Anatomically realistic volume conductor models of the human head are important for accurate forward modeling of the electric field during transcranial brain stimulation (TBS), electro- (EEG) and magnetoencephalography (MEG). In particular, the skull compartment exerts a strong influence on the field distribution due to its low conductivity, suggesting the need to represent its geometry accurately. However, automatic skull reconstruction from structural magnetic resonance (MR) images is difficult, as compact bone has a very low signal in magnetic resonance imaging (MRI). Here, we evaluate three methods for skull segmentation, namely FSL BET2, the unified segmentation routine of SPM12 with extended spatial tissue priors, and the skullfinder tool of BrainSuite. To our knowledge, this study is the first to rigorously assess the accuracy of these state-of-the-art tools by comparison with CT-based skull segmentations on a group of ten subjects. We demonstrate several key factors that improve the segmentation quality, including the use of multi-contrast MRI data, the optimization of the MR sequences and the adaptation of the parameters of the segmentation methods. We conclude that FSL and SPM12 achieve better skull segmentations than BrainSuite. The former methods obtain reasonable results for the upper part of the skull when a combination of T1- and T2-weighted images is used as input. The SPM12-based results can be improved slightly further by means of simple morphological operations to fix local defects. In contrast to FSL BET2, the SPM12-based segmentation with extended spatial tissue priors and the BrainSuite-based segmentation provide coarse reconstructions of the vertebrae, enabling the construction of volume conductor models that include the neck. We exemplarily demonstrate that the extended models enable a more accurate estimation of the electric field distribution during transcranial direct current stimulation (tDCS) for montages that involve extraencephalic electrodes. The methods provided by FSL and SPM12 are integrated into pipelines for the automatic generation of realistic head models based on tetrahedral meshes, which are distributed as part of the open-source software package SimNIBS for field calculations for transcranial brain stimulation.

The bidirectional reflectance distribution function (BRDF) is critical for rendering, and accurate material representation requires data-driven reflectance models. However, isotropic BRDFs are 3D functions, and measuring the reflectance of a flat sample can require a million incident and outgoing direction pairs, making the use of measured BRDFs impractical. In this paper, we address the problem of reconstructing a measured BRDF from a limited number of samples. We present a novel mapping of the BRDF space, allowing for extraction of descriptive principal components from measured databases, such as the MERL BRDF database. We optimize for the best sampling directions, and explicitly provide the optimal set of incident and outgoing directions in the Rusinkiewicz parameterization for n = {1, 2, 5, 10, 20} samples. Based on the principal components, we describe a method for accurately reconstructing BRDF data from these limited sets of samples. We validate our results on the MERL BRDF database, including favorable comparisons to previous sets of industry-standard sampling directions, as well as with BRDF measurements of new flat material samples acquired with a gantry system. As an extension, we also demonstrate how this method can be used to find optimal sampling directions when imaging a sphere of a homogeneous material; in this case, only two images are often adequate for high accuracy.