Abstract
This work studies the convex relaxation approach to the left ventricle (LV) segmentation which gives rise to a challenging multi-region seperation with the geometrical constraint. For each region, we consider the global Bhattacharyya metric prior to evaluate a gray-scale and a radial distance distribution matching. In this regard, the studied problem amounts to finding three regions that most closely match their respective input distribution model. It was previously addressed by curve evolution, which leads to sub-optimal and computationally intensive algorithms, or by graph cuts, which result in heavy metrication errors (grid bias). The proposed convex relaxation approach solves the LV segmentation through a sequence of convex sub-problems. Each sub-problem leads to a novel bound of the Bhattacharyya measure and yields the convex formulation which paves the way to build up the efficient and reliable solver. In this respect, we propose a novel flow configuration that accounts for labeling-function variations, in comparison to the existing flow-maximization configurations. We show it leads to a new convex max-flow formulation which is dual to the obtained convex relaxed sub-problem and does give the exact and global optimums to the original non-convex sub-problem. In addition, we present such flow perspective gives a new and simple way to encode the geometrical constraint of optimal regions. A comprehensive experimental evaluation on sufficient patient subjects demonstrates that our approach yields improvements in optimality and accuracy over related recent methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ben Ayed, I., Chen, H.M., Punithakumar, K., Ross, I., Li, S.: Graph cut segmentation with a global constraint: Recovering region distribution via a bound of the Bhattacharyya measure. In: CVPR 2010 (2010)
Ben Ayed, I., Li, S., Ross, I.: Embedding overlap priors in variational left ventricle tracking. IEEE Trans. Med. Imaging 28(12), 1902–1913 (2009)
Ben Ayed, I., Li, S., Ross, I., Islam, A.: Myocardium tracking via matching distributions. Int. J. of Comput. Assist. Radiol. and Surg. 4(1), 37–44 (2009)
Ben Ayed, I., Punithakumar, K., Li, S., Islam, A., Chong, J.: Left ventricle segmentation via graph cut distribution matching. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5762, pp. 901–909. Springer, Heidelberg (2009)
Bertsekas, D.P.: Nonlinear Programming. Athena Scientific (1999)
Boykov, Y., Funka Lea, G.: Graph cuts and efficient N-D image segmentation. Int. J. Comput. Vision 70(2), 109–131 (2006)
Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1124–1137 (2004), http://dx.doi.org/10.1109/TPAMI.2004.60
Bresson, X., Esedoglu, S., Vandergheynst, P., Thiran, J., Osher, S.: Fast global minimization of the active contour/snake model. J. Math. Imaging Vis. 28(2), 151–167 (2007)
Chan, T., Shen, J.H.: Image Processing And Analysis: Variational, PDE, Wavelet, and Stochastic Methods. SIAM, Philadelphia (2005)
Giusti, E.: Minimal surfaces and functions of bounded variation. Australian National University, Canberra (1977)
Jolly, M.-P.: Automatic recovery of the left ventricular blood pool in cardiac cine MR images. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 110–118. Springer, Heidelberg (2008)
Kaus, M.R., von Berg, J., Weese, J., Niessen, W., Pekar, V.: Automated segmentation of the left ventricle in cardiac MRI. Med. Image Anal. 8(3), 245–254 (2004), http://www.sciencedirect.com/science/article/B6W6Y-4D09D3J-1/2/d7268f23efbbbfa83da4665d311dee58
Lellmann, J., Kappes, J., Yuan, J., Becker, F., Schnörr, C.: Convex multi-class image labeling by simplex-constrained total variation. Tech. report, HCI, IWR, Uni. Heidelberg (2008)
Liu, H., Chen, Y., Ho, H.P., Shi, P.: Geodesic active contours with adaptive neighboring influence. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 741–748. Springer, Heidelberg (2005)
Nikolova, M., Esedoglu, S., Tony, F.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J. Appl. Math. 66(5), 1632–1648 (2006), http://link.aip.org/link/?SMM/66/1632/1
Pock, T., Chambolle, A., Cremers, D., Bischof, H.: A convex relaxation approach for computing minimal partitions. In: CVPR 2009 (2009)
Rockafellar, R.T.: The multiplier method of Hestenes and Powell applied to convex programming. J. Optimiz. Theory App. 12, 555–562 (1973)
Rockafellar, R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. 1(2), 97–116 (1976)
Rother, C., Minka, T., Blake, A., Kolmogorov, V.: Cosegmentation of image pairs by histogram matching - incorporating a global constraint into MRFs. In: CVPR 2006 (2006)
Yuan, J., Bae, E., Tai, X.C., Boycov, Y.: A study on continuous max-flow and min-cut approaches. Part I: Binary labeling. Tech report CAM-10-61, UCLA (2010)
Yuan, J., Bae, E., Tai, X.C.: A study on continuous max-flow and min-cut approaches. In: CVPR 2010 (2010)
Zhu, Y., Papademetris, X., Sinusas, A.J., Duncan, J.S.: Segmentation of the left ventricle from cardiac MR images using a subject-specific dynamical model. IEEE Trans. Med. Imaging 29(4), 669–687 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nambakhsh, M.S. et al. (2011). A Convex Max-Flow Segmentation of LV Using Subject-Specific Distributions on Cardiac MRI. In: Székely, G., Hahn, H.K. (eds) Information Processing in Medical Imaging. IPMI 2011. Lecture Notes in Computer Science, vol 6801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22092-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-22092-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22091-3
Online ISBN: 978-3-642-22092-0
eBook Packages: Computer ScienceComputer Science (R0)