Random Walks for Vector Field Denoising

Abstract

Figure 1. A simple discontinuous vector field (left) pertubed with a gaussian additive noise (middle left). The gaussian filter (middle right) blurs the interface, while the random walk (right) preserves it.Abstract-In recent years, several devices allow to directly measure real vector fields, leading to a better understanding of fundamental phenomena such as fluid simulation or brain water movement. This turns vector field visualization and analysis important tools for many applications in engineering and in medicine. However, real data is generally corrupted by noise, puzzling the understanding provided by those tools. Those tools thus need a denoising step as preprocessing, although usual denoising removes discontinuities, which are fundamental for vector field analysis. This paper proposes a novel method for vector field denoising based on random walks which preserve those discontinuities. It works in a meshless setting; it is fast, simple to implement, and shows a better performance than the traditional gaussian denoising technique.

Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains

“…While there is a comprehensive selection of tools to visualize uncertain data [19], we will use the classic dual color map. Stochastic processes, in particular random walks, are not only useful to describe the flow of uncertain particles, but they have also been used to smooth and denoise vector field data [18].…”

Topology Aware Vector Field Denoising

“…More recently, Westenberg and Erlt [2] proposed a 2D vector field denoising algorithm that suppress additive noise by thresholding vector wavelet coefficients. Close to this work, a class of vector field filters has been introduced as generalized random walks: for images [15], meshes [16], [17] and vector fields [6]. This work will use random walk filters with Gaussian or anisotropic kernels as instances for the proposed methodology, since they naturally represent the original data in a hierarchical form as a scale space.…”

“…The scale parameter is then the number of convolutions applied. We exemplify our editing interface using two types of scale-space: using the Gaussian kernel G σ and an anisotropic kernel [18], [6]:…”

“…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].…”