Abstract
In this paper we propose a Particle Filter-based propagation approach for the segmentation of vascular structures in 3D volumes. Because of pathologies and inhomogeneities, many deterministic methods fail to segment certain types of vessel. Statistical methods represent the solution using a probability density function (pdf). This pdf does not only indicate the best possible solution, but also valuable information about the solution’s variance. Particle Filters are used to learn the variations of direction and appearance of the vessel as the segmentation goes. These variations are used in turn in the particle filters framework to control the perturbations introduced in the Sampling Importance Resampling step (SIR). For the segmentation itself, successive planes of the vessel are modeled as states of a Particle Filter. Such states consist of the orientation, position and appearance (in statistical terms) of the vessel. The shape of the vessel and subsequently the particles pdf are recovered using globally active contours, implemented using circular shortest paths by branch and bound [1] that guarantees the global optimal solution. Promising results on the segmentation of coronary arteries demonstrate the potential of the proposed approach.
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Appleton, B., Sun, C.: Circular shortest paths by branch and bound. 36(11), 2513–2520 (November 2003)
Avants, B., Williams, J.: An adaptive minimal path generation technique for vessel tracking in cta/ce-mra volume images. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) MICCAI 2000. LNCS, vol. 1935, pp. 707–716. Springer, Heidelberg (2000)
Cañero, C., Radeva, P.: Vesselness enhancement diffusion. Pattern Recognition Letters 24(16), 3141–3151 (2003)
Caselles, V., Catté, F., Coll, B., Dibos, F.: A geometric model for active contours in image processing. Numerische Mathematik 66(1), 1–31 (1993)
Deschamps, T., Cohen, L.D.: Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Medical Image Analysis 5(4), 281–299 (2001)
Descoteaux, M., Collins, L., Siddiqi, K.: Geometric Flows for Segmenting Vasculature in MRI: Theory and Validation. In: Medical Imaging Computing and Computer-Assisted Intervention, pp. 500–507 (2004)
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
Doucet, A., de Freitas, J., Gordon, N.: Sequential Monte Carlo Methods in Practice. Springer, New York (2001)
Duda, R., Hart, P.: Pattern Classification and Scene Analysis. John Wiley and Sons, Chichester (1973)
Fearnhead, P., Clifford, P.: Online inference for well-log data. Journal of the Royal Statistical Society 65, 887–899 (2003)
Figueiredo, M., Leitao, J.: A nonsmoothing approach to the estimation of of vessel controus in angiograms. IEEE Transactions on Medical Imaging 14, 162–172 (1995)
Frangi, A., Niessen, W., Nederkoorn, P., Elgersma, O., Viergever, M.: Three-dimensional model-based stenosis quantification of the carotid arteries from contrast-enhanced MR angiography. In: Mathematical Methods in Biomedical Image Analysis, pp. 110–118 (2000)
Gordon, N.: Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation. IEE Proceedings 140, 107–113 (1993)
Gordon, N.: On Sequential Monte Carlo Sampling Methods for Bayesian Filtering. Statistics and Computing 10, 197–208 (2000)
Gordon, N.: A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking. IEEE Transactions on Signal Processing 50, 174–188 (2002)
Hart, M., Holley, L.: A method of Automated Coronary Artery Trackin in Unsubtracted Angiograms. IEEE Computers in Cardiology, 93–96 (1993)
Isard, M., Blake, A.: Contour Tracking by Stochastic Propagation of Conditional Density. In: European Conference on Computer Vision, vol. I, pp. 343–356 (1996)
Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active Contour Models. In: IEEE International Conference in Computer Vision, pp. 261–268 (1987)
Krissian, K., Malandain, G., Ayache, N., Vaillant, R., Trousset, Y.: Model based detection of tubular structures in 3d images. Computer Vision and Image Understanding 80, 130–171 (2000)
Lorigo, L., Faugeras, O., Grimson, E., Keriven, R., Kikinis, R., Nabavi, A., Westin, C.: Codimension-Two Geodesic Active Controus for the Segmentation of Tubular Structures. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. I: 444–451 (2000)
Malladi, R., Sethian, J.: A Real-Time Algorithm for Medical Shape Recovery. In: International Conference on Computer Vision, pp. 304–310 (1998)
Nain, D., Yezzi, A., Turk, G.: Vessel Segmentation Using a Shape Driven Flow. In: Medical Imaging Copmuting and Computer-Assisted Intervention (2004)
O’Donnell, T., Boult, T., Fang, X., Gupta, A.: The Extruded Generalized Cylider: A Deformable Model for Object Recovery. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 174–181 (1994)
Osher, S., Paragios, N.: Geometric Level Set Methods in Imaging, Vision and Graphics. Springer, Heidelberg (2003)
Petrocelli, R., Manbeck, K., Elion, J.: Three Dimentional Structue Recognition in Digital Angiograms using Gauss-Markov Models. IEEE Computers in Radiology, 101–104 (1993)
Rueckert, D., Burger, P., Forbat, S., Mohiadin, R., Yang, G.: Automatic Tracking of the Aorta in Cardiovascular MR images using Deformable Models. IEEE Transactions on Medical Imaging 16, 581–590 (1997)
Sato, Y., Nakajima, S., Atsumi, H., Koller, T., Gerig, G., Yoshida, S., Kikinis, R.: 3D Multiscale line filter for segmentation and visualization of curvilinear structures in medical images. In: Conference on Computer Vision, Virtual Reality and Robotics in Medicine and Media Robotics and Computer-Assisted Surgery, pp. 213–222 (1997)
Sethian, J.: A Review of the Theory, Algorithms, and Applications of Level Set Methods for Propagating Interfaces, pp. 487–499. Cambridge University Press, Cambridge (1995)
Sorantin, E., Halmai, C., Erbohelyi, B., Palagyi, K., Nyul, K., Olle, K., Geiger, B., Lindbichler, F., Friedrich, G., Kiesler, K.: Spiral-CT-based assesment of Tracheal Stenoses using 3D Skeletonization. IEEE Transactions on Medical Imaging 21, 263–273 (2002)
Toyama, K., Blake, A.: Probabilistic Tracking in a Metric Space. In: IEEE International Conference in Computer Vision, pp. 50–59 (2001)
Vasilevskiy, A., Siddiqi, K.: Flux Maximizing Geometric Flows. In: IEEE International Conference in Computer Vision, pp. I: 149–154 (2001)
West, W.: Modelling with mixtures. In: Bernardo, J., Berger, J., Dawid, A., Smith, A. (eds.) Bayesian Statistics. Clarendon Press (1993)
Yim, P., Choyke, P., Summers, R.: Grayscale Skeletonization of Small Vessels inMagnetic Resonance Angiography. IEEE Transactions on Medical Imaging 19, 568–576 (2000)
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Florin, C., Paragios, N., Williams, J. (2006). Globally Optimal Active Contours, Sequential Monte Carlo and On-Line Learning for Vessel Segmentation. In: Leonardis, A., Bischof, H., Pinz, A. (eds) Computer Vision – ECCV 2006. ECCV 2006. Lecture Notes in Computer Science, vol 3953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11744078_37
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