Filip Sadlo

Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction

This paper presents a method for filtered ridge extraction based on adaptive mesh refinement. It is applicable in situations where the underlying scalar field can be refined during ridge extraction. This requirement is met by the concept of Lagrangian coherent structures which is based on trajectories started at arbitrary sampling grids that are independent of the underlying vector field. The Lagrangian coherent structures are extracted as ridges in finite Lyapunov exponent fields computed from these grids of trajectories. The method is applied to several variants of finite Lyapunov exponents, one of which is newly introduced. High computation time due to the high number of required trajectories is a main drawback when computing Lyapunov exponents of 3-dimensional vector fields. The presented method allows a substantial speed-up by avoiding the seeding of trajectories in regions where no ridges are present or do not satisfy the prescribed filter criteria such as a minimum finite Lyapunov exponent.

Scalable 3D video of dynamic scenes

In this paper we present a scalable 3D video framework for capturing and rendering dynamic scenes. The acquisition system is based on multiple sparsely placed 3D video bricks, each comprising a projector, two grayscale cameras, and a color camera. Relying on structured light with complementary patterns, texture images and pattern-augmented views of the scene are acquired simultaneously by time-multiplexed projections and synchronized camera exposures. Using space–time stereo on the acquired pattern images, high-quality depth maps are extracted, whose corresponding surface samples are merged into a view-independent, point-based 3D data structure. This representation allows for effective photo-consistency enforcement and outlier removal, leading to a significant decrease of visual artifacts and a high resulting rendering quality using EWA volume splatting. Our framework and its view-independent representation allow for simple and straightforward editing of 3D video. In order to demonstrate its flexibility, we show compositing techniques and spatiotemporal effects.

Real-time simulations of bubbles and foam within a shallow water framework

Bubbles and foam are important fluid phenomena on scales that we encounter in our lives every day. While different techniques to handle these effects were developed in the past years, they require a full 3D fluid solver with free surfaces and surface tension. We present a shallow water based particle model that is coupled with a smoothed particle hydrodynamics simulation to demonstrate that real-time simulations of bubble and foam effects are possible with high frame rates. A shallow water simulation is used to represent the overall water volume. It is coupled to a particle-based bubble simulation with a flow field of spherical vortices. This bubble simulation is interacting with a smoothed particle hydrodynamics simulation including surface tension to handle foam on the fluid surface. The realism and performance of our approach is demonstrated with several test cases that run with high frame rates on a standard PC.

A practical structured light acquisition system for point-based geometry and texture

We present a simple and high-quality 3D scanning system based on structured light. It uses the common setup of a video projector, a computer-controlled turntable and a single camera. Geometry is acquired using a combination of gray code and phase-shift projections, and it is stored and processed in a point-based representation. We achieve high accuracy by careful calibration of camera, projector, and turntable axis. In addition, we make use of the projectors calibration and extend it to a calibrated light source, allowing for a simple reconstruction of material properties for each surface point. We alternatively use a Lambertian reflectance model, or fit a Phong reflectance model to the samples under different turntable orientations. The acquisition pipeline is entirely point-based, avoiding the need of triangulation during all processing stages.

Hierarchical Line Integration

This paper presents an acceleration scheme for the numerical computation of sets of trajectories in vector fields or iterated solutions in maps, possibly with simultaneous evaluation of quantities along the curves such as integrals or extrema. It addresses cases with a dense evaluation on the domain, where straightforward approaches are subject to redundant calculations. These are avoided by first calculating short solutions for the whole domain. From these, longer solutions are then constructed in a hierarchical manner until the designated length is achieved. While the computational complexity of the straightforward approach depends linearly on the length of the solutions, the computational cost with the proposed scheme grows only logarithmically with increasing length. Due to independence of subtasks and memory locality, our algorithm is suitable for parallel execution on many-core architectures like GPUs. The trade-offs of the method - lower accuracy and increased memory consumption - are analyzed, including error order as well as numerical error for discrete computation grids. The usefulness and flexibility of the scheme are demonstrated with two example applications: line integral convolution and the computation of the finite-time Lyapunov exponent. Finally, results and performance measurements of our GPU implementation are presented for both synthetic and simulated vector fields from computational fluid dynamics.

Illuminated lines revisited

For the rendering of vector and tensor fields, several texture-based volumetric rendering methods were presented in recent years. While they have indisputable merits, the classical vertex-based rendering of integral curves has the advantage of better zooming capabilities as it is not bound to a fixed resolution. It has been shown that lighting can improve spatial perception of lines significantly, especially if lines appear in bundles. Although OpenGL does not directly support lighting of lines, fast rendering of illuminated lines can be achieved by using basic texture mapping. This existing technique is based on a maximum principle which gives a good approximation of specular reflection. Diffuse reflection however is essentially limited to bidirectional lights at infinity. We show how the realism can be further increased by improving diffuse reflection. We present simplified expressions for the Phong/Blinn lighting of infinitesimally thin cylindrical tubes. Based on these, we propose a fast rendering technique with diffuse and specular reflection for orthographic and perspective views and for multiple local and infinite lights. The method requires commonly available programmable vertex and fragment shaders and only two-dimensional lookup textures.

Visualizing Lagrangian Coherent Structures and Comparison to Vector Field Topology

This paper takes a look at the visualization side of vector field anal ysis based on Lagrangian coherent structures. The Lagrangian coherent structures are extracted as height ridges of finite-time Lyapunov exponent fields. The result ing visualizations are compared to those from traditional instantaneous vector field topology of steady and unsteady vector fields: they often provide more and better interpretable information. The examination is applied to 3D vector fields from a dynamical system and practical CFD simulations.

Height Ridge Computation and Filtering for Visualization

Motivated by the growing interest in the use of ridges in scientific visualization, we analyze the two height ridge definitions by Eberly and Lindeberg. We propose a raw feature definition leading to a superset of the ridge points as obtained by these two definitions. The set of raw feature points has the correct dimensionality, and it can be narrowed down to either Eberlys or Lindebergs ridges by using Boolean filters which we formulate. While the straight-forward computation of height ridges requires explicit eigenvalue calculation, this can be avoided by using an equivalent definition of the raw feature set, for which we give a derivation. We describe efficient algorithms for two special cases, height ridges of dimension one and of co-dimension one. As an alternative to the aforementioned filters, we propose a new criterion for filtering raw features based on the distance between contours which generally makes better decisions, as we demonstrate on a few synthetic fields, a topographical dataset, and a fluid flow simulation dataset. The same set of test data shows that it is unavoidable to use further filters to eliminate false positives. For this purpose, we use the angle between feature tangent and slope line as a quality measure and, based on this, formalize a previously published filter.

Time-Dependent Visualization of Lagrangian Coherent Structures by Grid Advection

Lagrangian coherent structures play an important role in the analysis of unsteady vector fields because they represent the time-dependent analog to vector field topology. Nowadays, they are often obtained as ridges in the finite-time Lyapunov exponent of the vector field. However, one drawback of this quantity is its very high computational cost because a trajectory needs to be computed for every sample in the space-time domain. A focus of this paper are Lagrangian coherent structures that are related to predefined regions such as boundaries, i.e. related to flow attachment and flow separation phenomena. It presents an efficient method for computing the finite-time Lyapunov exponent and its height ridges only in these regions, and in particular,grid advection for the efficient computation of time series of the finite-time Lyapunov exponent, exploiting temporal coherence.

Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

This paper presents an approach to a time‐dependent variant of the concept of vector field topology for 2‐D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle‐type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite‐time Lyapunov exponent field. The proposed approach is evaluated on both 2‐D time‐dependent synthetic and vector fields from computational fluid dynamics.