We present a novel approach enabling interactive visualization of volumetric Locally Refined B-splines (LR-splines). To this end we propose a highly efficient algorithm for direct visualization of scalar and vector fields given by an LR-spline. For the case of scalar fields a volume rendering approach is designed, along with methods for the necessary adaptive sampling distance, on-the-fly trimming with a surface geometry given by a STereoLithography (STL)-file, and local volume illumination based on on-the-fly evaluation of the derivative of the underlying LR-spline function. For vector fields we design a two-stage algorithm consisting of the computation of stream lines with adaptive step size and their rendering with tubes. In both cases, the common basic ingredient to achieve interactive frame rates is an acceleration structure based on a k-d forest together with suitable data structures. The algorithms are designed to fully utilize modern graphics processing unit (GPU) capabilities. Important applications where LR-spline volumes emerge are given for instance by approximation of large-scale simulation and sensor data, and Isogeometric Analysis (IGA). For the first case -- approximation of large three dimensional point clouds with an associated field -- we provide an extension of the multilevel B-spline approximation (MBA) algorithm to the case of volumetric LR-splines. We showcase interactive rendering achieved by our approach on different representative use cases, stemming from simulations of wind flow around a telescope, Magnetic Resonance (MR) imaging of a human brain, and simulations of a fluidized bed used for mixing and coating particles in industrial processes.
The visualization of a scalar field is commonly done by modeling the scalar field as a participating medium, where a modifiable transfer function specifies how field values are mapped to emitted color and transparency. In the simplest case, where the field consists of discrete samples over a regular grid, an abundance of results is available, see e.g., Levoy @cite_15 for an early example or Engel at al. @cite_0 for an overview. Octrees allow a voxel grid to have different resolutions across the domain, which reduces the amount of data needed for a given scene. This is used in e.g., GigaVoxels @cite_14 , which offers real-time rendering of several billion voxels. GigaVoxels is only effective when there is an a priorily known location of significant regions of empty space.
@cite_0 @cite_15 @cite_14
2020429267 2800554784 2031619085 2462462929
We present a novel method to obtain fine-scale detail in 3D reconstructions generated with low-budget RGB-D cameras or other commodity scanning devices. As the depth data of these sensors is noisy, truncated signed distance fields are typically used to regularize out the noise, which unfortunately leads to over-smoothed results. In our approach, we leverage RGB data to refine these reconstructions through shading cues, as color input is typically of much higher resolution than the depth data. As a result, we obtain reconstructions with high geometric detail, far beyond the depth resolution of the camera itself. Our core contribution is shading-based refinement directly on the implicit surface representation, which is generated from globally-aligned RGB-D images. We formulate the inverse shading problem on the volumetric distance field, and present a novel objective function which jointly optimizes for fine-scale surface geometry and spatially-varying surface reflectance. In order to enable the efficient reconstruction of sub-millimeter detail, we store and process our surface using a sparse voxel hashing scheme which we augment by introducing a grid hierarchy. A tailored GPU-based Gauss-Newton solver enables us to refine large shape models to previously unseen resolution within only a few seconds. The low spatial resolution of light-field image poses significant difficulties in exploiting its advantage. To mitigate the dependency of accurate depth or disparity information as priors for light-field image super-resolution, we propose an implicitly multi-scale fusion scheme to accumulate contextual information from multiple scales for super-resolution reconstruction. The implicitly multi-scale fusion scheme is then incorporated into bidirectional recurrent convolutional neural network, which aims to iteratively model spatial relations between horizontally or vertically adjacent sub-aperture images of light-field data. Within the network, the recurrent convolutions are modified to be more effective and flexible in modeling the spatial correlations between neighboring views. A horizontal sub-network and a vertical sub-network of the same network structure are ensembled for final outputs via stacked generalization. Experimental results on synthetic and real-world data sets demonstrate that the proposed method outperforms other state-of-the-art methods by a large margin in peak signal-to-noise ratio and gray-scale structural similarity indexes, which also achieves superior quality for human visual systems. Furthermore, the proposed method can enhance the performance of light field applications such as depth estimation. In uncertain scalar fields where data values vary with a certain probability, the strength of this variability indicates the confidence in the data. It does not, however, allow inferring on the effect of uncertainty on differential quantities such as the gradient, which depend on the variability of the rate of change of the data. Analyzing the variability of gradients is nonetheless more complicated, since, unlike scalars, gradients vary in both strength and direction. This requires initially the mathematical derivation of their respective value ranges, and then the development of effective analysis techniques for these ranges. This paper takes a first step into this direction: Based on the stochastic modeling of uncertainty via multivariate random variables, we start by deriving uncertainty parameters, such as the mean and the covariance matrix, for gradients in uncertain discrete scalar fields. We do not make any assumption about the distribution of the random variables. Then, for the first time to our best knowledge, we develop a mathematical framework for computing confidence intervals for both the gradient orientation and the strength of the derivative in any prescribed direction, for instance, the mean gradient direction. While this framework generalizes to 3D uncertain scalar fields, we concentrate on the visualization of the resulting intervals in 2D fields. We propose a novel color diffusion scheme to visualize both the absolute variability of the derivative strength and its magnitude relative to the mean values. A special family of circular glyphs is introduced to convey the uncertainty in gradient orientation. For a number of synthetic and real-world data sets, we demonstrate the use of our approach for analyzing the stability of certain features in uncertain 2D scalar fields, with respect to both local derivatives and feature orientation. In this paper, we propose a non-local structured prior for volumetric multi-view 3D reconstruction. Towards this goal, we present a novel Markov random field model based on ray potentials in which assumptions about large 3D surface patches such as planarity or Manhattan world constraints can be efficiently encoded as probabilistic priors. We further derive an inference algorithm that reasons jointly about voxels, pixels and image segments, and estimates marginal distributions of appearance, occupancy, depth, normals and planarity. Key to tractable inference is a novel hybrid representation that spans both voxel and pixel space and that integrates non-local information from 2D image segmentations in a principled way. We compare our non-local prior to commonly employed local smoothness assumptions and a variety of state-of-the-art volumetric reconstruction baselines on challenging outdoor scenes with textureless and reflective surfaces. Our experiments indicate that regularizing over larger distances has the potential to resolve ambiguities where local regularizers fail.