Interpreting Galilean Invariant Vector Field Analysis via Extended Robustness

The topological notion of robustness introduces mathematically rigorous approaches to interpret vector field data. Robustness quantifies the structural stability of critical points with respect to perturbations and has been shown to be useful for increasing the visual interpretability of vector fields. However, critical points, which are essential components of vector field topology, are defined with respect to a chosen frame of reference. The classical definition of robustness, therefore, depends also on the chosen frame of reference. We define a new Galilean invariant robustness framework that enables the simultaneous visualization of robust critical points across the dominating reference frames in different regions of the data. We also demonstrate a strong connection between such a robustness-based framework with the one recently proposed by Bujack et al., which is based on the determinant of the Jacobian. Our results include notable observations regarding the definition of stable features within the vector field data

Flexible Moment Invariant Bases for 2D Scalar and Vector Fields

Complex moments have been successfully applied to pattern detection tasks in two-dimensional real, complex, and vector valued functions. In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and\npresent superior bases that are optimal with respect to all three criteria for both scalar and vector fields

Automatic improvement of continuous colormaps in Euclidean colorspaces

Colormapping is one of the simplest and most widely used data visualization methods within and outside the visualization community. Uniformity, order, discriminative power, and smoothness of continuous colormaps are the most important criteria for evaluating and potentially improving colormaps. We present a local and a global automatic optimization algorithm in Euclidean color spaces for each of these design rules in this work. As a foundation for our optimization algorithms, we used the CCC-Tool colormap specification (CMS); each algorithm has been implemented in this tool. In addition to synthetic examples that demonstrate each method's effect, we show the outcome of some of the methods applied to a typhoon simulation

The making of continuous colormaps

Continuous colormaps are integral parts of many visualization techniques, such as heat-maps, surface plots, and flow visualization. Despite that the critiques of rainbow colormaps have been around and well-acknowledged for three decades, rainbow colormaps are still widely used today. One reason behind the resilience of rainbow colormaps is the lack of tools for users to create a continuous colormap that encodes semantics specific to the application concerned. In this paper, we present a web-based software system, CCC-Tool (short for Charting Continuous Colormaps) under the URL https://ccctool.com, for creating, editing, and analyzing such application-specific colormaps. We introduce the notion of "colormap specification (CMS)" that maintains the essential semantics required for defining a color mapping scheme. We provide users with a set of advanced utilities for constructing CMS's with various levels of complexity, examining their quality attributes using different plots, and exporting them to external application software. We present two case studies, demonstrating that the CCC-tool can help domain scientists as well as visualization experts in designing semantically-rich colormaps