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Issue No.11 - November (2011 vol.17)

pp: 1637-1649

Joe Kniss , University of New Mexico, Albuquerque

Guanyu Wang , University of New Mexico, Albuquerque

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.120

ABSTRACT

We present a simple and robust method for image and volume data segmentation based on manifold distance metrics. This is done by treating the image as a function that maps the 2D (image) or 3D (volume) to a 2D or 3D manifold in a higher dimensional feature space. We explore a range of possible feature spaces, including value, gradient, and probabilistic measures, and examine the consequences of including these measures in the feature space. The time and space computational complexity of our segmentation algorithm is O(N), which allows interactive, user-centric segmentation even for large data sets. We show that this method, given appropriate choice of feature vector, produces results both qualitatively and quantitatively similar to Level Sets, Random Walkers, and others. We validate the robustness of this segmentation scheme with comparisons to standard ground-truth models and sensitivity analysis of the algorithm.

INDEX TERMS

Hypothesis testing, visual evidence, data segmentation, extraction of surfaces (isosurfaces, material boundaries), multifield, multimodal, and multivariate data, uncertainty visualization.

CITATION

Joe Kniss, Guanyu Wang, "Supervised Manifold Distance Segmentation",

*IEEE Transactions on Visualization & Computer Graphics*, vol.17, no. 11, pp. 1637-1649, November 2011, doi:10.1109/TVCG.2010.120REFERENCES

- [1] C. Bajaj, V. Pascucci, and D. Schikore, “The Contour Spectrum,”
Proc. IEEE Visualization Conf. '97, pp. 167-173, 1997.- [2] S. Beucher and C. Lantuejoul, “Use of Watersheds in Contour Detection,”
Proc. Int'l Workshop Image Processing: Real-Time Edge and Motion Detection/Estimation, Sept. 1979.- [3] A. Bieniek and A. Moga, “An Efficient Watershed Algorithm Based on Connected Components,”
Pattern Recognition, vol. 33, no. 6, pp. 907-916, 2000.- [4] J. Chen, S. Paris, and F. Durand, “Real-Time Edge-Aware Image Processing with the Bilateral Grid,”
Proc. ACM SIGGRAPH '07, 2007.- [5] D. Comaniciu and P. Meer, “Mean Shift: A Robust Approach Toward Feature Space Analysis,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 5, pp. 603-619, May 2002.- [6] A. Criminisi, T. Sharp, and A. Blake, “GeoS: Geodesic Image Segmentation,”
Proc. European Conf. Computer Vision (ECCV, Part 1), D. Forsyth, P. Torr, and A. Zisserman, eds., pp. 99-112, 2008.- [7] S. Djurcilov, K. Kim, P.F.J. Lermusiaux, and A. Pang, “Volume Rendering Data with Uncertainty Information,”
Proc. Joint Eurographic-IEEE TCVG Symp. Visualization, pp. 243-252, 2001.- [8] R.O. Duda, P.E. Hart, and D.G. Stork,
Pattern Classification. Wiley, 2000.- [9] P. Felzenszwalb and D. Huttenlocher, “Efficient Graph-Based Image Segmentation,”
Int'l J. Computer Vision, vol. 59, no. 2, pp. 167-181, Sept. 2004.- [10] J. Freixenet, X. Muoz, D. Raba, J. Mart, and X. Cuf, “Yet Another Survey on Image Segmentation: Region and Boundary Information Integration,”
Proc. European Conf. Computer Vision (ECCV), pp. 408-422, 2002.- [11] K. Fukunaga and L.D. Hostetler, “The Estimation of the Gradient of a Density Function, with Applications in Pattern Recognition,”
IEEE Trans. Information Theory, vol. IT-21, no. 1, pp. 32-40, Jan. 1975.- [12] B. Georgescu and C.M. Christoudias, “Edge Detection and Image Segmentation System,” http://www.caip.rutgers.edu/riul/ research code.html, Mar. 2009.
- [13] L. Grady, “Multilabel Random Walker Image Segmentation Using Prior Models,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR '05), 2005.- [14] L. Grady, “Walker Algorithm and Script,” http://cns-web.bu. edulgrady/, Mar. 2009.
- [15] L. Grady and A.K. Sinop, “Fast Approximate Random Walker Segmentation Using Eigenvector Precomputation,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), 2008.- [16] J. Hanc, S. Tuleja, and M. Hancova, “Simple Derivation of Newtonian Mechanics from the Principle of Least Action,”
Am. J. Physics, vol. 71, pp. 386-391, 2003.- [17] L. Ibanez, W. Schroeder, L. Ng, and J. Cates,
The ITK Software Guide: The Insight Segmentation and Registration Toolkit. Kitware, Inc., 2003.- [18] T.R. Jones, A. Carpenter, and P. Golland, “Voronoi-Based Segmentation of Cells on Image Manifolds,”
Proc. First Int'l Workshop Computer Vision for Biomedical Image Applications (CVBIA), pp. 535-543, 2005.- [19] G. Kindlmann and J.W. Durkin, “Semi-Automatic Generation of Transfer Functions for Direct Volume Rendering,”
Proc. IEEE Symp. Volume Visualization (VVS '98), pp. 79-86, 1998.- [20] J. Kniss, G. Kindlmann, and C. Hansen, “Multidimensional Transfer Functions for Interactive Volume Rendering,”
IEEE Trans. Visualization and Computer Graphics, vol. 8, no. 3, pp. 270-285, July-Sept. 2002.- [21] J.M. Kniss, R. van Uitert, A. Stephens, G.-S. Li, T. Tasdizen, and C. Hansen, “Statistically Quantitative Volume Visualization,”
Proc. IEEE Visualization Conf., p. 37, 2005.- [22] D. Laidlaw, “Geometric Model Extraction from Magnetic Resonance Volume Data,” PhD thesis, California Inst. of Tech nology, 1995.
- [23] M. Levoy, “Display of Surfaces from Volume Data,” PhD thesis, Univ. of North Carolina, 1989.
- [24] C. Lundstrom, P. Ljung, A. Persson, and A. Ynnerman, “Uncertainty Visualization in Medical Volume Rendering Using Probabilistic Animation,”
IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 6, pp. 1648-1655, Nov./Dec. 2007.- [25] D. Marr and E.C. Hildreth, “Theory of Edge Detection,”
Proc. Royal Soc. of London. Series B, Biological Sciences, vol. 207, pp. 187-217, Feb. 1980.- [26] C. Olston and J.D. Mackinlay, “Visualizing Data with Bounded Uncertainty,”
Proc. IEEE Symp. Information Visualization (InfoVis '02), pp. 37-40, 2002.- [27] S. Osher and J.A. Sethian, “Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,”
J. Computational Physics, vol. 79, pp. 12-49, 1988.- [28] S. Paris and F. Durand, “A Topological Approach to Hierarchical Segmentation Using Mean Shift,”
Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR '07), 2007.- [29] P. Perona and J. Malik, “Scale-Space and Edge Detection Using Anisotropic Diffusion,”
IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629-639, July 1990.- [30] Y. Sato, C.-F. Westin, A. Bhalerao, S. Nakajima, N. Shiraga, S. Tamura, and R. Kikinis, “Tissue Classification Based on 3D Local Intensity Structures for Volume Rendering,”
IEEE Trans. Visualization and Computer Graphics, vol. 6, no. 2, pp. 160-180, Apr.-June 2000.- [31] N. Sochen, R. Kimmel, and R. Malladi, “From High Energy Physics to Low Level Vision,”
Proc. ONR Workshop, vol. 5, pp. 236-247, 1996.- [32] M. Thorup, “Undirected Single-Source Shortest Paths with Positive Integer Weights in Linear Time,”
J. ACM, vol. 46, no. 3, pp. 362-394, 1999.- [33] C. Tomasi and R. Manduchi, “Bilateral Filtering for Gray and Color Images,”
Proc. IEEE Int'l Conf. Computer Vision, 1998.- [34] F. Tzeng, E. Lum, and K. Ma, “An Intelligent System Approach to Higher Dimensional Classification of Volume Data,”
IEEE Trans. Visualization and Computer Graphics, vol. 11, no. 3, pp. 273-284, May/June 2005.- [35] F. Tzeng and K. Ma, “A Cluster-Space Visual Interface for Arbitrary Dimensional Classification of Volume Data,”
Proc. IEEE Technical Committee on Visualization and Graphics (TCVG) Symp. Visualization, 2004. |