Tensor approximation in visualization and graphics

In this course, we will introduce the basic concepts of tensor approximation (TA) – a higher-order generalization of the SVD and PCA methods – as well as its applications to visual data representation, analysis and visualization, and bring the TA framework closer to visualization and computer graphics researchers and practitioners. The course will cover the theoretical background of TA methods, their properties and how to compute them, as well as practical applications of TA methods in visualization and computer graphics contexts. In a first theoretical part, the attendees will be instructed on the necessary mathematical background of TA methods to learn the basics skills of using and applying these new tools in the context of the representation of large multidimensional visual data. Specific and very noteworthy features of the TA framework are highlighted which can effectively be exploited for spatio-temporal multidimensional data representation and visualization purposes. In two application oriented sessions, compact TA data representation in scientific visualization and computer graphics as well as decomposition and reconstruction algorithms will be demonstrated. At the end of the course, the participants will have a good basic knowledge of TA methods along with a practical understanding of its potential application in visualization and graphics related projects

Scalable Boolean Tensor Factorizations using Random Walks

Tensors are becoming increasingly common in data mining, and consequently, tensor factorizations are becoming more and more important tools for data miners. When the data is binary, it is natural to ask if we can factorize it into binary factors while simultaneously making sure that the reconstructed tensor is still binary. Such factorizations, called Boolean tensor factorizations, can provide improved interpretability and find Boolean structure that is hard to express using normal factorizations. Unfortunately the algorithms for computing Boolean tensor factorizations do not usually scale well. In this paper we present a novel algorithm for finding Boolean CP and Tucker decompositions of large and sparse binary tensors. In our experimental evaluation we show that our algorithm can handle large tensors and accurately reconstructs the latent Boolean structure

Interactive high fidelity visualization of complex materials on the GPU

Documento submetido para revisão pelos pares. A publicar em Computers & Graphics. ISSN 0097-8493. 37:7 (nov. 2013) p. 809–819High fidelity interactive rendering is of major importance for footwear designers, since it allows experimenting with virtual prototypes of new products, rather than producing expensive physical mock-ups. This requires capturing the appearance of complex materials by resorting to image based approaches, such as the Bidirectional Texture Function (BTF), to allow subsequent interactive visualization, while still maintaining the capability to edit the materials' appearance. However, interactive global illumination rendering of compressed editable BTFs with ordinary computing resources remains to be demonstrated. In this paper we demonstrate interactive global illumination by using a GPU ray tracing engine and the Sparse Parametric Mixture Model representation of BTFs, which is particularly well suited for BTF editing. We propose a rendering pipeline and data layout which allow for interactive frame rates and provide a scalability analysis with respect to the scene's complexity. We also include soft shadows from area light sources and approximate global illumination with ambient occlusion by resorting to progressive refinement, which quickly converges to an high quality image while maintaining interactive frame rates by limiting the number of rays shot per frame. Acceptable performance is also demonstrated under dynamic settings, including camera movements, changing lighting conditions and dynamic geometry.Work partially funded by QREN project nbr. 13114 TOPICShoe and by National Funds through the FCT - Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within projectPEst-OE/EEI/UI0752/2011

Noisy Tensor Completion for Tensors with a Sparse Canonical Polyadic Factor

In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDECOMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and then instantiate these bounds for the case of additive white Gaussian noise. We also provide an ADMM-type algorithm for solving the complexity-regularized maximum likelihood problem and validate the theoretical finding via experiments on synthetic data set

Joint Material and Illumination Estimation from Photo Sets in the Wild

Faithful manipulation of shape, material, and illumination in 2D Internet images would greatly benefit from a reliable factorization of appearance into material (i.e., diffuse and specular) and illumination (i.e., environment maps). On the one hand, current methods that produce very high fidelity results, typically require controlled settings, expensive devices, or significant manual effort. To the other hand, methods that are automatic and work on 'in the wild' Internet images, often extract only low-frequency lighting or diffuse materials. In this work, we propose to make use of a set of photographs in order to jointly estimate the non-diffuse materials and sharp lighting in an uncontrolled setting. Our key observation is that seeing multiple instances of the same material under different illumination (i.e., environment), and different materials under the same illumination provide valuable constraints that can be exploited to yield a high-quality solution (i.e., specular materials and environment illumination) for all the observed materials and environments. Similar constraints also arise when observing multiple materials in a single environment, or a single material across multiple environments. The core of this approach is an optimization procedure that uses two neural networks that are trained on synthetic images to predict good gradients in parametric space given observation of reflected light. We evaluate our method on a range of synthetic and real examples to generate high-quality estimates, qualitatively compare our results against state-of-the-art alternatives via a user study, and demonstrate photo-consistent image manipulation that is otherwise very challenging to achieve

Tensor Approximation for Multidimensional and Multivariate Data

Tensor decomposition methods and multilinear algebra are powerful tools to cope with challenges around multidimensional and multivariate data in computer graphics, image processing and data visualization, in particular with respect to compact representation and processing of increasingly large-scale data sets. Initially proposed as an extension of the concept of matrix rank for 3 and more dimensions, tensor decomposition methods have found applications in a remarkably wide range of disciplines. We briefly review the main concepts of tensor decompositions and their application to multidimensional visual data. Furthermore, we will include a first outlook on porting these techniques to multivariate data such as vector and tensor fields

固有値分解とテンソル分解を用いた大規模グラフデータ分析に関する研究

筑波大学 (University of Tsukuba)201