ORIGINAL ARTICLE Electric-field-based Transfer Functions for Volume Visualization Yipeng Song 1 • Jie Yang 1 • Lei Zhou 1 • Yuemin Zhu 2 Received: 1 April 2014 / Accepted: 3 July 2014 Ó Taiwanese Society of Biomedical Engineering 2015 Abstract Transfer functions play a crucial role in direct volume rendering. The intensity and gradient magnitude (IGM) space is one of the most commonly used transfer function spaces, in which boundaries between different materials appear as arches. However, there are often overlapping regions of adjacent arches in the space, which makes it difficult for users to design good transfer functions for exploring and visualizing tissues of interest. To deal with this problem, the present study proposes a transfer function space based on electric field theory. For each voxel, the volume charge density and electric force mag- nitude in its local neighborhood are calculated. Then, the two properties are used to create the transfer function space. Compared with the IGM space, the proposed space significantly reduces the number of overlapping regions of adjacent arches and produces more compact arches. Thus, users can design appropriate transfer functions for tissues of interest and obtain meaningful visualizations. Results for various datasets are used to illustrate the effectiveness of the proposed method. Keywords Electric force field  Volume charge density  Transfer functions  Direct volume rendering 1 Introduction Direct volume rendering has been proven to be one of the most powerful techniques for visualizing three-dimensional (3D) volume data, such as computed tomography (CT) images and magnetic resonance imaging (MRI) images. Its rendering results mainly rely on transfer functions [1–3]. In direct volume rendering, transfer functions are functions that specify the mapping from voxel values to optical properties [4]: T : V 1  V 2  V n ! O 1  O 2  O n where V i represents different data properties at each voxel (e.g., gradient magnitude [5], distance [6], and curvature [7]) whose cartesian product constructs the transfer func- tion space. O i represents different optical properties (e.g., color and opacity) and T is the mapping rules from data properties to optical properties. Transfer functions play a fundamental role in direct volume rendering, as they de- termine which tissues of interest are visualized by different opacity values and how they are visually displayed by different color values. Transfer functions are an active and ongoing research topic in direct volume rendering. Kindlmann and Durkin [5] employed the intensity and gradient magnitude (IGM) to generate a two-dimensional (2D) IGM space, in which the boundary of different materials is shown as an arch. Kniss et al. [1] extended the conception and utilized ma- nipulation widgets to interactively design transfer functions by selecting peaks of the arches. Rottger et al. [8] added spatial information into the 2D IGM space. Wu and Qu [9] presented a framework based on image-similarity and ge- netic algorithms, by which users can directly edit features in the rendered images. Wang et al. [10] automatically separated initial features in the space by modeling it using & Jie Yang jieyang@sjtu.edu.cn 1 Institute of Image Processing and Pattern Recognition, Shanghai Jiaotong University, Shanghai 200240, China 2 CNRS UMR5220, CREATIS, Inserm U1044, INSA Lyon, University of Lyon, 69100 Lyon, France 123 J. Med. Biol. Eng. DOI 10.1007/s40846-015-0027-6