Proceedings of the 29th Annual International Conference of the IEEE EMBS Cité Internationale, Lyon, France August 23-26, 2007.
ThP2B3.6
Airway Segmentation and Measurement in CT Images Irene Cheng, Sharmin Nilufar, Carlos Flores-Mir and Anup Basu, Senior Member, IEEE Abstract—In this paper we describe a methodology for constructing the airways from Cone Beam CT data and representing changes before and after a medical procedure. A seed region is automatically detected for the first CT slice using a heuristic algorithm incorporating morphological filtering. Our approach then extracts relevant contours on 3D slices by using gradient vector flow (GVF) snakes, modified by an edge detection and snake-shifting step. Following this, a 3D model is constructed. We then estimate the volume of the airway based on segmented 3D shape.
I. INTRODUCTION Medical imaging modalities can be broadly categorized into two classes: anatomical modalities and functional modalities. Anatomical modalities that describe the structure of organism include X-ray, CT-scans, magnetic resonance imaging (MRI), ultrasound, laparoscopy images and so on. Functional modalities provide physiological information, including positron emission tomography (PET), functional MRI (fMRI), electro encephalography (EEG), magneto encephalography (MEG) and so on [13, 20]. CBCT (cone beam computer tomography) is a newly developed technology that comes as an improvement over conventional CT for maxillofacial imaging. The improvements are related to scanning time, radiation dose, and efficiency in the number of images taken. Besides the obvious application for diagnosis of hard tissue alterations the quality of the images generated (definition) and the possibility of changing the contrast or brightness of the images allows the evaluation of soft tissue characteristics. Currently this technology is used to evaluate bone characteristics, presence of tumors or lesions, three-dimensional location of structures and its relationship with surrounding tissues, tooth positioning and root length, etc. Future use in dentistry is also foreseen for upper airway characteristics and measuring soft tissue profile changes during treatment. Medical image registration technique can be divided into four different approaches: control-point based registration, moment based registration, contour based registration, and optimization based registration [13]. In control-point based registration, a number of landmarks that usually define a set of unique features of images are used for the registration process. The registration process can be manual, semi-automatic or automatic. Although this registration process is very easy and fast, provision to add markers must be made in the pre-acquisition phase. Markers can be invasive or noninvasive. Non-invasive markers are relatively less accurate than the invasive markers. Invasive markers are used by several authors for satisfactory and fast registration of medical images [11, 18, 22]. Manuscript received April 2, 2007, accepted June 7, 2007. This work was supported in part by ASRA, iCORE from Alberta and NSERC, CANADA. Irene Cheng is an NSERC Research Fellow at the Computer and Information Sciences Department, University of Pennsylvania, email:
[email protected]. Sharmin Nilufar and Anup Basu are with the department of Computing Science, University of Alberta, email: {sharmin, anup}@cs.ualberta.ca. Carlos Flores-Mir is with the Graduate Orthodontic Department at the University of Alberta, email:
[email protected].
1-4244-0788-5/07/$20.00 ©2007 IEEE
Among the non-invasive techniques the most widely used markers are glued to the skin [17, 19]. Moment based methods are reductive registration methods where the image center of gravity and its principal axes are calculated from the zero-th and first order moments. Then, the center of gravity and the principal orientations are aligned to obtain the registration. The results obtained with this method are not very robust and precise, and the application is usually limited to matching simple objects in image pairs [6]. Contour based registration methods usually give good results for the registration of images with prominent edges or contours. Significant preprocessing is required to extract contour of images. Many different methods can be applied to extract edge or contour; for example, template matching, active contour model, zero crossings, and so on. Minimizing mean square error (MSE) and comparing intensity values of edge pixels is frequently used to match contours. Feature characteristics like location, edge strength and orientation are taken into account to compute a joint probability distribution of corresponding edge points in two images [1, 5, 7, 8, 14, 23]. Optimization based registration of images is achieved by optimizing a similarity criterion, such as a correlation coefficient, a correlation function, a sum of absolute differences or correlation information entropy. This method is usually used widely for monomodal images. Since the pixel intensity values are usually not related in different modalities it is not very helpful for registering the images from separate modalities [12]. Recently several improved optimization methods are proposed for multimodal image registration [10, 13, 27]. Several research methodologies have been proposed for airway segmentation and measurement on different image modalities especially on CT and MRI images. Most of these methods focus on the segmentation and reconstruction of lower airway trees. Sonka et al. [25] proposed a method which combines conventional threedimensional seed region growing with rule-based two-dimensional segmentation to segment airway trees from three-dimensional sets of CT images. Aykac et al. [2] proposed a fully automatic method for segmentation and analysis of airway tree in CT images of the thorax. A grayscale morphological reconstruction technique is applied to identify candidate airways on CT slices. Finally, bounded space dilation is used to label connected airways and construct 3-D airway tree. A robust method for lower airway segmentation based on fuzzy connectivity is presented in [26] by Tschirren et al. In this method small adaptive regions of interest are employed which follow the airway branches during segmentation. This method works on various types of CT-scans without any need for manual adjustment of any parameter. The algorithm consists of segmentation of airway tree, its skeletonization, and identification of the airway. Segmentation on the basis of multi CT image of the lung is describes by Miki el al. [21], where a region growing method is used to extract airway lumen. At the starting point of trachea in CT images, a grayscale intensity specific to a tissue of the airway wall was determined and supplied to subsequent CT images to trace and construct a 3-D airway model of the airway tree. Finally, the 3-D airway model was skeletonized to identify the branching of airway. Zhou et al. [30] described a segmentation algorithm of lungs, airway of bronchus, lung lobes and fissures based on the anatomical structures and statistical intensity distributions in CT images. The segmentation process used here is based on the recursive region-
795
splitting process. A dynamic parameter optimization technique is proposed to enhance the compatibility and robustness of the segmentation system for different CT images. Although numerous methods have been proposed for upper airway segmentation there is a lack of effective research work to routinely quantify and analyze upper airways with the CT and MR imaging protocols. Only few researchers focus on the segmentation of upper airway. Liu et al. [16] performed a study to diagnose upper airway disorders in children by delineating the upper airway and surrounding structures with magnetic resonance (MR) imaging. A fuzzy connectedness framework is chosen for the segmentation. This method first specifies a local fuzzy relation on voxels called “affinity.” This fuzzy relation indicates how the voxels hang together locally within the scene in the object of interest. Finally, fuzzy connectedness is a global fuzzy relation that decides how the voxels dangle together globally in the scene to form the object. Shi et al. [24] applied a simple gray scale thresholding based method within a defined region of interest to segment and measure the upper airway using cone-beam computed tomography (CBCT). We propose an approach for tracking the contour of the airway by using Gradient Vector Flow (GVF) snakes and using the contour of an adjacent CT slice to track the current slice. The usual GVF algorithm is modified by adding edge detection and snake-shifting steps, to work robustly for our problem. Following this step, we consider measuring the airway volume at different points in time, possibly before and after a medical procedure The remainder of this report is organized as follows: Section 2 describes a strategy for airway CT contour tracking using snakes. Results of the airway contour detection and tracking is discussed in Section 3. In Section 4 we discuss how the tracked contours can be used for 3D volume visualization and measurement. Section 5 provides concluding remarks and an outline of future research. II. TRACKING AIRWAY CONTOUR We used an active contour model to detect the boundary of slices of the upper airway. To segment the upper airway from CT slices we use GVF snake proposed by Xu and Prince [28, 29]. Traditional GVF snake potentials do not work well for airway segmentation in CT images. We thus modify the GVF snake by adding edge detection and snake shifting techniques that used prior knowledge of the application domain. A. Gradient Vector Flow Snake A snake or active
contour
X ( s ) = [ x( s ), y ( s )], s ∈ [0,1] ,
is
a
curve
which moves through the
spatial domain of an image under the influence of image forces. The two major limitations of traditional snakes related to the contour initialization and poor convergence to concave boundaries were overcome by introducing the concept of GVF snake. In GVF snake a new static external force field was introduced which replaced the standard external force field in the traditional snake. The new static external force is called gradient vector flow force and is defined (g)
by Fext
= V ( x, y ) , which does not change with time or depend
on the position of the snake itself. The GVF snake can be represented by following equation:
xt ( s, t ) = αx ′′( s ) − β x ′′′( s ) + V The first term represents the internal energy, which is composed of a first-order continuity term and a second-order continuity term. The first-order term has larger values where there is a discontinuity in the curve, and the second-order curvature term is large where the
curve has a sharp bend. The values of
α
and
β
at a point, control
the stretching and bending of the contour at that point. If
α =0
at
a point, the snakes become first order discontinuous and if β = 0 the second order discontinuity can occur and a corner is developed. The parametric curve solving the above dynamic equation is termed a GVF snake. Standard numerical methods can be used to solve for this equation and yield the GVF snake. The gradient vector flow field is defined as the vector field V ( x, y ) = (u ( x, y ), v( x, y )) that minimizes the following energy functional:
E = ∫∫ µ (u x2 + u y2 + v x2 + v 2y ) + ∇f
2
2
v − ∇f dxdy
Where f(x,y) is the edge map of the image. The parameter µ is a regularizing parameter that adjusts the tradeoff between the first and second terms of the integrand and is set according to the level of noise present in the image. Also, when the value of the edge gradient is small, energy is dominated by the sum of the partial derivatives of the gradient field. When the gradient is large, the second term dominates. B. Edge Detection The CT slices we acquired usually have very low contrast. Thus, applying GVF snake directly to CT images leads to poor segmentation results. We apply edge detection before applying snakes to CT images (Figure 1). Several edge detection techniques were applied and the best result was obtained using Prewitt edge detection. Canny edge detection technique, which is used with snake in [15] to obtain liver segmentation in CT images, performs worst amongst all the edge detection algorithms in our case. The Prewitt method finds edges using the Prewitt approximation to the derivative. It returns edges at those points where the gradient of the image has a local maxima. On the other hand, Canny edge detection finds edges by looking for local maxima of the gradient of the image. The gradient is calculated using the derivative of a Gaussian filter. To detect strong and weak edges, two different thresholds are used in Canny edge detection. Although this method can detect true weak edges, it is very sensitive to noise. For Prewitt method we found that it can substantially reduce the number of inadequate snake attractors (noisy and weak edges) for the sensitivity threshold of 0.01. In Canny edge detection, it is very difficult to find an optimum threshold value which can perform equally well for all CT slices. Since this method includes the weak edges in the output which are connected to strong edges, it needs further modification as proposed in [15]. C. Snake Initialization The application of active contour models requires manual initialization. We used the prior knowledge of the shape of airway to automatically detect the airway in first slice of the CT image set. The contour detections for the next slices are also performed automatically. The detected contour of the first slice is used for the initial contour for the second slice and so on. D. Snake Propagation with Snake Shifting We use snake propagation technique to detect contour from 3-D CT images. If the inter-slice distance between two CT slices is large, the change of the relative airway position can be significant. As a result, during the snake propagation, it is possible that the initial contour of
796
one slice, which is obtained from the previous slice, may be located far away from the target object. In this situation the snake can be attracted by other closer objects with strong edge outside the airway area. Here we propose a shifting technique that uses prior knowledge of airway CT slices. The bones located very close to the airway causes problems with convergence. We can easily differentiate bones from the airway by its color. A simple heuristic is applied here to solve this problem. After detecting the final contour from each slice we detect the color of the segmented object and apply a threshold gray scale value to differentiate these two objects. If the snake detects the object outside the airway area then we simply shift the initial contour upward by n pixels, where n is the number of overlapping pixels in the vertical direction (Figure 4 left). In most of the cases the snake converges properly and segments the airway area after shifting the snake 5 pixels upward.
snake convergence, using the snake shifting method. Figure 5 shows various contours detected for different CT slices.
Figure 2: Normalized graph cut based segmentation with 10 regions (left) and 15 regions (middle); (Right) seed detected using our heuristic algorithm incorporating morphological filtering.
Figure 1: (Left) a CT slice; (middle) Prewitt edges; (right) Canny edges. III. AIRWAY CONTOUR DETECTION RESULTS Our algorithm was tested on a database consisting of 40 image slices obtained from a patient before and after surgery. These before and after slices represent similar airway positions, with the start and end slices in both cases (before and after) being carefully selected by clinical experts. Each slice is 412 x 412 pixels, with pixel size equal to 3.527 mm x 3.527 mm. The inter-slice distance is 2.5 mm. Images are stored in the Digital Imaging and Communications in Medicine (DICOM) format. A DICOM file contains a header, which stores information about the patient’s name, the type of scan, and image dimension. All the slices are converted into a PGM (Portable Gray Map) format which is more suitable for easier processing. The header information of the PGM provides the file type (ASCII or binary), the size of the image pixel matrix, and the gray level. All experiments are carried out in MATLAB 7. The basic Matlab programs of GVF snake are downloaded from the author’s website and modified to get the best result for CT image slices. Several parameters of the GVF active contour model such as elasticity, rigidity, viscosity and external force weight are adjusted to obtain the best result for upper airway segmentation. The seed detection program first detects dark regions, which include airways and the background. We then clean up noise and perform morphological opening operation to remove small dark regions. Finally, the inside dark region is detected and the background is deleted to create the initial seed (Figure 3, left). Our technique detects the initial seed around the airway, and starting with this seed a GVF based algorithm and easily detect the first slice contour accurately. We considered using segmentation algorithms to help detect the initial airway contour. However, even advanced segmentation algorithms do not seem to work very well in detecting the airway regions as one of the segments. For example, the results of a recent normalized graph cuts based [4] algorithm is shown in Figure 2. Clearly, the 10 and 15 segments detected with this algorithm do not seem to localize the airway region very well. Improved Result using Snake shifting Figure 4 (left) shows a problem with the convergences of GVF snake when the bone located very close to the airway attracts the snake towards it. Figure 4 (right) shows the improvement in the
Figure 3: (Left) Seed, white region, detected using our heuristic algorithm; (Right) convergence of GVF snake starting with the boundary of the seed on the left.
Figure 4: (Left) Detected contour before snake shifting; (right) after shifting snake by 5 pixels.
Figure 5: Examples of some of the critical contours of airway images detected by GVF snake. The result of our contour detection method on airway CT images is evaluated for accuracy. We define the accuracy as the relative number of acceptable contours of the airway CT slices that can be detected in an assessment. Medical expertise is needed to assess the contours that are obtained by our method. An orthodontist skilled in radiotherapy planning was asked to accept or reject the contours detected for the 40 CT slices. For the given dataset, all the contours detected by our approach were considered to be acceptable. IV. AIRWAY VOLUME VISUALIZATION AND MEASUREMENT We considered visualization of the contours detected for better understanding of the shape of the airways. Figure 6 shows the airways seen from different viewing angles.
797
TABLE II: Airway volumes between CT slices Slice #s Vol. Before Vol. After 1-2 7,964.16 23,957.23 2-3 8,484.09 21,136.85 3-4 10,719.08 18,746.31 4-5 12,879.43 18,062.16 5-6 13,542.76 18,538.23 6-7 12,250.51 18,907.96 7-8 10,877.78 17,564.56 8-9 9,613.66 15,541.14 9-10 9,294.45 13,820.83 10-11 9,815.87 12,064.94 11-12 9,378.79 10,334.02 12-13 8,191.26 9,227.13 13-14 7,305.50 9,437.98 14-15 7,352.24 10,854.49 15-16 8,060.90 12,276.48 16-17 8,744.78 12,889.85 17-18 9,607.10 13,120.03 18-19 10,282.20 13,788.14 19-20 10,938.06 15,148.18 Total Volume 185,302.60 285,416.49
(Left view) After (top) before (bottom) (Right) After (top) before (bottom)
Figure 6: Visualization of airways based on automatically detected contours. Volume measurement techniques have been used in the medical imaging community as early as in the 1950s [3]. We would like to look into the effect of airway volume on breathing in future clinical studies, and are thus investigating techniques of accurate volume measurement with a minimum amount of user intervention. Table I shows the areas of the different CT contours that were detected automatically using the vector flow tracking method described before. TABLE I: Areas of Airway in CT slices Contour No. Before (mm2) After (mm2) 1 3,556.32 10,002.40 2 2,828.86 9,169.42 3 3,991.70 7,759.66 4 4,590.54 7,240.39 5 5,734.19 7,209.35 6 5,106.09 7,623.16 7 4,697.17 7,503.37 8 4,014.00 6,558.86 9 3,679.36 5,880.22 10 3,756.34 5,183.76 11 4,098.85 4,476.83 12 3,414.59 3,799.64 13 3,140.33 3,583.12 14 2,709.37 3,970.58 15 3,178.67 4,723.91 16 3,270.27 5,099.67 17 3,730.60 5,212.42 18 3,956.18 5,283.69 19 4,271.60 5,750.11 20 4,915.99 6,373.78 If we consider the average area between two consecutive slices, and multiply by the distance (2.5 mm) between them, then the airway volume from the before sequence is 186,012.1 mm3 and for the after sequence it is 285,540.6 mm3. However, this approximation may not be accurate, especially when two consecutive slices have areas that are not very close. In this case, a more accurate estimate of the volume can be derived assuming a locally conical shape between two consecutive CT slices (Figure 7). Under this assumption, the volume of a segment can be estimated as:
Figure 7: Approximating volume of an airway CT slice. To calculate h, we further assume circular regions, with: 2
Ai = π × ri ; or , ri =
Ai ; i = 1,2 π
Using similar triangles (Figure 8) it can be shown that:
h=
r1 × ST ( r1 − r2 )
From this it follows that the volume between two consecutive CT slices is equal to:
1 r1 × ST {( A1 − A 2 ) + ST × A 2 } 3 ( r1 − r2 )
1 1 1 1 hA1 − ( h − ST ) A2 = h ( A1 − A 2 ) + h × ST × A 2 3 3 3 3 Where: A1: Larger area; A2: Smaller area; ST: Distance between two consecutive CT slices; h: Height of cone assuming A1 and A2 are areas of two consecutive slices. Figures 7 & 8 shows the interpretation of these terms.
Figure 8: Similar triangles for deriving h.
798
From Table II it can be seen that the airway volumes assuming locally conical shapes are 185,302.60 mm3 and 285,416.49 mm3, which are very close to the approximate volumes calculated earlier. This shows that when the distance between CT slices is sufficiently small, a simple approximation may be sufficient for computing volumes. V. CONCLUSION AND FUTURE WORK In this work we described a method for segmentation of airways using cone beam CT images, and measuring the volume of airways. The method proposed is completely automatic, based on heuristics to localize a seed on the initial contour followed by contour detection and tracking for adjacent CT slices. In future work, we need to generalize the approach considering other acquisition techniques, such as MRI, since airway volume may be sensitive to the breathing phase. We will reduce the inter-slice distance to 0.5 mm or smaller for higher precision. Exact measurements with a phantom head including airways will be used to have precise ground truth for comparison.
ACKNOWLEDGMENT The authors acknowledge the support of Chris Kerr in the implementations.
REFERENCES [1] N. A. Álvarez, J. M. Sanchiz, J. Badenas, F. Pla and G. Casañ, “Contour Based Image Registration using Mutual Information,” Pattern Recognition and Image Analysis, vol. 3522, pp. 227-234, 2005. [2] D. Aykac, E.A. Hoffman, G. McLennan J.M. Reinhardt, “Segmentation and Analysis of the Human Airway Tree From Three-Dimensional X-Ray CT Images,” IEEE Transaction of Medical Imaging, Volume 22 Issue 8 August 2003. [3] C.B. Chapman, O. Baker, J. Reynolds and F.J. Bonte, “Use of biplane cinefluorography for measurement of ventricular volume,” Circulation: Journal of the American Heart Association, pp. 1105-1117, Dec. 1958. [4] T. Cour, F. Benezit and J. Shi, “Spectral Segmentation with Multiscale Graph Decomposition,” Proceedings of the IEEE Computer Vision and Pattern Recognition Conference, 2005. [5] C. Davatzikos, J. L. Prince and R. N. Bryan, “Brain Image Registration Based on Cortical Contour Mapping,” Nuclear Science Symposium and Medical Imaging Conference, vol. 3, pp. 1823-1826, 1993. [6] G.J. Ettinger, W.E.L. Grimson and T. Lozano-Perez, “Automatic 3D Image Registration for Medical Change Detection Applications,” Applications of Computer Vision in Medical Image Processing, AAAI spring symposium series, pp. 182–185, 1994. [7] B. Fischer and J. Modersitzki, “Curvature Based Image Registration,” Journal of Matematical. Imaging and Vision. Vol. 18, no.1, 81-85, 2003. [8] P. Gut, L. Chmielewsk, P. Kukolowicz and A. Dabrowsk, “Edge-Based Robust Image Registration for Incomplete and Partly Erroneous Data,” Proceedings of the 9th International Conference on Computer Analysis of Images and Patterns, pp. 309 - 316, 2001. [9] M. Garland and P. Heckbert, “Simplification using Quadric Error Metrics,” SIGGRAPH, pp. 209-216, 1997. [10] S. Henn, “A Full Curvature Based Algorithm for Image Registration,” Journal of Mathematical Imaging and Vision, vol. 24, no. 2, pp.195 – 208, 2006. [11] P. Hemler, T. Sumanaweera, R. Pichumani, P. A. Elsen, S. Napel, J. Drace, and J. Adler, “A System for Multimodality Image Fusion of the
Spine,” Applications of Computer Vision in Medical Image Processing, Spring Symposium Series, Stanford, California, March 1994. [12] J. Jin, Q. Wang and Y. Shen, “Global Optimization of Medical Image Registration Based on Nonlinear Correlation Measurement,” Proceedings of the IEEE Engineering in Medicine and Biology Society Conference, Shanghai, China, 2005. [13] K. Kneöaurek, M. Ivanovic, J. Machac and D. A. Weber, “Medical Image Registration,” USA Europhysics News, vol. 31, no. 4, 2000. [14] C. Liu, K. Li and Z. Liu, “Medical Image Registration by Maximization of Combined Mutual Information and Edge Correlative Deviation,” Proceedings of the IEEE Engineering in Medicine and Biology Society Conference, Shanghai, China, September, 2005. [15] F. Liu, B. Zhao, P.K. Kijewski, L. Wang and L.H. Schwartz “Liver segmentation for CT images using GVF snake,” Medical Physics, volume 32, Issue 12 pp 3699-706, December, 2005 [16] Liu J., Udupa J K, Odhnera D, McDonough J M, Arens R. “System for Upper Airway Segmentation and Measurement with MR Imaging and Fuzzy Connectedness,” Academic Radiology, Volume 10, Issue 1, Pages 13-24 January 2003 [17] C. R. Maurer, G. B. Aboutanos, B. M. Dawant, R. J. Maciunas and J. M. Fitzpatrick, “Registration of 3-D Images Using Weighted Geometrical Features,” IEEE Transactions on Medical Imaging, vol.15, no.6, pp.836849, 1996. [18] C. R. Maurer, J. M. Fitzpatrick, R. L. Galloway, M. Y. Wang, R. J. Maciunas and G. S. Allen, “The Accuracy of Image Guided Neurosurgery using Implantable Fiducial Markers,” Computer Assisted Radiology, pp.1197-1202, 1995. [19] G. Q. Maguire, M. Noz, H. Rusinek, J. Jaeger, E. L. Kramer, J. J. Sanger and G. Smith, “Graphics Applied to Medical Image Registration,” IEEE Computer Graphics and Applications, vol.11, no.2, pp. 20–28, 1991. [20] J. B. A. Maintz and M. A. Viergever, “A Survey of Medical Image Registration,” Medical Image Analysis, vol. 2, no.1, pp. 1–37, Oxford University Press, 1998. [21] T. Miki, S. Wada, M. Nakamura, K. Tsubota, T. Yamaguchi, Y. Suda and G. Tamura, “Computer-aided segmentation and quantification of the human airway tree on the basis of multi CT images,” Journal of Biomechanics, Vol. 39, Supplement 1, 2006. [22] T. Peters, B. Davey, P. Munger, and R. Comeau, A. Evans and A. Olivier. “Three-Dimensional Multimodal Image-Guidance for Neurosurgery,” IEEE Transactions on Medical Imaging, vol.15, no.2, pp.121-128, 1996. [23] R. Rosas-Romero, J. Rodriguez-Asomoza, V. Alarcon-Aquino, D. Baez-Lopez, “Multi-Modal Medical Image Registration Based on Non-Rigid Transformations and Feature Point Extraction by using Wavelets,” IEEE Conference on Instrumentation and Measurement Technology, vol. 1, pp. 763-766, 2004. [24] H. Shi, W.C. Scarfe and A.G. Farman, “Upper airway segmentation and dimensions estimation from cone-beam CT image datasets,” International Journal of Computer Assisted Radiology and Surgery, Volume 1, November, 2006 [25] M. Sonka, W. Park, E.A. Hoffman, “Rule-based detection of intrathoracic airway trees,” IEEE Trans. on Med. Imaging, 1996; vol. 15:314–326. [26] J. Tschirren, E.A. Hoffman, G. McLennan and M. Sonka, “Intrathoracic Airway Trees: Segmentation and Airway Morphology Analysis From LowDose CT Scans,” IEEE Trans. on Medical Imaging, Vol. 24, Issue. 12, December 2005. [27] M. P. Wachowiak and T. M. Peters, “High-Performance Medical Image Registration Using New Optimization Techniques,” IEEE Transactions on Information Technology in Biomedicine, vol. 10, no.2, pp. 344- 353 April, 2006. [28] C. Xu and J.L. Prince, “Gradient Vector Flow: A New External Force for Snakes,” Proc. IEEE Conf. on Comp. Vis. Pattern Recognition (CVPR), Los Alamitos: Comp. Soc. Press, pp. 66-71, June 1997. [29] C. Xu and J.L. Prince, “Snakes, Shapes, and Gradient Vector Flow,” IEEE Transactions on Image Processing, 7(3), pp. 359-369, March 1998. [30] X. Zhou, T. Hayashi, T. Hara, H. Fujita, R. Yokoyama, T. Kiryu and H. Hoshi, “Automatic segmentation and recognition of anatomical lung structures from high-resolution chest CT images,” Computerized Medical Imaging and Graphics, Volume 30, Issue 5Pages 299-313, July 2006.
799
