Visual exploration of volumetric datasets to discover the embedded features and spatial structures is a challenging and tedious task. In this paper we present a semi-automatic approach to this problem that works by visually segmenting the intensity-gradient 2D histogram of a volumetric dataset into an exploration hierarchy. Our approach mimics user exploration behavior by analyzing the histogram with the normalized-cut multilevel segmentation technique. Unlike previous work in this area, our technique segments the histogram into a reasonable set of intuitive components that are mutually exclusive and collectively exhaustive. We use information-theoretic measures of the volumetric data segments to guide the exploration. This provides a data-driven coarse-to-fine hierarchy for a user to interactively navigate the volume in a meaningful manner.

Identifying and visualizing meaningful features in large volume datasets remains a significant challenge. Visualization of the features that you know are in the data is hard. It is even harder to find the features that you do not know are there. While we have made significant strides in building up a substantial body of knowledge over the last two decades in direct volume rendering, much of these advances have addressed issues surrounding how to depict the data; what to depict remains an important problem. We seek a visualization approach that highlights meaningful information, guides users to explore, and allows the users to associate high-level knowledge with low-level raw data. We carry this out by visually segmenting the intensity-gradient histogram of a volumetric dataset into a hierarchy for exploration.

In practice, users manually search for regions of interest by inspecting different areas of a feature space. Popular exploration subspaces for such a feature space include 1D density and 2D intensity-gradient. Histograms are often used to aid this search. We mimic the user search process by applying image segmentation to recursively divide the histogram into intuitive regions. We show effective discovery of interesting regions by traversing a hierarchy.

• We mimic user explorations by visually segmenting the 2D histograms. We show these automatic 2D histogram segments well-approximate meaningful 3D volume segments that covers the entire dataset
• We progressively visualize the volume dataset by traversing a hierarchy of coarse to fine volumetric segments.
• We assist the exploration by using information-theoretic measures of the volumetric data segments. We evaluate the entropies of the segments and the information gains of the subdivisions
• We provide intuitive interactions for users to explore segments at different sizes. Users effectively identify regions of interest by traversing the hierarchy of segments.

      

Visible Male Head

We present the head of the visible human male dataset as an example. Similar to the Foot dataset, Step 1 shows the bones. Step 2 shows the teeth. Steps 3, 4, and 5 divide the low-intensity arc region progressively and show the flesh (step 4) and the skin (step 5). Step 6 divides the low-intensity and high-gradient regions into the sinus and some noise. We remove the noise and show the bone, skin, teeth, and sinus in the final visualization.

Hurricane Isabel

We visualize the pressure field of the hurricane Isabel dataset. This is a continuous scalar field with no abrupt boundaries and is different from the previous examples with clear material changes. The figure shows the exploration hierarchy of the hurricane. Step 1 separates the land and the atmospheric regions. Step 2 segments the hurricane eye from the atmospheric region. The rainbands from the eyewall structures of the hurricane are separated in Step 3. By inspecting the entropy of the segments in (c), we decide to switch our focus onto the eye of the hurricane. Steps 4 and 5 show regions of different pressures in the hurricane eye. We compose the final visualization with the hurricane eye segments, the eyewall and the rainbands. (a) and (b) show the separated eyewall and the rainbands.

      

We present a hierarchy of normalized-cut-assisted visual segmentation of an intensity-gradient histogram to assist in the volume exploration process. We address the information challenge by using a visual segmentation of intensity-gradient histograms to locate various meaningful volumetric segments. These segments completely cover the intensity-gradient domain in the image space and identify features of different sizes. We show that any cut in the segmentation hierarchy covers the entire dataset. Exploring along this hierarchy addresses the completeness challenge. We assist the volumetric data exploration process by using information-theoretic measures. The users can identify meaningful components and material boundaries through a concise interactive exploration procedure. These interactions address the semantic challenge by allowing users to adaptively explore the dataset and associate their knowledge with the corresponding data segments.

• Hierarchical Exploration of Volumes Using Multilevel Segmentation of the Intensity-Gradient Histograms.
  C.Y. Ip, A. Varshney, and J. JaJa IEEE Transactions on Visualization and Computer Graphics (IEEE SciVis 2012), 2012

This work has been supported in part by the NSF grants: CCF 05-41120, CMMI 08-35572, CNS 09-59979 and the NVIDIA CUDA Center of Excellence. Any opinions, findings, conclusions, or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the research sponsors.