Verifiable Visualization for Isosurface Extraction

Abstract

Fig. 1. Through the verification methodology presented on this paper we were able to uncover a convergence problem within a publicly available marching-based isosurfacing code (top left) and fix it (top right). The problem causes the mesh normals to disagree with the known gradient field when refining the voxel size h (bottom row). The two graphs show the convergence of the normals before and after fixing the code.Abstract-Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whether anomalies in isosurface features can be attributed to the underlying physical process or to artifacts from the extraction process. Such scientific scrutiny is at the heart of verifiable visualization -subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. More concretely, we derive formulas for the expected order of accuracy (or convergence rate) of several isosurface features, and compare them to experimentally observed results in the selected codes. This technique is practical: in two cases, it exposed actual problems in implementations. We provide the reader with the range of responses they can expect to encounter with isosurface techniques, both under "normal operating conditions" and also under adverse conditions. Armed with this information -the results of the verification process -practitioners can judiciously select the isosurface extraction technique appropriate for their problem of interest, and have confidence in its behavior.

A Systematic Review on the Practice of Evaluating Visualization

“…However, Etiene et al [17] recently have pointed out that asymptotic error measures can be more powerful in finding problems in an implementation.…”

Generative Data Models for Validation and Evaluation of Visualization Techniques

“…Visualization algorithms should be subject to the same verification process that is used in other components of the scientific pipeline-this is also called verifiable visualization [35]. We expect that semi-automatic verification techniques, such as fuzzing, could greatly benefit from generative models due to extra knowledge about the parameter space.…”

Verifying Volume Rendering Using Discretization Error Analysis

“…Globus and Uselton [11] first pointed out the need to verify not only visualization algorithms but also their implementations, and Kirby and Silva suggested a research program around verification [18]. The verification of isosurface algorithms was discussed by Etiene et al [8], [9], where a systematic evaluation identified and corrected problems in several implementations of isosurface extraction techniques. Zheng et al [47] address CT reconstruction and interpolation errors in direct volume rendering algorithms using a verifiable framework based on projection errors.…”

“…The error computation and analysis will proceed differently depending on whether an analytical solution for the VRI is available or not. We highlight that previous frameworks for verification of visualization algorithms could benefit from the fact that analytical solutions can be easily constructed [9]. For the case of the VRI, this is no longer true, and therefore we should not rely on known solutions.…”