||Model Based Motion Estimation in Medical Image Sequences
||Institute of Computer Science and Information Engineering
cellular microscopic images
Motion analysis is very useful for recognizing target patterns from a sequence of images. Applications in motion estimation and target tracking become especially important in medical and biomedical researches nowadays. However, traditional methods which are optimal for rigid body motion are not suitable for medical analysis due to the object deformation and noise problems. In this study, we tried to propose adequate motion estimation methods for several medical motion applications which include motion field estimation from ultrasound images, tag line tracking from tagged magnetic resonance (MR) images, and live cell tracking from microscopic images.
Generally, the usual problems in medical motion analysis include: speckle noises and temporal de-correlation of the speckle patterns in ultrasound images; large motion and tag decaying problems in tagged MR images; and low contrast in pseudopods and topological changes in cellular microscopic images. To overcome these problems, it is necessary to integrate a priori knowledge based on the physical properties into the motion estimation process. In this study, we first designed a hierarchical maximum a posteriori estimator together with an ultrasonic feature model for ultrasound image sequences. A motion compounding method is also proposed to reduce speckle noises and to enhance image quality based on the proposed motion estimation method. To cope with the problems of large motion and tag decaying, we proposed to incorporate a cardiac motion model based prediction scheme and a candidate pre-screening technique together with the deformable models to track the tag lines. To segment and track highly deformable cells, we have presented an automatic method based on the framework of modified T-snakes coupled with the knowledge of cellular life model.
The proposed motion estimation methods were compared with several existing methods via a series of experiments with both simulated and clinical image sequences. Experimental results showed that motion could be accurately assessed in different types of imaging modalities. The proposed systems can help to perform better quantification and analyses in clinical applications. It will certainly help medical doctors to achieve better observation and more accurate assessments, and thus result in better diagnostic quality.
CHAPTER 1 INTRODUCTION 1
1.1 Motivation 1
1.2 Background and Related Works 4
1.2.1 Motion Analysis in Ultrasound Images 4
1.2.2 Cardiac Motion Analysis in Tagged MR Images 6
1.2.3 Cellular Motion Analysis in Microscopic Images 7
1.3 Overview of the Proposed Method and Thesis Organization 9
CHAPTER 2 HIERARCHICAL FEATURE WEIGHTED MOTION ESTIMATION AND MOTION COMPOUNDING 11
2.1 Overview 11
2.2 Block-Matching Algorithm and Maximum Likelihood Motion Estimation 12
2.3 Maximum A Posteriori (MAP) Motion Estimation 17
2.4 Hierarchical MAP Motion Estimation 18
2.5 Vector Post-Processing Using Adaptive Feature Weighted Filtering 22
2.6 Motion Compounding 27
CHAPTER 3 MOTION MODEL BASED TAG LINE TRACKING 32
3.1 Overview 32
3.2 Preprocessing 32
3.3 Active Contour Model for Tag Line Tracking 36
3.4 Temporal Prediction Using Motion Model 38
3.5 Candidate Pre-Screening 41
3.6 Strain Analysis and Visualization 42
CHAPTER 4 LIVE CELL TRACKING BASED ON CELLULAR STATE RECOGNITION 44
4.1 Overview 44
4.2 Preprocessing 46
4.3 T-Snake 49
4.4 Recognition of Cellular State 52
4.5 Division Operator 57
CHAPTER 5 EXPERIMENTAL RESULTS 60
5.1 Motion Estimation Results in Ultrasound Images 60
5.1.1 Synthetic Experiments 60
5.1.2 Clinical Experiments 69
5.2 Motion Compounding Results in Ultrasound Images 73
5.2.1 Motion-Simulated Phantom Experiments 73
5.3.2 Clinical Experiments 76
5.3 Motion Estimation Results in Tagged MR Images 84
5.3.1 Motion-Simulated Phantom Experiments 84
5.3.2 Clinical Experiments 85
5.4 Motion Estimation Results in Cell Tracking from Microscopic Images 87
CHAPTER 6 DISCUSSION 97
6.1 Hierarchical Feature Weighted Motion Estimation and Motion Compounding 97
6.2 Motion Model Based Tag Line Tracking 99
6.3 Live Cell Tracking Based on Cellular State Recognition 102
CHAPTER 7 CONCLUSION 104
 B.K.P. Horn and B.G. Schunck, “Determining optical flow,” Artif. Intell., vol. 17, pp. 185-203, 1981.
 H.S. Wang and R.M. Mersereau, “Fast algorithms for the estimation of motion vectors,” IEEE Trans. Image Process., vol. 8, no. 3, pp. 435-438, 1999.
 H. Gu, Y. Shirai, and M. Asada, “MDL-based segmentation and motion modeling in a long image sequence of scene with multiple independently moving objects,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 18, no. 1, pp. 58-64, 1996.
 M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis., vol. 1, no. 4, pp. 321-331, 1988.
 L. Gao, K.J. Parker, R.M. Lerner, and Levinson SF, “Imaging of the elastic properties of tissue–a review,” Ultrasound Med. Biol., vo. 22, no. 8, pp. 959-977, 1996.
 I.A. Hein and W.D. O’Brien, “Current time-domain methods for assessing tissue motion by analysis from reflected ultrasound echoes–a review,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 40, no. 2, pp. 84-102, 1993.
 G.E. Mailloux, F. Langlois, P.Y. Simard, and M. Bertrand, “Restoration of the velocity field of the heart from two-dimensional echocardiograms,” IEEE Trans. Med. Imaging, vol. 8, no. 2, pp. 143-153, 1989.
 A.J. Healey and S. Leeman, “Speckle reduction methods in ultrasound pulse-echo imaging,” in IEE Proc. of Acoustic Sensing and Imaging, pp. 68-76, 1993.
 A.N. Evans and M.S. Nixon, “Mode filtering to reduce ultrasound speckle for feature extraction,” in IEE Proc. of Vision, Image and Signal Processing, vol. 142, no. 2, pp. 87-94, 1995.
 M.A. Guttman, E.A. Zerhouni, and E.R. McVeigh, “Analysis of cardiac function from MR images,” IEEE Comput. Graph Appl., vol. 17, no.1, pp. 30-38, 1997.
 H.B. Hillenbrand, J.A.C. Lima, D.A. Bluemke, G.M. Beache, and E.R. McVeigh, “Assessment of myocardial systolic function by tagged magnetic resonance imaging,” J. Cardiov. Magn. Reson., vol. 2, no. 1, pp. 57-66, 2000.
 J.C.M. Mombach and J.A. Glazier, “Single cell motion in aggregates of embryonic cells,” Phys. Rev. Lett., vol. 76, pp. 3032-3035, 1996.
 J.P. Rieu, N. Kataoka, and Y. Sawada, “Quantitative analysis of cell motion during sorting in two-dimensional aggregates of dissociated hydra cells,” Phys. Rev. E, vol. 57, pp. 924-931, 1998.
 J.H.C. Wang, P. Goldschmidt-Clermont, J. Wille, and F.C.P. Yin, “Specificity of endothelial cell reorientation in response to cyclic mechanical stretching,” J. Biomech., vol. 34, pp. 1563-1572, 2001.
 N. Bonnet, M. Matos, M. Polette, J.M. Zahm, B. Nawrocki-Raby, and P. Birembaut, “A density-based cellular automaton model for studying the clustering of noninvasive cells,” IEEE Trans. Biomed. Eng., vol. 51, pp. 1274-1276, 2004.
 I. Patras, M. Worring, and R. van den Boomgaard, “Dense motion estimation using regularization constraints on local parametric models,” IEEE Trans. Image Process., vol. 13, no. 11, pp. 1432-1443, 2004.
 C. Bergeron and E. Dubois, “Gradient-based algorithms for block-oriented MAP estimation of motion and application to motion-compensated temporal interpolation,” IEEE Trans. Circuits Syst. Video Technol., vol.1, no. 1, pp. 72-85, 1992.
 C. Bouman and K. Sauer, “A generalized Gaussian image model for edge-preserving MAP estimation,” IEEE Trans. Image Process., vol. 2, no. 3, pp. 296-310, 1993.
 E.R. Davies, Machine vision: theory, algorithms, practicalities, 2nd edition, Academic Press, 1997.
 B.H. Friemel, L.N. Bohs, and G.E. Trahey, “Relative performance of two-dimensional speckle-tracking techniques: normalized correlation, non-normalized correlation and sum-absolute-difference,” in Proc. of IEEE Ultrasound Symposium, pp. 1481-1484, 1995.
 M.G. Strintzis and I. Kokkinidis, “Maximum likelihood motion estimation in ultrasound image sequences,” IEEE Signal Process. Lett., vol. 4, no. 6, pp. 156-157, 1997.
 B. Cohen and I. Dinstein, “New maximum likelihood motion estimation schemes for noisy ultrasound images,” Pattern Recognit., vol. 35, no. 2, pp. 455-463, 2002.
 A. Boukerroui, J. A. Noble, and M. Brady, “Velocity estimation in ultrasound images: a block matching approach,” in Proc. of 18th Information Processing in Medical Imaging, pp. 586-598, 2003.
 J. Revell, M. Mirmehdi, and D. McNally, “Ultrasound speckle tracking for strain estimation,” Technical Report CSTR-04-005, Dept. of Computer Science, Univ. of Bristol, 2003.
 J. Revell, M. Mirmehdi, and D. McNally, “Motion trajectories for ultrasound displacement quantification,” in Proc. of 7th Medical Image Understanding and Analysis, pp. 193-196, 2003.
 C. Pellot-Barakit, F. Frouin, M.F. Insana, and A. Herment, “Ultrasound elastography based on multiscale estimations of regularized displacement fields,” IEEE Trans. Med. Imaging, vol. 23, no. 2, pp. 153-163, 2004.
 F. Yeung, S.F. Levinson, and K.J. Parker, “Multilevel and motion model-based ultrasonic speckle tracking algorithms,” Ultrasound Med. Biol., vol. 24, no. 3, pp. 427-441, 1998.
 R.L. Maurice and M. Bertrand, “Lagrangian speckle model and tissue-motion estimation-theory,” IEEE Trans. Med. Imaging, vol. 18, no. 7, pp. 593-603, 1999.
 E.A. Zerhouni, D.M. Parish, W.J. Rogers, A. Yang, and E.P. Shapiro, “Human heart: tagging with MR imaging – a method for noninvasive assessment of myocardial motion,” Radiology, vol. 169, no. 1, pp. 59-63, 1988.
 L. Axel and L. Dougherty, “MR imaging of motion with spatial modulation of magnetization,” Radiology, vol. 171, no. 3, pp. 841-845, 1989.
 J.L. Prince and E.R. McVeigh, “Motion estimation from tagged MR image sequences,” IEEE Trans. Med. Imaging, vol. 11, no. 2, pp. 238-249, 1992.
 L. Dougherty, J.C. Asmuth, A.S. Blom, L. Axel, and R. Kumar, “Validation of an optical flow method for tag displacement estimation,” IEEE Trans. Med. Imaging, vol. 18, no. 4, pp. 359-63, 1999.
 T.S. Denney, “Estimation and detection of myocardial tags in MR image without user-defined myocardial contours,” IEEE Trans. Med. Imaging, vol. 18, no. 4, pp. 330-344, 1999.
 A.A. Amini, Y. Chen, R.W. Curwen, V. Mani, and J. Sun, “Coupled b-snake grids and constrained thin-plate splines for analysis of 2-D tissue deformations from tagged MRI,” IEEE Trans. Med. Imaging, vol. 17, no. 3, pp. 334-56, 1998.
 A.A. Amini, Y. Chen, M. Elayyadi, and P. Radeva, “Tag surface reconstruction and tracking of myocardial beads from SPAMM-MRI with parametric b-spline surfaces,” IEEE Trans Med. Imaging, vol. 20, no. 2, pp. 94-103, 2001.
 M. Stuber, E. Nagel, S.E. Fischer, M.A. Spiegel, M.B. Scheidegger, and P. Boesiger, “Quantification of the local heartwall motion by magnetic resonance myocardial tagging,” Comput. Med. Imaging Graph., vol. 22, no. 3, pp. 217-28, 1998.
 N.F. Osman, E.R. McVeigh, and J.L. Prince, “Imaging heart motion using harmonic phase MRI,” IEEE Trans. Med. Imaging, vol. 19, no. 3, pp. 186-202, 2000.
 X. Liu, E. Murano, M. Stone, and J.L. Prince, “HARP tracking refinement using seeded region growing,” In: Proc. of IEEE Int. Symp. on Biomedical Imaging, pp. 372-375, 2007.
 A.M. Khalifam, A.B.M. Youssef, and N.F. Osman, “Improved harmonic phase (HARP) method for motion tracking a tagged cardiac MR images,” In: Proc. of IEEE Engineering in Medicine and Biology Conf., pp. 4298-4301, 2005.
 P. Dieterich, M. Odenthal-Schnittler, C. Mrowietz, M. Krämer, L. Sasse, H. Oberleithner, and H.J. Schnittler, “Quantitative morphodynamics of endothelial cells within confluent cultures in response to fluid shear stress,” Biophys. J., vol. 79, pp. 1285-1297, 2000.
 X. Chen, X. Zhou, and T. C. Wong, “Automated segmentation, classification, and tracking of cancer cell nuclei in time-lapse microscopy,” IEEE Trans. Biomed. Eng., vol. 53, pp. 762-766, 2006.
 H.S. Wu, J. Barba, and J. Gil, “Iterative thresholding for segmentation of cells from noisy images,” J. Microsc., vol. 197, pp. 296-304, 2000.
 C. Wählby, I.M. Sintorn, F. Erlandsson, G. Borgefors, and E. Bengtsson, “Combining intensity, edge and shape information for 2D and 3D segmentation of cell nuclei in tissue sections,” J. Microsc., vol. 215, pp. 67-76, 2004.
 F. Leymarie and M.D. Levine, “Tracking deformable objects in the plane using an active contour model,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 15, pp. 617-634, 1993.
 C. Zimmer, E. Labruyère, V. Meas-Yedid, N. Guillén, and J.C. Olivo-Marin, “Segmentation and tracking of migrating cells in videomicroscopy with parametric active contours: a tool for cell-based drug testing,” IEEE Trans. Med. Imaging, vol. 21, pp. 1212-1221, 2002.
 N. Ray, S.T. Acton, and K. Ley, “Tracking leukocytes in vivo with shape and size constrained active contours,” IEEE Trans. Med. Imaging, vol. 21, pp. 1222-1235, 2002.
 O. Debeir, H.P. Van, R. Kiss, and C. Decaestecker, “Tracking of migrating cells under phase-contrast video microscopy with combined mean-shift processes,” IEEE Trans. Med. Imaging, vol. 24, pp. 697-711, 2005.
 T. McInerney, and D. Terzopoulos, “T-snake: topologically adaptive snakes,” Med. Image Anal., vol. 4, pp. 73-91, 2000.
 F.A. Velasco and J.L. Marroquin, “Growing snakes: active contours for complex topologies,” Pattern Recognit., vol. 36, pp. 475-482, 2003.
 C.B. Burckhardt, “Speckle in ultrasound b-mode scans,” IEEE Trans. Sonics Ultrason., vol. 25, no. 1, pp. 1-6, 1978.
 G.E. Sleefe, and P.P. Lele, “Tissue characterization based on scatterer number density estimation,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 35, no. 6, pp. 749-757, 1988.
 H. Liu, T.H. Hong, M. Herman, T. Camus T, and R. Chellapa, “Accuracy vs efficiency trade-offs in optical flow algorithms,” Comput. Vis. Image Underst., vol. 72, no. 3, pp. 271-286, 1998.
 C.H. Lee and L.H. Chen, “A fast motion estimation algorithm based on the block sum pyramid,” IEEE Trans. Image Process., vol. 6, no. 11, pp. 1587-1590, 1997.
 Y.S. Chen, Y.P. Hung, and C.S. Fuh, “Fast block matching algorithm based on the winner-update strategy,” IEEE Trans. Image Process., vol. 10, no. 8, pp. 1212-1222, 2001.
 W. Li and E. Salari, “Successive elimination algorithm for motion estimation,” IEEE Trans. Image Process., vol. 4, no. 1, pp. 105-107, 1995.
 K.M. Nam, J.S. Kim, R.H. Park, and Y.S. Shim, “A fast hierarchical motion vector estimation algorithm using mean pyramid,” IEEE Trans. Circuits Syst. Video Technol., vol. 5, no. 4, pp. 344-351, 1995.
 E. Mémin, P. Pérez, “Dense estimation and object-based segmentation of the optical flow with robust techniques,” IEEE Trans. Image Process., vol. 7, no. 5, pp. 703-719, 1998.
 J.Y. Lu, K.S. Wu, and J.C. Lin, “Fast full search in motion estimation by hierarchical use of Minkowski’s inequality (HUMI),” Pattern Recognit., vol. 31, no. 7, pp. 945-952, 1998.
 R.F. Wagner, S.W. Smith, J.M. Sandrik, and H. Lopez, “Statistics of speckle in ultrasound b-scans,” IEEE Trans. Sonics Ultrason., vol. 30, no. 3, pp. 156-163, 1983.
 T. Loupas, W.N. McDicken, and P.L. Allan, “An adaptive weighted median filter for speckle suppression in medical ultrasonic images,” IEEE Trans. Circuits Syst., vol. 36, no. 1, pp. 129-135, 1989.
 M. Karaman, M.A. Kutay, and G. Bozdagi, “An adaptive speckle suppression filter for medical ultrasonic imaging,” IEEE Trans. Med. Imaging, vol. 14, no. 2, pp. 283-292, 1995.
 J. Souquet, “State of the art in digital broadband medical ultrasound imaging,” Comptes Rendus de l’Academie des Sciences Series IV Physics, vol. 2, no. 8, pp. 1091-1098, 2001.
 R. Entrekin, P. Jackson, J.R. Jago, and B.A. Porter, “Real time spatial compound imaging in breast ultrasound: technology and early clinical experience,” Medica mundi, vol. 43, no. 3, pp. 35-43, 1999.
 A. Rafiee, M.H. Moradi, and M.R. Farzaneh, “A novel genetic-neuro-fuzzy filter for speckle noise reduction from sonographical images,” J. Digit. Imaging, vol. 57, no. 4, pp. 292-300, 2004.
 R. Rohling, A. Gee, and L. Berman, “Three-dimensional spatial compounding of ultrsound images,” Med. Image Anal., vol. 1, no. 3, pp. 177-193, 1997.
 J.F. Krücker, C.R. Meyer, G.L. LeCarpentier, and J.B. Fowlkes, “3D spatial compounding of ultrasound images using image-based nonrigid registration,” Ultrasound Med. Biol., vol. 26, no. 9, pp. 1475-1488, 2000.
 U. Techavipoo, Q. Chen, T. Varghese, J.A. Zagzebski, and E.L. Madsen EL, “Noise reduction using spatial-angular compounding for elastography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 51, no. 5, pp. 510-520, 2004.
 G. Cincotti, G. Loi, and M. Pappalardo, “Frequency decomposition and compounding of ultrasound medical images with wavelet packets,” IEEE Trans. Med. Imaging, vol. 20, no. 8, pp. 176-771, 2001.
 P.C. Li and C.L. Wu, “Strain compounding: spatial resolution and performance on human images,” Ultrasound Med. Biol., vol. 27, no. 11, pp. 1535-1541, 2001.
 S.K. Jespersen, J.E. Wilhjelm, and H. Sillesen, “In vitro spatial compound scanning for improved visualization of atherosclerosis,” Ultrasound Med. Biol., vol. 26, no. 8, pp. 1357-1362, 2000.
 R.R. Entrekin, B.A. Porter, H.H. Sillesen, A.D. Wong, P.L. Cooperberg, and C.H. Fix, “Real-time spatial compound imaging: application to breast, vascular, and musculoskeletal ultrasound,” Seminar in Ultrasound, CT, and MRI, vol. 22, no. 1, pp. 50-64, 2001.
 S.C. Kofoed, M.L.M. Grønholdt, and J.E. Wilhjelm, “Real-time spatial compound imaging improves reproducibility in the evaluation of atherosclerotic carotid plaques,” Ultrasound Med. Biol., vol. 27, no. 10, pp. 1311-1317, 2001.
 S. Huber, M. Wagner, M. Mdel, and H. Czembirek, “Real-time spatial compound imaging in breast ultrasound,” Ultrasound Med. Biol., vol. 28, no. 2, pp. 155-163, 2002.
 K. Xue, P. He, and Y. Wang, “A motion compensated ultrasound spatial compounding algorithm,” in Proc. of 19th Intl. Conf. of IEEE EMBS, vol. 2, pp. 818-821, 1997.
 A.R. Groves and R.N. Rohling, “Two-dimensional spatial compounding with warping,” Ultrasound Med. Biol., vol. 30, no. 7, pp. 929-942, 2004.
 V. Lukin, N. Ponomarenko, and I. Bunaeva, “Post-processing of multi-look and sequentially formed images in radar and ultrasonic coherent systems,” in Proc. of 46th IEEE Intl. Midwest Symp. on Circuits and Systems, vol. 2, pp. 745-751, 2004.
 J.E. Wilhjelm, M.S. Jensen, T. Brandt, B. Sahl, K. Martinsen, S.K. Jespersen, and E. Falk, “Some imaging strategies in multi-angle spatial compounding,” in Proc. of IEEE Ultrasonics Symp., pp. 1615-1618, 2000.
 C. Kotropoulos, X. Magnisalis, I. Pitas, and M.G. Strintzis, “Nonlinear ultrasonic image processing based on signal-adaptive filters and self-organizing neural networks,” IEEE Trans. Image Process., vol. 3, no. 1, pp. 65-77, 1994.
 P. Clarysse, C. Basset, L. Khouas, P. Croisille, D. Friboulet, C. Odet, and I.E. Magnin, “Two-dimensional spatial and temporal displacement and deformfation field fitting from cardiac magnetic resonance tagging,” Med. Image. Anal., vol. 4, pp. 253-268, 2000.
 D.J. Williams and M. Shah, “A fast algorithm for active contours and curvature estimation,” CVGIP: Image Understanding, vol. 5, no. 1, pp. 14-26, 1992.
 C.W. Ngo, T.C. Pong, and H.J. Zhang, “Motion analysis and segmentation through spatiao-temporal slices processing,” IEEE Trans. Image Process., vol. 12, no. 3, pp. 341-55, 2003.
 Y.K. Cheng, Y.T. Lin, and S.Y. Kung, “A feature tracking algorithm using neighborhood relaxation with multi-candidate pre-screening,” In: Proc. of the Int. Conf. on Image Processing, pp. 513-516, 1996.
 S.H. Lee, O. Kwon, and R.H. Park, “Motion vector correction based on the pattern-like image analysis,” IEEE Trans. Consum. Electron., vol. 49, no. 3, pp. 479-84, 2003.
 J.M. Bundy and C.H. Lorenz, “TAGASIST: a post-processing and analysis tools package for tagged magnetic resonance imaging,” Comput. Med. Imaging Graph., vol. 21, no. 4, pp. 225-232, 1997.
 K. Wu, D. Gauthier, and M.D. Levin, “Live cell image segmentation,” IEEE Trans. Biomed. Eng., vol. 42, pp. 1-12, 1995.
 N. Otsu, “A threshold selection method from gray level histogram,” IEEE Trans. Syst. Man Cybern., vol. SMC-9, pp. 62-66, 1979.
 I.T. Jolliffe, Principal Component Analysis, Springer-Verlag, New York, 2002.
 M. Pechenizkiy, A. Tsymbal, and S. Puuronen, “PCA-based feature transformation for classification: issues in medical diagnostics,” in Proc. of 17th IEEE Symp. Computer-Based Medical Systems, pp. 535-540, 2004.
 M.A. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cogn. Neurosci., vol. 3, pp. 71-86, 1991.
 P. Zrÿd, “A new plant cell image segmentation algorithm,” in Proc. of the 8th Int. Conf. on Image Analysis and Processing, pp. 229-234, 1995.
 J.L. Barron, D.J. Fleet, and S.S. Beauchemin, “Performance of optical flow techniques,” Int. J. Comput. Vis., vol. 12, no. 1, pp. 43-77, 1994.
 P. Brodatz, Textures, Dover Publications, New York, 1966.
 J. Meunier and M. Bertrand, “Ultrasonic texture motion analysis: theory and simulation,” IEEE Trans. Med. Imaging, vol. 14, no. 2, pp. 293-300, 1995.
 C. Xu and J.L. Prince, “Snakes, shapes, and gradient vector flow,” IEEE Trans. Image Process., vol. 7, no. 3, pp. 359-369, 1998.
 D.S. Fieno, R.J. Kim, E.L. Chen, J.W. Lomasney, F.J. Klocke, and R.M. Judd, “Contrast-enhanced magnetic resonance imaging of myocardium at risk: distinction between reversible and irreversible injury throughout infarct healing,” J. Am. Coll. Cardiol., vol. 36, no. 6, pp. 1985-1991, 2000.
 C.L. Ho, T.Y. Mou, P.S. Chiang, C.L. Weng, and N.H. Chow, “Mini chamber system for long-term maintenance and observation of cultured cells,” Biotechniques, vol. 38, pp. 267-273, 2005.
 S.E. Chen and R.E. Parent, “Shape averaging and its applications to industrial design,” IEEE Comput. Graph. Appl., vol. 9, pp. 47-54, 1989.
 W. Tvaruskó, M. Bentele, T. Misteli, R. Rudolf, C. Kaether, D.L. Spector, H.H. Gerdes, and R. Eils, “Time-resolved analysis and visualization of dynamic processes in living cells,” in Proc. Natl. Acad. Sci. USA 96, pp. 7950-7955, 1999.