Abstract
In this paper we describe a rotation-invariant attribute filter based on estimating the sphericity or roundness of objects by efficiently computing surface area and volume of connected components. The method is based on an efficient algorithm to compute all iso-surfaces of all nodes in a Max-Tree. With similar properties to moment-based attributes like sparseness, non-compactness, and elongation, our sphericity attribute can supplement these in finding blood-vessels in time-of-flight MR angiograms. We compare the method to a discrete surface area method based on adjacency, which has been used for urinary stone detection. Though the latter is faster, it is less accurate, and lacks rotation invariance.
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References
Heijmans, H.J.A.M.: Connected morphological operators for binary images. Comp. Vis. Image Understand. 73, 99–120 (1999)
Salembier, P., Serra, J.: Flat zones filtering, connected operators, and filters by reconstruction. IEEE Trans. Image Proc. 4, 1153–1160 (1995)
Breen, E.J., Jones, R.: Attribute openings, thinnings and granulometries. Comp. Vis. Image Understand. 64(3), 377–389 (1996)
Salembier, P., Oliveras, A., Garrido, L.: Anti-extensive connected operators for image and sequence processing. IEEE Trans. Image Proc. 7, 555–570 (1998)
Meijster, A., Wilkinson, M.H.F.: A comparison of algorithms for connected set openings and closings. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 484–494 (2002)
Wilkinson, M.H.F., Westenberg, M.A.: Shape preserving filament enhancement filtering. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 770–777. Springer, Heidelberg (2001)
Westenberg, M.A., Roerdink, J.B.T.M., Wilkinson, M.H.F.: Volumetric attribute filtering and interactive visualization using the max-tree representation. IEEE Trans. Image Proc. 16, 2943–2952 (2007)
Urbach, E.R., Roerdink, J.B.T.M., Wilkinson, M.H.F.: Connected shape-size pattern spectra for rotation and scale-invariant classification of gray-scale images. IEEE Trans. Pattern Anal. Mach. Intell. 29, 272–285 (2007)
Naegel, B., Passat, N., Boch, N., Kocher, M.: Segmentation using vector-attribute filters: Methodology and application to dermatological imaging. In: Proc. Int. Symp. Math. Morphology (ISMM 2007), pp. 239–250 (2007)
Purnama, K.E., Wilkinson, M.H.F., Veldhuizen, A.G., van Ooijen, P.M.A., Lubbers, J., Sardjono, T.A., Verkerke, G.J.: Branches filtering approach for max-tree. In: Proc. 2nd Int. Conf. Comput. Vision Theory Applic (VISAPP 2007), Barcelona, March 8-11, pp. 328–332 (2007)
Ouzounis, G.K., Giannakopoulos, S., Simopoulos, C.E., Wilkinson, M.H.F.: Robust extraction of urinary stones from CT data using attribute filters. In: Proc. Int. Conf. Image Proc. (in press, 2009)
Udupa, J.K.: Multidimensional digital boundaries. CVGIP: Graphical Models and Image Processing 56(4), 311–323 (1994)
Najman, L., Couprie, M.: Building the component tree in quasi-linear time. IEEE Trans. Image Proc. 15, 3531–3539 (2006)
Sladoje, N., Nyström, I., Saha, P.K.: Measurements of digitized objects with fuzzy borders in 2d and 3d. Image Vis. Comput. 23, 123–132 (2005)
Kaufman, A., Mueller, K.: Overview of volume rendering. In: The Visualization Handbook. Academic Press, London (2005)
Cignoni, P., Marino, P., Montani, C., Puppo, E., Scopigno, R.: Speeding up isosurface extraction using interval trees. IEEE Trans. Visualization Comp. Graph. 3, 150–170 (1997)
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Kiwanuka, F.N., Ouzounis, G.K., Wilkinson, M.H.F. (2009). Surface-Area-Based Attribute Filtering in 3D. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds) Mathematical Morphology and Its Application to Signal and Image Processing. ISMM 2009. Lecture Notes in Computer Science, vol 5720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03613-2_7
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DOI: https://doi.org/10.1007/978-3-642-03613-2_7
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