Abstract
Multidimensional transfer functions can perform more sophisticated classification of volumetric objects compared to 1-D transfer functions. However, visualizing and manipulating the transfer function space is non-intuitive when its dimension goes beyond 3-D, thus making user interaction difficult. In this paper, we propose to address the multidimensional transfer function design problem by taking a two-level clustering approach, where the first-level clustering by the self-organizing map (SOM) projects high-dimensional feature data to a 2-D topology preserving map, and the second-level clustering on the SOM neurons reduces the design freedom from a large number of SOM neurons to a manageable number of clusters. Based on the two-level clustering results, we propose a novel volume exploration scheme that provides top-down navigation to users exploring the volume. Guided by an informative volume overview, interesting structures in the volume are discovered interactively by the user selecting clusters to visualize and modifying the clustering results when necessary. Our interface keeps track of each interesting structure discovered, which not only enables users to inspect individual structures closely, but also allows them to compose the final visualization by fusing the structures deemed important.
Similar content being viewed by others
References
Bajaj, C., Pascucci, V., Schikore, D.: The contour spectrum. In: Proceedings of IEEE Visualization (VIS ’97), pp. 167–173 (1997)
Bevk, M., Kononenko, I.: A statistical approach to texture description of medical images: a preliminary study. In: Proceedings of the 15th IEEE Symposium on Computer-Based Medical Systems, pp. 239–244 (2002)
Bogdan, M., Rosenstiel, W.: Detection of cluster in self-organizing maps for controlling a prostheses using nerve signals. In: Proceedings of European symposium on artificial neural networks, pp. 131–136 (2001)
Brugger, D., Bogdan, M., Rosenstiel, W.: Automatic cluster detection in Kohonen’s SOM. IEEE Trans. Neural Netw. 19(3), 442–459 (2008)
Caban, J.J., Rheingans, P.: Texture-based transfer functions for direct volume rendering. IEEE Trans. Vis. Comput. Graph. 14(6), 1364–1371 (2008)
Cai, L., Tay, W.-L., Nguyen, B.P., Chui, C.-K., Ong, S.-H.: Automatic transfer function design for medical visualization using visibility distributions and projective color mapping. Comput. Med. Imaging Graph. 37(7), 450–458 (2013)
Correa, C.D., Ma, K.-L.: Size-based transfer functions: a new volume exploration technique. IEEE Trans. Vis. Comput. Graph. 14(6), 1380–1387 (2008)
Correa, C.D., Ma, K.-L.: The occlusion spectrum for volume visualization and classification. IEEE Trans. Vis. Comput. Graph. 15(6), 1465–1472 (2009)
Fujishiro, I., Azuma, T., Takeshima, Y.: Automating transfer function design for comprehensible volume rendering based on 3D field topology analysis. In: Proceedings of IEEE Visualization (Vis ’99), pp. 467–563 (1999)
Gajdoš, P., Platoš, J.: GPU based parallelism forself-organizing map. In: Proceedings of the third internationalconference on intelligent human computer interaction (IHCI 2011), vol. 179 of advances in intelligent systems and computing, pp. 231–242. Springer, Berlin, Heidelberg (2011)
Guo, H., Xiao, H., Yuan, X.: Multi-dimensional transfer function design based on flexible dimension projection embedded in parallel coordinates. In: Proceedings of IEEE pacific visualization symposium (PacificVis), pp. 19–26 (2011)
Haidacher, M., Patel, D., Bruckner, S., Kanitsar, A., Gröller, M.: Volume visualization based on statistical transfer-function spaces. In: Proceedings of IEEE pacific visualization symposium (PacificVis), pp. 17–24 (2010)
Hladuvka, J., König, A., Gröller, E.: Curvature-based transfer functions for direct volume rendering. Proc. Spring Conf. Comput. Graph. 16, 58–65 (2000)
Hsieh, T.-J., Yang, Y.-S., Wang, J.-H., Shen, W.-J.: Feature extraction using bionic particle swarm tracing for transfer function design in direct volume rendering. Vis. Comput. 30(1), 33–44 (2014)
Ip, C.Y., Varshney, A., JaJa, J.: Hierarchical exploration of volumes using multilevel segmentation of the intensity-gradient histograms. IEEE Trans. Vis. Comput. Graph. 18, 2355–2363 (2012)
Khan, N.M., Kyan, M., Guan, L.: Intuitive volume exploration through spherical self-organizing map. In: Advances in self-organizing maps, pp. 75–84. Springer (2013)
Kiang, M.Y.: Extending the kohonen self-organizing map networks for clustering analysis. Comput. Stat. Data Anal. 38(2), 161–180 (2001)
Kim, H.S., Schulze, J.P., Cone, A.C., Sosinsky, G.E., Martone, M.E.: Dimensionality reduction on multi-dimensional transfer functions for multi-channel volume data sets. Inf. Vis. 9(3), 167–180 (2010)
Kindlmann, G., Durkin, J.W.: Semi-automatic generation of transfer functions for direct volume rendering. In: Proceedings of IEEE symposium on volume visualization, pp. 79–86 (1998)
Kniss, J., Kindlmann, G., Hansen, C.: Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets. In: Proceedings of IEEE visualization (VIS ’01), pp. 255–262. IEEE Computer Society (2001)
Kniss, J., Kindlmann, G., Hansen, C.: Multidimensional transfer functions for interactive volume rendering. IEEE Trans. Vis. Comput. Graph. 8(3), 270–285 (2002)
Kohonen, T.: The self-organizing map. Proc. IEEE 78(9), 1464–1480 (1990)
Lau, D.P., Chng, C.B., Chui, C.K.: New device for single-stage in-office secondary tracheoesophageal puncture: animal studies. Head Neck (2014)
Linsen, L., Van Long, T., Rosenthal, P., Rosswog, S.: Surface extraction from multi-field particle volume data using multi-dimensional cluster visualization. IEEE Trans. Vis. Comput. Graph. 14(6), 1483–1490 (2008)
Maciejewski, R., Chen, W., Woo, I., Ebert, D.S.: Structuring feature space—a non-parametric method for volumetric transfer function generation. IEEE Trans. Vis. Comput. Graph. 15(6), 1473–1480 (2009)
Moutarde, F., Ultsch, A. et al.: U\(*\) F clustering: a new performant “cluster-mining” method based on segmentation of self-organizing maps. In: Proceedings of workshop on self-organizing maps (2005)
Nguyen, B.P., Tay, W.-L., Chui, C.-K., Ong, S.-H.: A clustering-based system to automate transfer function design for medical image visualization. Vis. Comput. 28(2), 181–191 (2012)
Opolon, D., Moutarde, F.: Fast semi-automatic segmentation algorithm for self-organizing maps. In: Proceedings of European symposium on artifical neural networks (2004)
Petrilis, D., Halatsis, C.: Two-level clustering of web sites using self-organizing maps. Neural Process. Lett. 27(1), 85–95 (2008)
Pinto, F.d.M., Freitas, C.M.: Design of multi-dimensional transfer functions using dimensional reduction. In: Proceedings of eurographics/IEEE-VGTC symposium on visualization, pp. 131–138. Eurographics Association (2007)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22, 888–905 (2000)
Shi, J., Malik, J.: Normalized cut segmentation code. University of Pennsylvania, Computer and Information Science Department (2004)
Su, M.-C., Liu, T.-K., Chang, H.-T.: An efficient initialization scheme for the self-organizing feature map algorithm. In: Proceedings of international joint conference on neural networks, vol. 3, pp. 1906–1910. IEEE (1999)
Tzeng, F.-Y., Lum, E.B., Ma, K.-L.: An intelligent system approach to higher-dimensional classification of volume data. IEEE Trans. Vis. Comput. Graph. 11(3), 273–284 (2005)
Tzeng, F.-Y., Ma, K.-L.: A cluster-space visual interface for arbitrary dimensional classification of volume data. In: Proceedings of eurographics/IEEE-VGTC symposium on visualization, pp. 17–24 (2004)
Ultsch, A.: Self-organizing neural networks for visualisation and classification. In: Information and classification, pp. 307–313. Springer (1993)
Ultsch, A.: Maps for the visualization of high-dimensional data spaces. In: Proceedings of workshop on self-organizing maps, pp. 225–230 (2003)
Ultsch, A.: U\(*\)-matrix: a tool to visualize clusters in high dimensional data. Fachbereich Mathematik und Informatik (2003)
Vesanto, J., Alhoniemi, E.: Clustering of the self-organizing map. IEEE Trans. Neural Netw. 11(3), 586–600 (2000)
Šereda, P., Bartroli, A.V., Serlie, I.W.O., Gerritsen, F.A.: Visualization of boundaries in volumetric data sets using LH histograms. IEEE Trans. Vis. Comput. Graph. 12(2), 208–218 (2006)
Šereda, P., Vilanova, A., Gerritsen, F.A.: Automating transfer function design for volume rendering using hierarchical clustering of material boundaries. In: Proceedings of Eurographics/IEEE-VGTC symposium on visualization, pp. 243–250 (2006)
Wang, L., Zhao, X., Kaufman, A.E.: Modified dendrogram of attribute space for multidimensional transfer function design. IEEE Trans. Vis. Comput. Graph. 18(1), 121–131 (2012)
Wang, Y., Chen, W., Zhang, J., Dong, T., Shan, G., Chi, X.: Efficient volume exploration using the gaussian mixture model. IEEE Trans. Vis. Comput. Graph. 17(11), 1560–1573 (2011)
Wang, Y., Zhang, J., Lehmann, DirkJ., Theisel, H., Chi, X.: Automating transfer function design with valley cell-based clustering of 2D density plots. In: Proceedings of eurographics conference on visualization, pp. 1295–1304 (2012)
Weber, G.H., Dillard, S.E., Carr, H., Pascucci, V., Hamann, B.: Topology-controlled volume rendering. IEEE Trans. Vis. Comput. Graph. 13(2), 330–341 (2007)
Wesarg, S., Kirschner, M.: 3D visualization of medical image data employing 2D histograms. In: Proceedings of second international conference in visualisation (VIZ ’09), pp. 153 –158 (2009)
Wu, S., Chow, T.W.: Clustering of the self-organizing map using a clustering validity index based on inter-cluster and intra-cluster density. Pattern Recogn. 37(2), 175–188 (2004)
Zhao, X., Kaufman, A.: Multi-dimensional reduction and transfer function design using parallel coordinates. In: Proceedings of the 8th IEEE/EG international conference on volume graphics, pp. 69–76. Eurographics Association (2010)
Acknowledgments
The authors would like to thank all the anonymous reviewers for their insightful comments. This work is supported in part by National University of Singapore FRC Tier 1 Grant (WBS: R265-000-446-112).
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Cai, L., Nguyen, B.P., Chui, CK. et al. A two-level clustering approach for multidimensional transfer function specification in volume visualization. Vis Comput 33, 163–177 (2017). https://doi.org/10.1007/s00371-015-1167-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-015-1167-y