Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel boundary detection filter in the context of graphs, having as main application scenario the visual analysis of spatio-temporal data. More specifically, we propose the equivalent for graphs of the so-called Laplacian of Gaussian edge detection filter, which is widely used in image processing. The proposed filter is able to reveal interesting spatial patterns while still enabling the definition of entropy of time slices. The entropy reveals the degree of randomness of a time slice, helping users to identify expected and unexpected phenomena over time. The effectiveness of our approach appears in applications involving synthetic and real data sets, which show that the proposed methodology is able to uncover interesting spatial and temporal phenomena. The provided examples and case studies make clear the usefulness of our approach as a mechanism to support visual analytic tasks involving spatio-temporal data.

Dynamic networks naturally appear in a multitude of applications from different fields. Analyzing and exploring dynamic networks in order to understand and detect patterns and phenomena is challenging, fostering the development of new methodologies, particularly in the field of visual analytics. In this work, we propose a novel visual analytics methodology for dynamic networks, which relies on the spectral graph wavelet theory. We enable the automatic analysis of a signal defined on the nodes of the network, making viable the robust detection of network properties. Specifically, we use a fast approximation of a graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The coefficients naturally encode the spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This methodology allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using usage scenarios and comparisons involving real dynamic networks.

Kernel-based methods have experienced a substantial progress in the last years, tuning out an essential mechanism for data classification, clustering and pattern recognition. The effectiveness of kernel-based techniques, though, depends largely on the capability of the underlying kernel to properly embed data in the feature space associated to the kernel. However, visualizing how a kernel embeds the data in a feature space is not so straightforward, as the embedding map and the feature space are implicitly defined by the kernel. In this work, we present a novel technique to visualize the action of a kernel, that is, how the kernel embeds data into a high-dimensional feature space. The proposed methodology relies on a solid mathematical formulation to map kernelized data onto a visual space. Our approach is faster and more accurate than most existing methods while still allowing interactive manipulation of the projection layout, a game-changing trait that other kernel-based projection techniques do not have.

In this paper, we introduce a novel meshfree framework for animating free surface viscous liquids with jet buckling effects, such as coiling and folding. Our method is based on Smoothed Particle Hydrodynamics (SPH) fluids and allows more realistic and complex viscous behaviors than the previous SPH frameworks in computer animation literature. The viscous liquid is modeled by a non-Newtonian fluid flow and the variable viscosity under shear stress is achieved using a viscosity model known as Cross model. We demonstrate the efficiency and stability of our framework in a wide variety of animations, including scenarios with arbitrary geometries and high resolution of SPH particles. The interaction of the viscous liquid with complex solid obstacles is performed using boundary particles. Our framework is able to deal with different inlet velocity profiles and geometries of the injector , as well as moving inlet jet along trajectories given by cubic Hermite splines. Moreover, the simulation speed is significantly accelerated by using Computer Unified Device Architecture (CUDA) computing platform.

Abstract Multidimensional projection‐based visualization methods typically rely on clustering and attribute selection mechanisms to enable visual analysis of multidimensional data. Clustering is often employed to group similar instances according to their distance in the visual space. However, considering only distances in the visual space may be misleading due to projection errors as well as the lack of guarantees to ensure that distinct clusters contain instances with different content. Identifying clusters made up of a few elements is also an issue for most clustering methods. In this work we propose a novel multidimensional projection‐based visualization technique that relies on representative instances to define clusters in the visual space. Representative instances are selected by a deterministic sampling scheme derived from matrix decomposition, which is sensitive to the variability of data while still been able to handle classes with a small number of instances. Moreover, the sampling mechanism can easily be adapted to select relevant attributes from each cluster. Therefore, our methodology unifies sampling, clustering, and feature selection in a simple framework. A comprehensive set of experiments validate our methodology, showing it outperforms most existing sampling and feature selection techniques. A case study shows the effectiveness of the proposed methodology as a visual data analysis tool.

Abstract In this work we propose a new discretization method for the Laplace–Beltrami operator defined on point‐based surfaces. In contrast to the existing point‐based discretization techniques, our approach does not rely on any triangle mesh structure, turning out truly mesh‐free. Based on a combination of Smoothed Particle Hydrodynamics and an optimization procedure to estimate area elements, our discretization method results in accurate solutions while still being robust when facing abrupt changes in the density of points. Moreover, the proposed scheme results in numerically stable discrete operators. The effectiveness of the proposed technique is brought to bear in many practical applications. In particular, we use the eigenstructure of the discrete operator for filtering and shape segmentation. Point‐based surface deformation is another application that can be easily carried out from the proposed discretization method.

Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decomposition is usually achieved by using mesh-based methods such as finite differences or finite elements. This work presents a new meshless approach to the Helmholtz-Hodge decomposition for the analysis of 2D discrete vector fields. It embeds into the SPH particle-based framework. The proposed method is efficient and can be applied to extract features from a 2D discrete vector field and to multiphase fluid flow simulation to ensure incompressibility.