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Mathematical Problems in Engineering
Volume 2016, Article ID 4547138, 13 pages
Research Article

A Clustering-Based Automatic Transfer Function Design for Volume Visualization

1College of Computer Science, Sichuan University, Chengdu 610065, China
2Guangdong Provincial Key Laboratory of Computer Vision and Virtual Reality Technology, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
3Department of Computer Science and Engineering, The Chinese University of Hong Kong, Sha Tin, Hong Kong
4Department of Computer Science, Caritas Institute of Higher Education, Tseung Kwan O, Hong Kong
5Centre for Smart Health, School of Nursing, Hong Kong Polytechnic University, Hung Hom, Hong Kong

Received 12 April 2016; Revised 6 September 2016; Accepted 26 September 2016

Academic Editor: Alberto Borboni

Copyright © 2016 Tianjin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The two-dimensional transfer functions (TFs) designed based on intensity-gradient magnitude (IGM) histogram are effective tools for the visualization and exploration of 3D volume data. However, traditional design methods usually depend on multiple times of trial-and-error. We propose a novel method for the automatic generation of transfer functions by performing the affinity propagation (AP) clustering algorithm on the IGM histogram. Compared with previous clustering algorithms that were employed in volume visualization, the AP clustering algorithm has much faster convergence speed and can achieve more accurate clustering results. In order to obtain meaningful clustering results, we introduce two similarity measurements: IGM similarity and spatial similarity. These two similarity measurements can effectively bring the voxels of the same tissue together and differentiate the voxels of different tissues so that the generated TFs can assign different optical properties to different tissues. Before performing the clustering algorithm on the IGM histogram, we propose to remove noisy voxels based on the spatial information of voxels. Our method does not require users to input the number of clusters, and the classification and visualization process is automatic and efficient. Experiments on various datasets demonstrate the effectiveness of the proposed method.