A Local/Global Approach to Mesh Parameterization

We present a novel approach to parameterize a mesh with disk topology to the plane in a shape‐preserving manner. Our key contribution is a local/global algorithm, which combines a local mapping of each 3D triangle to the plane, using transformations taken from a restricted set, with a global “stitch” operation of all triangles, involving a sparse linear system. The local transformations can be taken from a variety of families, e.g. similarities or rotations, generating different types of parameterizations. In the first case, the parameterization tries to force each 2D triangle to be an as‐similar‐as‐possible version of its 3D counterpart. This is shown to yield results identical to those of the LSCM algorithm. In the second case, the parameterization tries to force each 2D triangle to be an as‐rigid‐as‐possible version of its 3D counterpart. This approach preserves shape as much as possible. It is simple, effective, and fast, due to pre‐factoring of the linear system involved in the global phase. Experimental results show that our approach provides almost isometric parameterizations and obtains more shape‐preserving results than other state‐of‐the‐art approaches. We present also a more general “hybrid” parameterization model which provides a continuous spectrum of possibilities, controlled by a single parameter. The two cases described above lie at the two ends of the spectrum. We generalize our local/global algorithm to compute these parameterizations. The local phase may also be accelerated by parallelizing the independent computations per triangle.     

Structure Preserving Manipulation and Interpolation for Multi‐element 2D Shapes

This paper presents a method that generates natural and intuitive deformations via direct manipulation and smooth interpolation for multi‐element 2D shapes. Observing that the structural relationships between different parts of a multi‐element 2D shape are important for capturing its feature semantics, we introduce a simple structure called a feature frame to represent such relationships. A constrained optimization is solved for shape manipulation to find optimal deformed shapes under user‐specified handle constraints. Based on the feature frame, local feature preservation and structural relationship maintenance are directly encoded into the objective function. Beyond deforming a given multi‐element 2D shape into a new one at each key frame, our method can automatically generate a sequence of natural intermediate deformations by interpolating the shapes between the key frames. The method is computationally efficient, allowing real‐time manipulation and interpolation, as well as generating natural and visually plausible results.     

Reusable Visualizations and Animations for Surgery Planning

For surgical planning, the exploration of 3D visualizations and 2D slice views is essential. However, the generation of visualizations which support the specific treatment decisions is very tedious. Therefore, the reuse of once designed visualizations for similar cases can strongly accelerate the process of surgical planning. We present a new technique that enables the easy reuse of both medical visualization types: 3D scenes and 2D slice views. We introduce the keystates as a concept to describe the state of a visualization in a general manner. They can be easily applied to new datasets to create similar visualizations. Keystates can be shared between surgeons of one specialization to reproduce and document the planning process for collaborative work. Furthermore, animations can support the surgeon on individual exploration and are also useful in collaborative environments, where complex issues must be presented in a short time. Therefore, we provide a framework, where animations can be visually designed by surgeons during their exploration process without any programming or authoring skills. We discuss several transitions between different visualizations and present an application from clinical routine.     

Distortion-Free Steganography for Polygonal Meshes

We present a technique for steganography in polygonal meshes. Our method hides a message in the indexed rep‐resentation of a mesh by permuting the order in which faces and vertices are stored. The permutation is relative to a reference ordering that encoder and decoder derive from the mesh connectivity in a consistent manner. Our method is distortion‐free because it does not modify the geometry of the mesh. Compared to previous steganographic methods for polygonal meshes our capacity is up to an order of magnitude better. Our steganography algorithm is universal and can be used instead of the standard permutation steganography algorithm on arbitrary datasets. The standard algorithm runs in Ω (n² log² n log log n) time and achieves optimal O(nlog n) bit capacity on datasets with n elements. In contrast, our algorithm runs in O(n) time, achieves a capacity that is only one bit per element less than optimal, and is extremely simple to implement.     

Lighting and Occlusion in a Wave-Based Framework

We present novel methods to enhance Computer Generated Holography (CGH) by introducing a complex‐valued wave‐based occlusion handling method. This offers a very intuitive and efficient interface to introduce optical elements featuring physically‐based light interaction exhibiting depth‐of‐field, diffraction, and glare effects. Fur‐thermore, an efficient and flexible evaluation of lit objects on a full‐parallax hologram leads to more convincing images. Previous illumination methods for CGH are not able to change the illumination settings of rendered holo‐grams. In this paper we propose a novel method for real‐time lighting of rendered holograms in order to change the appearance of a previously captured holographic scene. These functionalities are features of a bigger wave‐based rendering framework which can be combined with 2D framebuffer graphics. We present an algorithm which uses graphics hardware to accelerate the rendering.     

Discrete Distortion in Triangulated 3‐Manifolds

We introduce a novel notion, that we call discrete distortion, for a triangulated 3‐manifold. Discrete distortion naturally generalizes the notion of concentrated curvature defined for triangulated surfaces and provides a powerful tool to understand the local geometry and topology of 3‐manifolds. Discrete distortion can be viewed as a discrete approach to Ricci curvature for singular flat manifolds. We distinguish between two kinds of distortion, namely, vertex distortion, which is associated with the vertices of the tetrahedral mesh decomposing the 3‐manifold, and bond distortion, which is associated with the edges of the tetrahedral mesh. We investigate properties of vertex and bond distortions. As an example, we visualize vertex distortion on manifold hypersurfaces in R⁴ defined by a scalar field on a 3D mesh. distance fields.     

Lazy Solid Texture Synthesis

Existing solid texture synthesis algorithms generate a full volume of color content from a set of 2D example images. We introduce a new algorithm with the unique ability to restrict synthesis to a subset of the voxels, while enforcing spatial determinism. This is especially useful when texturing objects, since only a thick layer around the surface needs to be synthesized. A major difficulty lies in reducing the dependency chain of neighborhood matching, so that each voxel only depends on a small number of other voxels. Our key idea is to synthesize a volume from a set of pre‐computed 3D candidates, each being a triple of interleaved 2D neighborhoods. We present an efficient algorithm to carefully select in a pre‐process only those candidates forming consistent triples. This significantly reduces the search space during subsequent synthesis. The result is a new parallel, spatially deterministic solid texture synthesis algorithm which runs efficiently on the GPU. Our approach generates high resolution solid textures on surfaces within seconds. Memory usage and synthesis time only depend on the output textured surface area. The GPU implementation of our method rapidly synthesizes new textures for the surfaces appearing when interactively breaking or cutting objects.     

Deformable 3D Shape Registration Based on Local Similarity Transforms

In this paper, a new method for deformable 3D shape registration is proposed. The algorithm computes shape transitions based on local similarity transforms which allows to model not only as‐rigid‐as‐possible deformations but also local and global scale. We formulate an ordinary differential equation (ODE) which describes the transition of a source shape towards a target shape. We assume that both shapes are roughly pre‐aligned (e.g., frames of a motion sequence). The ODE consists of two terms. The first one causes the deformation by pulling the source shape points towards corresponding points on the target shape. Initial correspondences are estimated by closest‐point search and then refined by an efficient smoothing scheme. The second term regularizes the deformation by drawing the points towards locally defined rest positions. These are given by the optimal similarity transform which matches the initial (undeformed) neighborhood of a source point to its current (deformed) neighborhood. The proposed ODE allows for a very efficient explicit numerical integration. This avoids the repeated solution of large linear systems usually done when solving the registration problem within general‐purpose non‐linear optimization frameworks. We experimentally validate the proposed method on a variety of real data and perform a comparison with several state‐of‐the‐art approaches.     

Interactive Physics‐based Ink Splattering Art Creation

This paper presents an interactive system for ink splattering, a form of abstract art that artists splat ink onto the canvas. The default input device of our system is a pressure‐sensitive 2D stylus, the most common sketching tool for digital artists, and we propose two interaction mode: ink‐flicking mode and ink‐dripping mode , that are designed to be analogous to the artistic techniques of ink splattering in real world. The core of our ink splattering system is a novel three‐stage ink splattering framework that simulates the physics‐based interaction of ink with different mediums including brush heads, air and paper. We have implemented the physical engine in CUDA and the whole simulation process runs at interactive speed.     

Patch‐based Texture Interpolation

In this paper, we present a novel exemplar‐based technique for the interpolation between two textures that combines patch‐based and statistical approaches. Motivated by the notion of texture as a largely local phenomenon, we warp and blend small image neighborhoods prior to patch‐based texture synthesis. In addition, interpolating and enforcing characteristic image statistics faithfully handles high frequency detail. We are able to create both intermediate textures as well as continuous transitions. In contrast to previous techniques computing a global morphing transformation on the entire input exemplar images, our localized and patch‐based approach allows us to successfully interpolate between textures with considerable differences in feature topology for which no smooth global warping field exists.     

InSpectr: Multi‐Modal Exploration,Visualization, and Analysis of Spectral Data

This paper addresses the increasing demand in industry for methods to analyze and visualize multimodal data involving a spectral modality. Two data modalities are used: high‐resolution X‐ray computed tomography (XCT) for structural characterization and low‐resolution X‐ray fluorescence (XRF) spectral data for elemental decomposition. We present InSpectr, an integrated tool for the interactive exploration and visual analysis of multimodal, multiscalar data. The tool has been designed around a set of tasks identified by domain experts in the fields of XCT and XRF. It supports registered single scalar and spectral datasets optionally coupled with element maps and reference spectra. InSpectr is instantiating various linked views for the integration of spatial and non‐spatial information to provide insight into an industrial component's structural and material composition: views with volume renderings of composite and individual 3D element maps visualize global material composition; transfer functions defined directly on the spectral data and overlaid pie‐chart glyphs show elemental composition in 2D slice‐views; a representative aggregated spectrum and spectra density histograms are introduced to provide a global overview in the spectral view. Spectral magic lenses, spectrum probing and elemental composition probing of points using a pie‐chart view and a periodic table view aid the local material composition analysis. Two datasets are investigated to outline the usefulness of the presented techniques: a 3D virtually created phantom with a brass metal alloy and a real‐world 2D water phantom with insertions of gold, barium, and gadolinium. Additionally a detailed user evaluation of the results is provided.     

An Optimal Control Approach for Texture Metamorphosis

In this paper, we introduce a new texture metamorphosis approach for interpolating texture samples from a source texture into a target texture. We use a new energy optimization scheme derived from optimal control principles which exploits the structure of the metamorphosis optimality conditions. Our approach considers the change in pixel position and pixel appearance in a single framework. In contrast to previous techniques that compute a global warping based on feature masks of textures, our approach allows to transform one texture into another by considering both intensity values and structural features of textures simultaneously. We demonstrate the usefulness of our approach for different textures, such as stochastic, semi‐structural and regular textures, with different levels of complexities. Our method produces visually appealing transformation sequences with no user interaction.     

Modeling a Generic Tone-mapping Operator

Although several new tone‐mapping operators are proposed each year, there is no reliable method to validate their performance or to tell how different they are from one another. In order to analyze and understand the behavior of tone‐mapping operators, we model their mechanisms by fitting a generic operator to an HDR image and its tone‐mapped LDR rendering. We demonstrate that the majority of both global and local tone‐mapping operators can be well approximated by computationally inexpensive image processing operations, such as a per‐pixel tone curve, a modulation transfer function and color saturation adjustment. The results produced by such a generic tone‐mapping algorithm are often visually indistinguishable from much more expensive algorithms, such as the bilateral filter. We show the usefulness of our generic tone‐mapper in backward‐compatible HDR image compression, the black‐box analysis of existing tone mapping algorithms and the synthesis of new algorithms that are combination of existing operators.     

Learning Line Features in 3D Geometry

Feature detection in geometric datasets is a fundamental tool for solving shape matching problems such as partial symmetry detection. Traditional techniques usually employ a priori models such as crease lines that are unspecific to the actual application. Our paper examines the idea of learning geometric features. We introduce a formal model for a class of linear feature constellations based on a Markov chain model and propose a novel, efficient algorithm for detecting a large number of features simultaneously. After a short user‐guided training stage, in which one or a few example lines are sketched directly onto the input data, our algorithm automatically finds all pieces of geometry similar to the marked areas. In particular, the algorithm is able recognize larger classes of semantically similar but geometrically varying features, which is very difficult using unsupervised techniques. In a number of experiments, we apply our technique to point cloud data from 3D scanners. The algorithm is able to detect features with very low rates of false positives and negatives and to recognize broader classes of similar geometry (such as “windows” in a building scan) even from few training examples, thereby significantly improving over previous unsupervised techniques.     

Virtual Klingler Dissection: Putting Fibers into Context

Fiber tracking is a standard tool to estimate the course of major white matter tracts from diffusion tensor magnetic resonance imaging (DT‐MRI) data. In this work, we aim at supporting the visual analysis of classical streamlines from fiber tracking by integrating context from anatomical data, acquired by a T₁‐weighted MRI measurement. To this end, we suggest a novel visualization metaphor, which is based on data‐driven deformation of geometry and has been inspired by a technique for anatomical fiber preparation known as Klingler dissection. We demonstrate that our method conveys the relation between streamlines and surrounding anatomical features more effectively than standard techniques like slice images and direct volume rendering. The method works automatically, but its GPU‐based implementation allows for additional, intuitive interaction.     

Conformal Flattening by Curvature Prescription and Metric Scaling

We present an efficient method to conformally parameterize 3D mesh data sets to the plane. The idea behind our method is to concentrate all the 3D curvature at a small number of select mesh vertices, called cone singularities, and then cut the mesh through those singular vertices to obtain disk topology. The singular vertices are chosen automatically. As opposed to most previous methods, our flattening process involves only the solution of linear systems of Poisson equations, thus is very efficient. Our method is shown to be faster than existing methods, yet generates parameterizations having comparable quasi‐conformal distortion.     

Visualization of Particle‐based Data with Transparency and Ambient Occlusion

Particle‐based simulation techniques, like the discrete element method or molecular dynamics, are widely used in many research fields. In real‐time explorative visualization it is common to render the resulting data using opaque spherical glyphs with local lighting only. Due to massive overlaps, however, inner structures of the data are often occluded rendering visual analysis impossible. Furthermore, local lighting is not sufficient as several important features like complex shapes, holes, rifts or filaments cannot be perceived well. To address both problems we present a new technique that jointly supports transparency and ambient occlusion in a consistent illumination model. Our approach is based on the emission‐absorption model of volume rendering. We provide analytic solutions to the volume rendering integral for several density distributions within a spherical glyph. Compared to constant transparency our approach preserves the three‐dimensional impression of the glyphs much better. We approximate ambient illumination with a fast hierarchical voxel cone‐tracing approach, which builds on a new real‐time voxelization of the particle data. Our implementation achieves interactive frame rates for millions of static or dynamic particles without any preprocessing. We illustrate the merits of our method on real‐world data sets gaining several new insights.     

Sample‐Based Manifold Filtering for Interactive Global Illumination and Depth of Field

We present a fast reconstruction filtering method for images generated with Monte Carlo–based rendering techniques. Our approach specializes in reducing global illumination noise in the presence of depth‐of‐field effects at very low sampling rates and interactive frame rates. We employ edge‐aware filtering in the sample space to locally improve outgoing radiance of each sample. The improved samples are then distributed in the image plane using a fast, linear manifold‐based approach supporting very large circles of confusion. We evaluate our filter by applying it to several images containing noise caused by Monte Carlo–simulated global illumination, area light sources and depth of field. We show that our filter can efficiently denoise such images at interactive frame rates on current GPUs and with as few as 4–16 samples per pixel. Our method operates only on the colour and geometric sample information output of the initial rendering process. It does not make any assumptions on the underlying rendering technique and sampling strategy and can therefore be implemented completely as a post‐process filter.