Powder-snow avalanches are natural phenomena that result from an instability in the snow cover on a mountain relief. It begins with a dense avalanche core moving fast down the mountain. During its evolution, the snow particles in the avalanche front mix with the air, forming a suspended turbulent cloud of snow dust surrounding the dense snow avalanche. This paper introduces a physically-based framework using the Finite Volume Method to simulate powder-snow avalanches under complex terrains. Specifically, the primary goal is to simulate the turbulent snow cloud dynamics within the avalanche in a visually realistic manner. Our approach relies on a multi-layer model that splits the avalanche into two main layers: dense and powder-snow. The dense-snow layer flow is simulated by solving a type of Shallow Water Equations suited for intricate basal surfaces, known as the Savage-Hutter model. The powder-snow layer flow is modeled as a two-phase mixture of miscible fluids and simulated using Navier-Stokes equations. Moreover, we propose a novel model for the transition layer, which is responsible for coupling the avalanche main layers, including the snow mass injected into the powder-snow cloud from the snow entrainment processes and its injection velocity. In brief, our framework comprehensively simulates powder-snow avalanches, allowing us to render convincing animations of one of the most complex gravity-driven flows.

We describe a simple method for reconstructing regions in the plane from well-distributed point samples. For that, we introduce the sphere-of-influence diagram, a planar diagram extracted from the Delaunay triangulation and the sphere-of-influence graph. The sphere-of-influence diagram is simple to understand and to implement, and supports an intuitive scaling parameter to handle variations in the distribution of samples. We report experiments reconstructing regions from point clouds of varying shape and density. We compare our results with those obtained by α-shapes and by ct-shapes.

Abstract This paper presents a novel and practical screen‐space liquid rendering for particle‐based fluids for real‐time applications. Our rendering pipeline performs particle filtering only in a narrow‐band around the boundary particles to provide a smooth liquid surface with volumetric rendering effects. We also introduce a novel boundary detection method allowing the user to select particle layers from the liquid interface. The proposed approach is simple, fast, memory‐efficient, easy to code and it can be adapted straightforwardly in the standard screen‐space rendering methods, even in GPU architectures. We show through a set of experiments how the prior screen‐space techniques can be benefited and improved by our approach.

Novelty detection is a binary task aimed at identifying whether a test sample is novel or unusual compared to a previously observed training set. A typical approach is to consider distance as a criterion to detect such novelties. However, most previous work does not focus on finding an optimum distance for each particular problem. In this paper, we propose to detect novelties by exploiting non-linear distances learned from multi-class training data. For this purpose, we adopt a kernelization technique jointly with the Large Margin Nearest Neighbor (LMNN) metric learning algorithm. The optimum distance tries to keep each known class' instances together while pushing instances from different known classes to remain reasonably distant. We propose a variant of the K-Nearest Neighbors (KNN) classifier that employs the learned distance to detect novelties. Besides, we use the learned distance to perform multi-class classification. We show quantitative and qualitative experiments conducted on synthetic and real data sets, revealing that the learned metrics are effective in improving novelty detection compared to other metrics. Our method also outperforms previous work regularly used for novelty detection.

São Paulo is the largest city in South America, with crime rates that reflect its size. The number and type of crimes vary considerably around the city, assuming different patterns depending on urban and social characteristics of each particular location. Previous works have mostly focused on the analysis of crimes with the intent of uncovering patterns associated to social factors, seasonality, and urban routine activities. Therefore, those studies and tools are more global in the sense that they are not designed to investigate specific regions of the city such as particular neighborhoods, avenues, or public areas. Tools able to explore specific locations of the city are essential for domain experts to accomplish their analysis in a bottom-up fashion, revealing how urban features related to mobility, passersby behavior, and presence of public infrastructures (e.g., terminals of public transportation and schools) can influence the quantity and type of crimes. In this paper, we present CrimAnalyzer, a visual analytic tool that allows users to study the behavior of crimes in specific regions of a city. The system allows users to identify local hotspots and the pattern of crimes associated to them, while still showing how hotspots and corresponding crime patterns change over time. CrimAnalyzer has been developed from the needs of a team of experts in criminology and deals with three major challenges: i) flexibility to explore local regions and understand their crime patterns, ii) identification of spatial crime hotspots that might not be the most prevalent ones in terms of the number of crimes but that are important enough to be investigated, and iii) understand the dynamic of crime patterns over time. The effectiveness and usefulness of the proposed system are demonstrated by qualitative and quantitative comparisons as well as by case studies run by domain experts involving real data. The experiments show the capability of CrimAnalyzer in identifying crime-related phenomena.

We introduce a novel liquid simulation approach that combines a spatially adaptive pressure projection solver with the Particle-in-Cell (PIC) method. The solver relies on a generalized version of the Finite Difference (FD) method to approximate the pressure field and its gradients in tree-based grid discretizations, possibly non-graded. In our approach, FD stencils are computed by using meshfree interpolations provided by a variant of Radial Basis Function (RBF), known as RBF-Finite-Difference (RBF-FD). This meshfree version of the FD produces differentiation weights on scattered nodes with high-order accuracy. Our method adapts a quadtree/octree dynamically in a narrow-band around the liquid interface, providing an adaptive particle sampling for the PIC advection step. Furthermore, RBF affords an accurate scheme for velocity transfer between the grid and particles, keeping the system's stability and avoiding numerical dissipation. We also present a data structure that connects the spatial subdivision of a quadtree/octree with the topology of its corresponding dual-graph. Our data structure makes the setup of stencils straightforward, allowing its updating without the need to rebuild it from scratch at each time-step. We show the effectiveness and accuracy of our solver by simulating incompressible inviscid fluids and comparing results with regular PIC-based solvers available in the literature.

Optimal transport has emerged as a promising and useful tool for supporting modern image processing applications such as medical imaging and scientific visualization. Indeed, the optimal transport theory enables great flexibility in modeling problems related to image registration, as different optimization resources can be successfully used as well as the choice of suitable matching models to align the images. In this paper, we introduce an automated framework for fundus image registration which unifies optimal transport theory, image processing tools, and graph matching schemes into a functional and concise methodology. Given two ocular fundus images, we construct representative graphs which embed in their structures spatial and topological information from the eye's blood vessels. The graphs produced are then used as input by our optimal transport model in order to establish a correspondence between their sets of nodes. Finally, geometric transformations are performed between the images so as to accomplish the registration task properly. Our formulation relies on the solid mathematical foundation of optimal transport as a constrained optimization problem, being also robust when dealing with outliers created during the matching stage. We demonstrate the accuracy and effectiveness of the present framework throughout a comprehensive set of qualitative and quantitative comparisons against several influential state-of-the-art methods on various fundus image databases.

Image registration is an important pre-processing step in several computer vision applications, being crucial in medical imaging systems where patients are examined and diagnosed almost exclusively by images. For fundus images, in which microscopic differences are significant to better support medical decisions, an accurate registration is imperative. Historically, geometric transformations derived from quadratic models have been widely used as a benchmark to perform registration on fundus images, but in this paper, we demonstrate that quadratic and other high-order mappings are not necessarily the best choices for this purpose, even for well-established state-of-the-art registration methods. From a novel overlapping metric designed to determine the best image transformation that maximizes the registration accuracy, we improve the assertiveness of several methods of the literature while still preserving the same computational burden initially reached by those methods.

Abstract This paper presents a novel method to detect free‐surfaces on particle‐based volume representation. In contrast to most particle‐based free‐surface detection methods, which perform the surface identification based on physical and geometrical properties derived from the underlying fluid flow simulation, the proposed approach only demands the spatial location of the particles to properly recognize surface particles, avoiding even the use of kernels. Boundary particles are identified through a Hidden Point Removal (HPR) operator used for visibility test. Our method is very simple, fast, easy to implement and robust to changes in the distribution of particles, even when facing large deformation of the free‐surface. A set of comparisons against state‐of‐the‐art boundary detection methods show the effectiveness of our approach. The good performance of our method is also attested in the context of fluid flow simulation involving free‐surface, mainly when using level‐sets for rendering purposes.

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 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.