Abstract
This work studies limits on estimating the width of thin tubular structures in 3D images. Based on nonlinear estimation theory we analyze the minimal stochastic error of estimating the width. Given a 3D analytic model of the image intensities of tubular structures, we derive a closed-form expression for the Cramér-Rao bound of the width estimate under image noise. We use the derived lower bound as a benchmark and compare it with three previously proposed accuracy limits for vessel width estimation. Moreover, by experimental investigations we demonstrate that the derived lower bound can be achieved by fitting a 3D parametric intensity model directly to the image data.
Chapter PDF
Similar content being viewed by others
Keywords
- Magnetic Resonance Angiography
- Tubular Structure
- Magnetic Resonance Angiography Image
- Vessel Width
- Thin Vessel
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Kirbas, C., Quek, F.: A Review of Vessel Extraction Techniques and Algorithms. ACM Computing Surveys 36, 81–121 (2004)
Hoogeveen, R., Bakker, C., Viergever, M.: Limits to the Accuracy of Vessel Diameter Measurement in MR Angiography. J. of Magnetic Resonance Imaging 8, 1228–1235 (1998)
Sato, Y., Yamamoto, S., Tamura, S.: Accurate Quantification of Small-Diameter Tubular Structures in Isotropic CT Volume Data Based on Multiscale Line Filter Responses. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 508–515. Springer, Heidelberg (2004)
Wörz, S., Rohr, K.: A New 3D Parametric Intensity Model for Accurate Segmentation and Quantification of Human Vessels. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 491–499. Springer, Heidelberg (2004)
Rohr, K.: Fundamental Limits in 3D Landmark Localization. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 286–298. Springer, Heidelberg (2005)
Sonka, M., Reddy, G., Winniford, M., Collins, S.: Adaptive Approach to Accurate Analysis of Small-Diameter Vessels in Cineangiograms. IEEE Trans. on Medical Imaging 16(1), 87–95 (1997)
Dougherty, G., Newmann, D.: Measurement of thickness and density of thin structures by computed tomography: A simulation study. Medical Physics 26, 1341–1348 (1999)
Sato, Y., Tanaka, H., Nishii, T., Nakanishi, K., Sugano, N., Kubota, T., Nakamura, H., Yoshikawa, H., Ochi, T., Tamura, S.: Limits on the Accuracy of 3-D Thickness Measurements in Magnetic Resonance Images – Effects of Voxel Anisotropy. IEEE Trans. on Medical Imaging 22, 1076–1088 (2003)
Bouma, H., Vilanova, A., van Vliet, L., Gerritsen, F.: Correction for the Dislocation of Curved Surfaces Caused by the PSF in 2D and 3D CT Images. IEEE Trans. on Pattern Analysis and Machine Intelligence 27, 1501–1507 (2005)
van Trees, H.: Detection, Estimation, and Modulation Theory, Part I. John Wiley and Sons, New York (1968)
Abramowitz, M., Stegun, I.: Pocketbook of Mathematical Functions. Verlag Harri Deutsch, Thun und Frankfurt/Main (1984)
Hoogeveen, R., Bakker, C., Viergever, M.: MR Phase-Contrast Flow Measurement With Limited Spatial Resolution in Small Vessels: Value of Model-Based Image Analysis. J. of Magnetic Resonance in Medicine 41, 520–528 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wörz, S., Rohr, K. (2006). Limits on Estimating the Width of Thin Tubular Structures in 3D Images. In: Larsen, R., Nielsen, M., Sporring, J. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2006. MICCAI 2006. Lecture Notes in Computer Science, vol 4190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11866565_27
Download citation
DOI: https://doi.org/10.1007/11866565_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44707-8
Online ISBN: 978-3-540-44708-5
eBook Packages: Computer ScienceComputer Science (R0)