Abstract The use of spatially varying reflectance models (SVBRDF) is the state of the art in physically based rendering and the ultimate goal is to acquire them from real world samples. Recently several promising deep learning approaches have emerged that create such models from a few uncalibrated photos, after being trained on synthetic SVBRDF datasets. While the achieved results are already very impressive, the reconstruction accuracy that is achieved by these approaches is still far from that of specialized devices. On the other hand, fitting SVBRDF parameter maps to the gibabytes of calibrated HDR images per material acquired by state of the art high quality material scanners takes on the order of several hours for realistic spatial resolutions. In this paper, we present a first deep learning approach that is capable of producing SVBRDF parameter maps more than two orders of magnitude faster than state of the art approaches, while still providing results of equal quality and generalizing to new materials unseen during the training. This is made possible by training our network on a large‐scale database of material scans that we have gathered with a commercially available SVBRDF scanner. In particular, we train a convolutional neural network to map calibrated input images to the 13 parameter maps of an anisotropic Ward BRDF, modified to account for Fresnel reflections, and evaluate the results by comparing the measured images against re‐renderings from our SVBRDF predictions. The novel approach is extensively validated on real world data taken from our material database, which we make publicly available under https://cg.cs.uni‐bonn.de/svbrdfs/ .

Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.

Large image deformations pose a challenging problem for the visualization and statistical analysis of 3D image ensembles which have a multitude of applications in biology and medicine. Simple linear interpolation in the tangent space of the ensemble introduces artifactual anatomical structures that hamper the application of targeted visual shape analysis techniques. In this work we make use of the theory of stationary velocity fields to facilitate interactive non-linear image interpolation and plausible extrapolation for high quality rendering of large deformations and devise an efficient image warping method on the GPU. This does not only improve quality of existing visualization techniques, but opens up a field of novel interactive methods for shape ensemble analysis. Taking advantage of the efficient non-linear 3D image warping, we showcase four visualizations: 1) browsing on-the-fly computed group mean shapes to learn about shape differences between specific classes, 2) interactive reformation to investigate complex morphologies in a single view, 3) likelihood volumes to gain a concise overview of variability and 4) streamline visualization to show variation in detail, specifically uncovering its component tangential to a reference surface. Evaluation on a real world dataset shows that the presented method outperforms the state-of-the-art in terms of visual quality while retaining interactive frame rates. A case study with a domain expert was performed in which the novel analysis and visualization methods are applied on standard model structures, namely skull and mandible of different rodents, to investigate and compare influence of phylogeny, diet and geography on shape. The visualizations enable for instance to distinguish (population-)normal and pathological morphology, assist in uncovering correlation to extrinsic factors and potentially support assessment of model quality.

Gaining insight into anatomic co variation helps the understanding of organismic shape variability in general and is of particular interest for delimiting morphological modules. Generation of hypotheses on structural co variation is undoubtedly a highly creative process, and as such, requires an exploratory approach. In this work we propose a new local anatomic covariance tensor which enables interactive visualizations to explore co variation at different levels of detail, stimulating rapid formation and (qualitative) evaluation of hypotheses. The effectiveness of the presented approach is demonstrated on a μCT dataset of mouse mandibles for which results from the literature are successfully reproduced, while providing a more detailed representation of co variation compared to state-of-the-art methods.