Support Vectors Learning for Vector Field Reconstruction

Abstract

Figure 1. Reconstruction of a real 3D velocity field captured by a PIV device with sparse, irregular sampling: magnitude (left) and phase (right).Abstract-Sampled vector fields generally appear as measurements of real phenomena. They can be obtained by the use of a Particle Image Velocimetry acquisition device, or as the result of a physical simulation, such as a fluid flow simulation, among many examples. This paper proposes to formulate the unstructured vector field reconstruction and approximation through Machine-Learning. The machine learns from the samples a global vector field estimation function that could be evaluated at arbitrary points from the whole domain. Using an adaptation of the Support Vector Regression method for multi-scale analysis, the proposed method provides a global, analytical expression for the reconstructed vector field through an efficient non-linear optimization. Experiments on artificial and real data show a statistically robust behavior of the proposed technique.

Outlier detection for particle image velocimetry data using a locally estimated noise variance

“…Smoothing or interpolating operation, the essence of constructing a reference vector field, can be conducted by thin-plate spline interpolation [30], moving least square method [31], support vector regression [32], smoothing in a reproducing kernel Hilbert space [2] and so on. Here, we employ the weighted part of a fast smoothing method [1], which automatically selects the smoothing level (the trade-off coefficient), to generate a reference vector field, avoiding the over smoothed or under smoothed reference.…”

“…Note that, the fixed H and L are not changed for different flow patterns, and the later experimental results illustrate that these numbers are really universal and do not depend on the flow. Under the condition of homogeneous Gaussian noise, we also conducted a series of experiments with this (32,32) synthetic cellular vortex flow field (N v = 2) with different outlier types and varied spurious vector ratios [28]. The detection procedures were repeated 100 times with different random noise and outliers (Monte-Carlo simulations) at every concentration point.…”

Topology Aware Vector Field Denoising

“…Classical denoising approaches, such as convolution filters [2], [3], [4], [5], [6], rely on the assumption that the information is present in the measured data at a stronger scale than noise. Successive applications of such convolution filters noise generate a scale space [7], [8] representing the original data hierarchically, helping for subsequent analysis, in particular topological singularities [9], [10].…”

Design de campos vetoriais em volumes usando RBF

“…Em termos mais gerais, através de medidas de um fenômeno real, experimentos ou simulações, os campos vetoriais podem ser amostrados em conjuntos finitos de dados e então, extrapolados em toda uma região desejada. Em Lage et al (2006), é proposto um método de reconstrução de campos vetoriais 2D a partir de um conjunto esparso de dados não estruturados. Basicamente, o algoritmo proposto, faz aproximações polinomiais locais e então utiliza o método da partição da unidade para construir a aproximação global.…”

“…Basicamente, o algoritmo proposto, faz aproximações polinomiais locais e então utiliza o método da partição da unidade para construir a aproximação global. Já o trabalho de Lage et al (2009), também trata de um método para reconstrução de campos vetoriais de dados esparsos porém, no contexto de aprendizado de máquina. Em Macêdo e Castro (2008), os autores utilizam a teoria do aprendizado estatístico com certos núcleos matriciais, garantindo propriedades de divergente livre e rotacional livre no campo recontruido.…”