape modeling with front propagation: a level set approach. IEEE Trans PAMI 1995;17(2): 158–75. [10] Caselles V, Kimmer R, Sapiro G. Geodesic active contours. Intern J Comput Vision 1997;22(1):61–79. [11] Petit E, Lemoine J, Djeziri S. An adaptative method to smooth discrete curves proposed as a final step for edge detection. Image Vision Comput 2001;19(2):145–52. [12] Li B, Hu HB, Zhuang TG. Contours embellishment using adaptive cubic B-spline in image segmentation. J Infrared Millim Waves 2001; 20(6):401– 5.
Jiayong Yan was born in 1975. He received BS in Biomedical Engineering from Xi’an Jiao tong University, China in 1998. He is currently a PhD candidate in Biomedical Engineering from Shanghai Jiao tong University, China. His research interests include medical image processing and ultrasound tumor treatment.
Tian-ge Zhuang is a professor of Biomedical Engineering in Shanghai Jiao tong University, Shanghai, China. He graduated from the Department of Electric Engineering in Jiao tong University, Shanghai China in 1957. From 1957 to 1979, he was working in the Department of EE and the Department Radio Engineering, both in Xi’an Jiao tong University. He transferred to Shanghai Jiao tong University in 1979 and has been in the Biomedical Engineering Department since then. From 1980 to 1982, he was a visiting scholar in the Biomedical Computer Laboratory, Washington University, St Louis, MO. From September 1993 to February 1994, he was a senior visiting scholar in the Medical Image Processing Group University of Pennsylvania. He has published more than 80 papers and is the author of three books: Fundamentals of Computer Tomography and Algorithms (1992), Applications of Computers in Biomedicine (1991), Applications of Computers in Biomedicine (2000, new edition). He is also the chief translator of the book: ’Radiological Imaging’ (by H.H. Barrett) from English to Chinese (1988). His research area spans from ‘Theory and Application of Computed Tomography’ to ‘Computer Assisted Surgery’ and ‘Picture Archiving and Communication System’. He is the senior member IEEE, and is the vice Chairman of ‘the Biomedical Information & Cybenetics Society of the Chinese Society of Biomedical Engineering’, the member of board of ‘The Biomedical Electronic Society of the Chinese Institute of Electronics’, the member of board of ‘the Society of All China Computed Tomography’. He has been the Chairman of the Department of Biomedical Engineering and the vice dean of the College of Life Sciences and Biotechnology, Shanghai Jiao tong University.
Binsheng Zhao received BS and MS in Electronic Engineering from National University of Defense Technology, China in 1984 and 1987 respectively and DSc from University of Heidelberg, Germany in 1994. She is currently an Assistant Attending Physicist in the Departments of Medical Physics and Radiology at Memorial Sloan-Kettering Cancer Center, New York. She has been working on development of advanced CT image processing algorithms for computer-aided detection and diagnosis (CAD) of lung cancer since 1997. Her research interests also include CAD developments for liver and lymph node metastases.
Lawrence H. Schwartz, MD, is an Associate Attending Radiologist and Director of the Laboratory for Computational Image Analysis in Radiology Department, Memorial Sloan-Kettering Cancer Center, New York. He has extensive experience in clinical trials in oncology, with conventional and novel imaging modalities. His interests include hepatobiliary imaging, medical informatics/PACS as well as therapeutic response assessment.
Lymph node segmentation from CT images using fast marching method Jiayong Yana, Tian-ge Zhuanga,*, Binsheng Zhaob, Lawrence H. Schwartzc a
Department of Biomedical Engineering, Shanghai Jiao tong University, 1954 Huashan Road, Shanghai 200030, China b Departments of Medical Physics and Radiology at Memorial Sloan-Kettering Cancer Center, New York, NY, USA c Department of Radiology at Radiology at Memorial Sloan-Kettering Cancer Center, New York, NY, USA Received 9 May 2003; accepted 19 September 2003
Abstract Accurate lymph node size analysis is important medically. This paper presents an improved fast marching method to perform semiautomatic segmentation for lymph node from CT images. In this work, we have incorporated the gray scale information of the target region into the fast marching speed term and have given a hard constraint for the stop criteria, instead of only using the spatial image gradient, to remedy the ‘boundary leaking’ problem of the traditional fast marching method. Various experimental results are provided to demonstrate the effectiveness of the proposed method. q 2004 Elsevier Ltd. All rights reserved. Keywords: Lymph node; Image segmentation; CT images; Fast marching
1. Introduction Lymph node size analysis is extremely important in a number of medical settings [1]. Node size can be an indicator of tumor activity, and enlarged nodes are generally targeted for further evaluation or treatment. A particularly important measure of the lymph node is its change in size over time. This change is used to determine if a treatment is successful or if a patient is getting worse [2]. On CT images, lymph nodes typically are intermediate in signal intensity; generally brighter than surrounding fat, but lower than contrast enhanced vessels. Often a portion of the node boundary is obscured in the image, either due to partial volume effects or sharing a boundary with other tissues of similar signal intensities. This may make it very difficult to segment the lymph node automatically with traditional segmentation techniques such as thresholding, region growing, or edge detection and linking. Until now, the measurement technique used most often in clinical practice is to estimate the lymph node size based on the boundary delineated manually by radiologists in several image slices. However, this is laborious, time-consuming and prone to human error. Honea et al. [2,3] have attempted to * Corresponding author. Tel.: þ 86-21-52540226. E-mail address: [email protected] (T. Zhuang). 0895-6111/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compmedimag.2003.09.003
semi-automatically segment lymph node with active contours and active surface methods. Their evaluation was mostly on phantom images, and many problems remain to be solved. The initial contour required was near to the target boundary. Directly using the resulted contour as the initial contour of next adjacent slice needs the interval between neighboring slices very small. Otherwise, it will be very difficult to obtain any desirable results. This paper attempts to improve the traditional fast marching method [4,5] to semi-automatically segment lymph nodes from CT images. Section 2 describes the traditional fast marching method in general. In Section 3, we describe how the technique has been improved and implemented for use on lymph node segmentation in CT images. Section 4 gives some of the experimental results. Finally, our conclusions are drawn in Section 5.
2. Fast marching method While deformable models have been widely used in medical imaging applications [6,7], they have severe limitations: they are unable to handle complex geometry and change topology without additional machinery. To overcome these difficulties, the level set method has been proposed [8,9]. In this approach, a 2D curve Cis represented
34
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
Fig. 1. Level set signed distance function.
by a marching closed hyper-curve CðtÞ : ½0; 1Þ ! R2 : Let F ~ then we have be the speed in the normal direction N;
›C ~ ¼ F N: ›t
ð1Þ
The essential idea of level set is to embed the marching front as the zero set of a 3D function fðs; tÞ ¼ ^d; where s [ R2 and d denotes the signed distance from position s to CðtÞ (Fig. 1). By embedding the interface as the zero level set of a higher dimensional function, the signed distant function remains continuous and at the same time corresponds to the propagating interface, which may change the topology. This is an important advantage. On the other hand, it has the disadvantage of a heavy computation requirement. In order to solve this problem, Sethian [4] proposed the fast marching method for monotonically advancing fronts. In this method, the speed term F is restricted to a one-way speed term at all time on every point, and the level set formulation is simplified to l7TlF ¼ 1:
ð2Þ
where T is the time at which the front crosses the given point. For a 2D problem, we are looking for a solution to the following equation: 2y 2 þx 2 2 ½maxðD2x i;j T; 0Þ þ maxðDi;j T; 0Þ þ maxðDi;j T; 0Þ 2 1=2 þ maxðDþy ¼ 1=Fi;j : i;j T; 0Þ
ð3Þ
where D2 and Dþ are backward and forward difference operators respectively. Given Iðx; yÞ; ðx; yÞ [ R2 for a 2D image, the objective is to detect the boundary of a shape in image Iðx; yÞ. Generally, fast marching method for boundary detection starts from a ‘seed point’, which is given manually or estimated from the other detected boundaries, and grows the trial front from this point. The front propagates in the normal direction with a special image-based speed Fðx; yÞ; which is often defined as a decreasing function [10] based on the image local gradient l7Iðx; yÞl: Up to now the main forms of Fðx; yÞ are
written as: Fðx; yÞ ¼ e2al7Iðx;yÞl ;
a.0
ð4Þ
and Fðx; yÞ ¼
1 ; 1 þ al7Iðx; yÞl
a.0
ð5Þ
where a is a constant. For more details of the traditional algorithm of fast marching to find the boundary of a shape, see Ref. [5]. Sethian [4,5] have proved that this algorithm is extremely fast even for 3D segmentation. Its time complexity is OðN log NÞ per time step while that of the original level set and the narrow band level set are OðN 3 Þ and OðN 2 Þ; respectively, where N is the number of points in each coordinate direction.
3. Improving fast marching method for lymph node segmentation Fast marching method has been widely applied to medical image segmentation [9] in recent years. However, due to intrinsic properties of lymph node images, such as low contrast and sharing partial boundary with other tissues of similar intensities, the boundary feature of the lymph node is usually not distinct enough and the image gradient information is generally weak. This causes the ‘boundary leaking’ problem when we directly apply the traditional fast marching method to detect the lymph node boundary. In order to solve this problem, we have improved the traditional fast marching method for the segmentation of lymph nodes in CT images in the following two aspects: (1) the speed term F; and (2) the stop criteria. 3.1. The speed term As is well known, the speed term F in the traditional fast marching method is mainly based on the local image gradient, as shown in Eqs. (4) and (5). However, the image gradient information of lymph node in CT images is
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
very weak. So it must incorporate with other image features. Motivated by the region-based strategy for image segmentation, we introduced the region information into the speed term of the traditional fast marching method. First, we developed a discrimination method to obtain the intensity likelihood between the target region and every pixel point in the image as ! 1 ðIðx; yÞ 2 mI Þ2 Lðx; yÞ ¼ pffiffiffiffi exp 2 ð6Þ 2s2I 2psI where Iðx; yÞ is the intensity of point ðx; yÞ; mI and sI are the mean intensity and standard deviation of the target region. mI and sI can be estimated from the intensity of a window centered at the seed point or the region already segmented. This function is then incorporated into the speed term in the traditional fast marching method, and a new speed function is therefore formed: Fnew ðx; yÞ ¼ Fðx; yÞLðx; yÞ
ð7Þ
Now the new speed term Fnew is not only based on the local image gradient, but also the target region intensity feature. This can better ensure that the advancing front moves from the seed point within the target region.
3.2. The stop criteria Stop criteria is another challenge associated with the fast marching method There are some stop criteria of the traditional fast marching method for the advancing front stopping on the boundary. However, they are valid only for some ideal situations and can hardly be used for clinical applications. As of yet, there are no properly designed stop criteria for noisy situations such as lymph node and other soft tissue segmentation on CT images. In this work, in order to reduce the likelihood of ‘boundary leaking’ as much as possible, a hard constraint is given to stop the front advancing. For a 2D image, when we manually select the seed point, we will also provide a circle with the seed point as its center. The circle encompasses the entire target, i.e. the lymph node. What is also of paramount importance, is that at least some part of the circumference should be very close (almost tangential) to the desired boundary (Fig. 2). This can be done easily with the computer mouse. When the front arrives at the circumference, it will stop advancing. For sequential 2D images, we attempted to set a stop constraint based on the boundary extracted from the neighboring slice and the intensity of the target region. Considering that the shape and the intensity of a lymph node do not vary substantially between the neighboring slices, we used the intensity within the segmented lymph node to estimate the mean intensity and deviation of the lymph node in the neighboring slice. Then we uniformly expanded the extracted boundary towards its outside with a certain distance
35
Fig. 2. The seed point and the initialized circle.
and used it to constrain the searching region in the neighboring image instead of the circle constraint given on the initial slice (Fig. 3). The seed point of the next slice can also be estimated from the segmented lymph node on the previous slice. For example, the geometric center was used in this paper. 3.3. Smooth the final advancing front Due to the disturbance of image noise and other surrounding soft tissues, the lymph node boundary detected with the proposed fast marching method may not be smooth enough The detected results should be adjusted interactively in some poor images although this is not often required. We selected a cubic B-spline function to smooth the segmentation results as the cubic B-spline can be easily adjusted locally without affecting the rest part of the detected boundary [11,12]. This is exactly what we need since only few part of final advancing front that deviates from the target boundary. The steps to smooth and adjust the results obtained by the presented method are as follows: 1. Sample the detected boundary, which is implicitly represented by the zero level set. 2. Drag the sampled points deviated from the target boundary to the desired position. 3. Using cubic B-spline function to interpolate the final boundary instead of the linear interpolation.
Fig. 3. The uniformly expanded boundary (outside one) used for the constraint of the next slice.
36
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
Fig. 4. The results obtained with different seed points and initial circles: (a) original image; (b) –(d) seed points and initial circles; (e) manual result; (f)– (h) results corresponding to (b)– (d).
4. Experimental results In this section, some examples are given to illustrate the efficiency and robustness of the proposed method for the segmentation of lymph nodes in approximately 400 CT images. First, we applied the method to 2D images with different seed points and initial circles. Some of the results are shown in Figs. 4 –6. The corresponding lymph node boundaries delineated manually by a radiologist are also shown for
comparison. In these examples, all of the parameters are identical, i.e. a ¼ 0:2; mI and sI are calculated from intensities of a 11 £ 11 window centered at the seed point From these results, we can see that although the image quality is quite poor, the proposed approach successfully and robustly detects most of the desired lymph node boundaries. In our experiments, most of the final advancing fronts did not need to be adjusted. Few final advancing fronts requested adjustment, but only one or two sampled points on them had such a need.
Fig. 5. The results obtained with different seed points and initial circles: (a) original image; (b) –(d) seed points and initial circles; (e) manual result; (f)– (h) results corresponding to (b)– (d).
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
37
Fig. 6. The results obtained with different seed points and initial circles: (a) original image; (b) –(d) seed points and initial circles; (e) manual result; (f)–(h) results corresponding to (b)–(d).
The proposed approach was then applied to sequential images containing lymph node tissue. One of these results is shown in Fig. 7. In this example, the parameter a is 0.2. mI and sI are calculated from the intensities of the lymph node region segmented in the neighboring slices. The seed point is estimated from the geometric center of the boundary obtained in the neighboring slice. Fig. 7c – f show that the proposed method obtains the desired lymph node boundaries. From these experiments, we can also see that
using the information between neighboring slices can effectively enhance the likelihood of automation for the sequential image segmentation.
5. Conclusions Based on the analysis of the existing problems in applying the traditional fast marching method to lymph
Fig. 7. The results of a sequential images: (a) the seed point and initial circle for the first image; (b) the result obtained from (a); (c) –(f) results obtained with sequential stop criteria proposed in this paper.
38
J. Yan et al. / Computerized Medical Imaging and Graphics 28 (2004) 33–38
node segmentation on CT images, the information of target region is incorporated into its speed term. This can better ensure that the advancing front moves from the seed point within the target region The proposed hard constraint for the stop criteria can effectively stop the advancing front near the target lymph node boundary. All of the experiments and comparisons show that the proposed approach allows for a fast and effective detection of lymph node boundary in CT images.
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Jiayong Yan was born in 1975. He received BS in Biomedical Engineering from Xi’an Jiao tong University, China in 1998. He is currently a PhD candidate in Biomedical Engineering from Shanghai Jiao tong University, China. His research interests include medical image processing and ultrasound tumor treatment.
Tian-ge Zhuang is a professor of Biomedical Engineering in Shanghai Jiao tong University, Shanghai, China. He graduated from the Department of Electric Engineering in Jiao tong University, Shanghai China in 1957. From 1957 to 1979, he was working in the Department of EE and the Department Radio Engineering, both in Xi’an Jiao tong University. He transferred to Shanghai Jiao tong University in 1979 and has been in the Biomedical Engineering Department since then. From 1980 to 1982, he was a visiting scholar in the Biomedical Computer Laboratory, Washington University, St Louis, MO. From September 1993 to February 1994, he was a senior visiting scholar in the Medical Image Processing Group University of Pennsylvania. He has published more than 80 papers and is the author of three books: Fundamentals of Computer Tomography and Algorithms (1992), Applications of Computers in Biomedicine (1991), Applications of Computers in Biomedicine (2000, new edition). He is also the chief translator of the book: ’Radiological Imaging’ (by H.H. Barrett) from English to Chinese (1988). His research area spans from ‘Theory and Application of Computed Tomography’ to ‘Computer Assisted Surgery’ and ‘Picture Archiving and Communication System’. He is the senior member IEEE, and is the vice Chairman of ‘the Biomedical Information & Cybenetics Society of the Chinese Society of Biomedical Engineering’, the member of board of ‘The Biomedical Electronic Society of the Chinese Institute of Electronics’, the member of board of ‘the Society of All China Computed Tomography’. He has been the Chairman of the Department of Biomedical Engineering and the vice dean of the College of Life Sciences and Biotechnology, Shanghai Jiao tong University.
Binsheng Zhao received BS and MS in Electronic Engineering from National University of Defense Technology, China in 1984 and 1987 respectively and DSc from University of Heidelberg, Germany in 1994. She is currently an Assistant Attending Physicist in the Departments of Medical Physics and Radiology at Memorial Sloan-Kettering Cancer Center, New York. She has been working on development of advanced CT image processing algorithms for computer-aided detection and diagnosis (CAD) of lung cancer since 1997. Her research interests also include CAD developments for liver and lymph node metastases.
Lawrence H. Schwartz, MD, is an Associate Attending Radiologist and Director of the Laboratory for Computational Image Analysis in Radiology Department, Memorial Sloan-Kettering Cancer Center, New York. He has extensive experience in clinical trials in oncology, with conventional and novel imaging modalities. His interests include hepatobiliary imaging, medical informatics/PACS as well as therapeutic response assessment.