Decoupled Opacity Optimization for Points, Lines and Surfaces

Abstract

Figure 1: Our method splits the previous opacity optimization technique [GRT13, GSM * 14] into two smaller problems, which accelerates the optimization and allows us to combine different geometry types (points, lines and surfaces) in a single unified framework. Compared to previous work our method is completely GPU-based, runs the optimization per pixel, and has view-independent parameters. Left: atmospheric trace gas pathways in an air flow provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) and right: streamlines and rain clouds (isosurfaces) at the boundary between troposphere and stratosphere in the cloud-topped boundary layer (CTBL) flow. AbstractDisplaying geometry in flow visualization is often accompanied by occlusion problems, making it difficult to perceive information that is relevant in the respective application. In a recent technique, named opacity optimization, the balance of occlusion avoidance and the selection of meaningful geometry was recognized to be a view-dependent, global optimization problem. The method solves a bounded-variable least-squares problem, which minimizes energy terms for the reduction of occlusion, background clutter, adding smoothness and regularization. The original technique operates on an object-space discretization and was shown for line and surface geometry. Recently, it has been extended to volumes, where it was solved locally per ray by dropping the smoothness energy term and replacing it by pre-filtering the importance measure. In this paper, we pick up the idea of splitting the opacity optimization problem into two smaller problems. The first problem is a minimization with analytic solution, and the second problem is a smoothing of the obtained minimizer in object-space. Thereby, the minimization problem can be solved locally per pixel, making it possible to combine all geometry types (points, lines and surfaces) consistently in a single optimization framework. We call this decoupled opacity optimization and apply it to a number of steady 3D vector fields.

Visualizing the Phase Space of Heterogeneous Inertial Particles in 2D Flows

“…Alternatively, transparency may be used, though this would require an order-dependent image compositing. While the direct plotting of trajectories provides a detailed view onto the individual particle behaviour, plotting all trajectories directly may result in dense line sets that exhibit a significant amount of occlusion, which could be reduced by opacity optimization [GTG17].…”

Fourier Opacity Optimization for Scalable Exploration

“…Thus, in this paper, we focus on the scalable visual data exploration of general scientific data. When it comes to 3D data, an inherent visualization problem that is shared among all visual primitives (points, lines, surfaces and volumes) is the occlusion problem [20], [23]. That is, highly relevant information might be hidden behind unimportant geometry, which is determined by a user-defined importance value.…”

“…Their approach was later extended to animated lines [21], opacity optimization for surfaces [22] and extinction optimization for volumes [1]. Ament et al [1] approximated the energy and reformulated the minimization in ray space, which enabled a significant acceleration for volume data, which was later carried into point, line and surface geometry by Günther et al [23] in their decoupled opacity optimization. However, the decoupled technique still does not scale well for large amounts of geometric primitives (points, lines and surfaces), due to an order-dependence that involves the construction and sorting of fragment linked lists [62], which is ultimately bounded by the available memory.…”

“…With this, opacity optimization becomes applicable to large scenes, as demonstrated here for a DT-MRI fiber tracking visualization of white-matter connectivity through the corpus callosum (left) and the cosmic web of 16 million stars in the DARK SKY simulation (right). Note that the DARK SKY simulation could not be rendered with decoupled opacity optimization [23] alone, because of its unbound memory consumption.…”

“…For the DARK SKY data set in Fig. 1 (right), the previous decoupled opacity optimization [23] is running out of memory, making it impossible to navigate through this data set. Even with a screen resolution small enough to render it with decoupled opacity optimization, our method needs only 4% of the memory and is 10× faster.…”