Abstract
Elongated objects are more difficult to filter than more isotropic ones because they locally comprise fewer pixels. For thin linear objects, this problem is compounded because there is only a restricted set of directions that can be used for filtering, and finding this local direction is not a simple problem. In addition, disconnections can easily appear due to noise. In this paper we tackle both issues by combining a linear filter for direction finding and a morphological one for filtering. More specifically, we use the eigen-analysis of the Hessian for detecting thin, linear objects, and a spatially-variant opening or closing for their enhancement and reconnection. We discuss the theory of spatially-variant morphological filters and present an efficient algorithm. The resulting spatially-variant morphological filter is shown to successfully enhance directions in 2D and 3D examples illustrated with a brain blood vessel segmentation problem.
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References
Gonzalez, R., Woods, R.: Digital Image Processing, 3rd edn. Prentice-Hall, Englewood Cliffs (2007)
Heijmans, H.: Morphological filters for dummies. In: Maragos, P., Schafer, R.W., Butt, M.A. (eds.) Mathematical Morphology and its Applications to Image and Signal Processing, proceedings for ISMM 1996, pp. 127–137. Kluwer Acad., Dordrecht (1996)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)
Smith, S.M., Brady, J.M.: Susan a new approach to low level image processing. Int. J. Comput. Vision 23(1), 45–78 (1997)
Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Sixth International Conference on Computer Vision, 1998, pp. 839–846 (1998)
Soille, P., Talbot, H.: Directional morphological filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(11), 1313–1329 (2001)
Heijmans, H., Buckley, M., Talbot, H.: Path openings and closings. Journal of Mathematical Imaging and Vision 22, 107–119 (2005)
Talbot, H., Appleton, B.: Efficient complete and incomplete paths openings and closings. Image and Vision Computing 25(4), 416–425 (2007)
Zana, F., Klein, J.C.: Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation. IEEE Transactions on Image Processing 10(7), 1010–1019 (2001)
Lindeberg, T.: Feature detection with automatic scale selection. International Journal of Computer Vision 30(2), 79–116 (1998)
Danielsson, P.E., Lin, Q.: Efficient detection of second-degree variations in 2D and 3D images. Journal of Visual Communication and Image Representation 12, 255–305 (2001)
Deguchi, K., Izumitani, T., Hontani, H.: Detection and enhancement of line structures in an image by anisotropic diffusion. Pattern Recognition Letters 23(12), 1399–1405 (2002)
Frangi, A., Niessen, W., Vincken, K., Viergever, M.: Multiscale vessel enhancement filtering. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 130–137. Springer, Heidelberg (1998)
Manniesing, R., Viergever, M., Niessen, W.: Vessel enhancing diffusion: A scale space representation of vessel structures. Medical Image Analysis 10(6), 815–825 (2006)
Perona, P.: Orientation diffusions. IEEE Trans. Image Processing 7, 457–467 (1998)
Lee, T., Talbot, H.: A fast method for detecting and matching linear features in images. In: Proc. DICTA, Brisbane, Australia, December 1995, pp. 649–654 (1995)
Vincent, L.: Minimal path algorithms for the robust detection of linear features in images. In: Mathematical Morphology and its Applications to Image and Signal processing, Amsterdam. Computational Imaging and Vision, Proceedings for ISMM 1998, vol. 12, pp. 331–338. Kluwer, Dordrecht (1998)
Cohen, L., Deschamps, T.: Segmentation of 3D tubular objects with adaptive front propagation and minimal tree extraction for 3D medical imaging. Computer Methods in Biomechanics and Biomedical Engineering 10(4), 289–305 (2007)
Verdú-Monedero, R., Angulo, J.: Spatially-variant directional mathematical morphology operators based on a diffused average squared gradient field. In: Blanc-Talon, J., Bourennane, S., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2008. LNCS, vol. 5259, pp. 542–553. Springer, Heidelberg (2008)
Tankyevych, O., Talbot, H., Dokladal, P.: Curvilinear morpho-Hessian filter. In: IEEE ISBI, pp. 1011–1014 (2008)
Serra, J.: Image analysis and mathematical morphology. Academic Press, London (1982)
Lerallut, R., Decencière, E., Meyer, F.: Image filtering using morphological amoebas. Image and Vision Computing 25(4), 395–404 (2007)
Dokládal, P., Dokládalová, E.: Grey-scale morphology with spatially-variant rectangles in linear time. In: Blanc-Talon, J., Bourennane, S., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2008. LNCS, vol. 5259, pp. 674–685. Springer, Heidelberg (2008)
Charif-Chefchaouni, M., Schonfeld, D.: Spatially-variant mathematical morphology. In: IEEE International Conference on Image Processing, 1994. Proceedings. ICIP 1994, November 1994, vol. 2, pp. 555–559 (1994)
Bouaynaya, N., Charif-Chefchaouni, M., Schonfeld, D.: Theoretical foundations of spatially-variant mathematical morphology part i: Binary images. IEEE Trans. Pattern Anal. Mach. Intell. 30(5), 823–836 (2008)
Bouaynaya, N., Schonfeld, D.: Theoretical foundations of spatially-variant mathematical morphology part ii: Gray-level images. IEEE Trans. Pattern Anal. Mach. Intell. 30(5), 837–850 (2008)
Agam, G., Armato, S.G., Wu, C.: Vessel tree reconstruction in thoracic CT scans with application to nodule detection. IEEE Transactions on Medical Imaging 24(4), 486–499 (2005)
Antiga, L.: Generalizing vesselness with respect to dimensionality and shape. In: ISC/NA-MIC Workshop on Open Science at MICCAI (August 2007)
Vincent, L.: Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms. IEEE Transactions on Image Processing 2(2), 176–201 (1993)
Sato, Y., Westin, C.F., Bhalerao, A., Nakajima, S., Shiraga, S., Tamura, S., Kikinis, R.: Tissue classification based on 3D local intensity structures for volume rendering. IEEE Transactions on Visualization and Computer Graphics 6(2), 160–180 (2000)
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Tankyevych, O., Talbot, H., Dokladál, P., Passat, N. (2009). Spatially-Variant Morpho-Hessian Filter: Efficient Implementation and Application. 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_13
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DOI: https://doi.org/10.1007/978-3-642-03613-2_13
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