Abstract: Existing texture-based 3D flow visualization techniques, e.g., volume Line Integral Convolution (LIC), are either limited to steady flows or dependent on special-purpose graphics cards. In this paper we present a texture-based hardware-independent technique for time-varying volume flow visualization. It is based on our Accelerated Unsteady Flow LIC (AUFLIC) algorithm (Liu and Moorhead, 2005), which uses a flow-driven seeding strategy and a dynamic seeding controller to reuse pathlines in the value scattering process to achieve fast time-dependent flow visualization with high temporal-spatial coherence. We extend AUFLIC to 3D scenarios for accelerated generation of volume flow textures. To address occlusion, lack of depth cuing, and poor perception of flow directions within a dense volume, we employ magnitude-based transfer functions and cutting planes in volume rendering to clearly show the flow structure and the flow evolution.

Keywords: texture-based flow visualization, unsteady 3D flow, LIC, UFLIC, volume rendering.

The extension of AUFLIC to the 3D case --- Volume AUFLIC (VAUFLIC), is straightforward. The flow-driven seeding strategy and the dynamic seeding controller work the same way for volume flows as for 2D scenarios. The small memory footprint of VAUFLIC allows it to be used for large unsteady volume flow visualization. The major difference is the application of volume rendering in the pipeline to display volumetric textures. Solid white noise is typically used as the initial input texture. Sparse noise used in volume LIC [1] for steady flow visualization may not be applied in VAUFLIC for time-varying flows since the successive texture feed-forward strategy damages the effectiveness of the initial sparse noise and allows for no further input.

Volume rendering has been successfully and extensively used in medical data visualization, though its application in rendering volume flows, e.g., LIC texture volumes, is still heavily limited by the daunting problem of designing appropriate transfer functions from this unusual kind of data. Without an effective transfer function, flow directions, interior structures, and depth cuing could not be revealed to provide an insight into the dense volume.

Although VAUFLIC texture values convey temporal-spatial correlation along flow lines, they can only be used to compute gradients as normals in the illumination stage to determine grey-scale voxel intensities. They offer no useful guidance for transfer function design due to lack of such intrinsic physical information (provided by, e.g., a volume CT data) that can be exploited to distinguish between different components such as bones and soft tissues. An image generated by using a flow-texture based transfer function in volume rendering shows only a dense cloud-like volume in which flow directions and depth cuing are hardly discernable. To address this problem, velocity magnitude as an important flow attribute may be considered in transfer function design to color-map voxels and enhance / suppress certain parts of the flow. Thus we employ a magnitude-based transfer function design in volume rendering (Figure 1). It is similar to but different from the bi-variate volume rendering model [2] used to render the mixture of two volume datasets with separate transfer functions. Our method also takes two volume datasets, i.e., flow texture and flow magnitude, as the input, though it only renders the former while the latter is just used to define color (strictly, hue) and opacity mappings in transfer functions to modulate grey-scale voxel intensities obtained from the former. The magnitude volume is a by-product of generating the texture volume in VAUFLIC and hence no additional computation is required. The bi-variate rendering model is unique in rendering a magnitude volume and a LIC volume in a weighted mixture and allowing for a shift in between for highlighting / suppression purpose, however, flow patterns are obscure. Flow directions and interior structures are clearly depicted by using our method.

[1] Interrante, V. and Grosch, C., "Visualizing 3D Flow," IEEE Computer Graphics and Applications, Vol. 18, No. 4, pp. 49-53, 1998.