An Efficient Plugin for Representing Heterogeneous Translucent Materials Sermet ¨ Onel Department of Computer Engineering Yas ¸ar University Email: sermet.onel@yasar.edu.tr Murat Kurt International Computer Institute Ege University Email: murat.kurt@ege.edu.tr Aydın ¨ Ozt¨ urk Department of Computer Engineering ˙ Izmir University Email: aydin.ozturk@izmir.edu.tr Abstract—This paper presents a plugin that adds an efficient representation of heterogeneous translucent materials to the Blender 3D modeling tool. Algorithm of the plugin is based on Singular Value Decomposition (SVD) method and Mitsuba renderer is the default rendering software used by the proposed plugin. We validate the efficiency of the proposed plugin by using a set of measured heterogeneous subsurface scattering data sets. Keywords—BSSRDF, Subsurface Scattering Model, Factoriza- tion, Heterogeneous Subsurface Scattering, Mitsuba Renderer, Blender 3D Modeling Tool I. I NTRODUCTION Efficient representation of heterogeneous translucent mate- rials in computer graphics is a common problem. A number of efficient methods have been proposed to represent the Bidi- rectional Scattering Surface Reflectance Distribution Function (BSSRDF) for homogeneous translucent materials [1], [2]. However, none of these methods could be generalized to provide proper outputs for heterogeneous translucent materials. The characteristics of having structural deficiencies, impurities and composite structures inside the object volume of heteroge- neous translucent materials require approaches with a different view point [3], [4], [5], [6], [7]. On the other hand, high storage needs and computational costs of these algorithms remain to be a major problem to be resolved. In this study, we use the Singular Value Decomposition (SVD) method for the BSSRDF representation of hetero- geneous translucent materials. The proposed approach was implemented in C++ and included in the source codes of Mitsuba renderer project [8]. The integration plugin which has already been available for use by [9], was modified and imported into the three dimensional (3D) Blender modeling tool [10]. Our plugin helps to render heterogeneous translucent ma- terials accurately and efficiently. As it can be seen in Figure 7 and Figure 8, the rendering output of the plugin gives hetero- geneous subsurface scattering effects visually plausibly. II. RELATED WORK The problem of representing BSSRDF for heterogeneous translucent materials has an extensive literature. Major efforts have been devoted to the development of some approximation models. The underlying approaches broadly can be classified into two groups. The first group includes the techniques that extend the Jensen’s Dipole Diffusion Approximation Model [1] and the second group consists of the techniques that are based on development of new material models. Jensen’s Dipole Diffusion Approximation model reduces computation time of eight dimensional BSSRDF [11] to ac- ceptable rates. This approach is effective on homogeneous translucent materials and extended by many researchers [12], [13], [14], [15], [16]. Nevertheless, the main observation of light being isotropic and modeling homogeneous translucent materials make this model inappropriate for heterogeneous BSSRDF representation. Jakob et al. [12] extended the Dipole Diffusion Approx- imation model by using anisotropic approach. This model improved the Jensen et al.’s model, however, the output of this model does not give visually plausible heterogeneous subsurface scattering effects. Mertens et al. [13] modeled human skin by using an interactive method to achieve local subsurface scattering. Donner and Jensen’s [14] study is based on using multiple dipoles and they represented their study on paper and human skin. Another study was presented by Jimenez et al. [15] in which human skin was represented. Considering the psychological states of human face, Jimenez et al. [16] also modeled facial appearance for different regions on the face. The second group of techniques includes Goesele et al.’s [5] compact model depending on underlying geometry, Tong et al.’s [6] model of quasi-homogeneous materials and Song et al.’s [7] SubEdit representation which allows interactive editing and rendering of translucent materials. Although these tech- niques classified in this group have made some improvements on heterogeneous BSSRDF representation, their design issues still prevent them to provide efficient solution for the problem. The Peers et al.s’ work [17] was an important step for the solution of the problem. In their study, they employed the Non- Negative Matrix Factorization (NMF) algorithm. Replacing the Tucker-based factorization on tensor decomposition with the NMF algorithm, the same algorithm was also used by Kurt et al. [3]. Kurt [18] also used Singular Value Decomposition method on tensor decomposition and reported that the under- lying algorithm has improved the computational efficiency for the data with two dimensional (2D) matrices [18]. This was the main motivation in our work and following his work, his corresponding algorithm was imported through our plugin and an efficient heterogeneous subsurface scattering representation was put into service for 3D modeling tools.