Fourier Opacity Optimization for Scalable Exploration

Abstract

Over the past decades, scientific visualization became a fundamental aspect of modern scientific data analysis. Across all data-intensive research fields, ranging from structural biology to cosmology, data sizes increase rapidly. Dealing with the growing large-scale data is one of the top research challenges of this century. For the visual exploratory data analysis, interactivity, a view-dependent visibility optimization and frame coherence are indispensable. In this work, we extend the recent decoupled opacity optimization framework to enable a navigation without occlusion of important features through large geometric data. By expressing the accumulation of importance and optical depth in Fourier basis, the computation, evaluation and rendering of optimized transparent geometry become not only order-independent, but also operate within a fixed memory bound. We study the quality of our Fourier approximation in terms of accuracy, memory requirements and efficiency for both the opacity computation, as well as the order-independent compositing. We apply the method to different point, line and surface data sets originating from various research fields, including meteorology, health science, astrophysics and organic chemistry.

Screen‐space Streamline Seeding Method for Visualizing Unsteady Flow in Augmented Reality

“…The method was not designed for unsteady flow, and therefore our methods (V1 and V2) are compared with it under a steady flow setting, which is obtained by selecting a specific frame of unsteady flow. The second baseline method is an opacity optimization method proposed by Rojo et al, 36 which is based on depth ordering of streamlines. This method considers uniformly seeded 4000 streamlines and optimizes their opacities.…”

Transmittance‐based Extinction and Viewpoint Optimization

“…The maximal resolution is thereby constraint by the available GPU memory. To circumvent this limitation, several approaches are imaginable, including sparse or hierarchical representations, compression algorithms, or approximations by projection into a different function basis [BRGG20].…”

“…Ament et al [AZD17] extended a linear visibility optimization from semi‐transparent geometry [GRT13,GRT14,GSME*14] to volume data and realized that the optimization has a closed‐form solution if smoothing is done separately in a post‐process. This idea has later been picked up for geometric data [GTG17,BRGG20,ZRPD20]. The problem is that this formulation reduces the visibility of a voxel indirectly based on how much importance is gathered in front or behind it, which does not measure how visible a certain voxel truly is.…”

“…Either way, a measure is needed that determines how much of the relevant information is visible on the screen. Previous opacity and extinction optimization approaches [GRT13, GRT14, GSME*14, GTG17, AZD17, BRGG20] all utilized a metric that assessed the visibility of important information indirectly . That is, an energy was defined that rises when occlusions occur, but how well the resulting structures are actually visible on screen was not calculated directly.…”

A Comparison of Rendering Techniques for 3D Line Sets With Transparency

“…Recently, Moment-Based Order-Independent Transparency (MBOIT) has been introduced by Münstermann et al [21]. The embedding of importance-based transparency control into MBOIT was demonstrated by Rojo et al [3]. MBOIT approximates the transmittance function pixel-wise by power moments or trigonometric moments, and applies logarithmic scaling to the absorbance to enforce orderindependency and facilitate additive compositing.…”