A volume dataset contains an infinite number of disjoint isosurfaces at different target scalar field values, while its field structure is often characterized by spatial configurations of a finite number of feature isosurfaces that segment the volume dataset into several important components. The project is concerned with analyzing effective uses of contour tree in volume rendering of 3D dataset. We aim to extract data information and understand data set through depicting topological relationships based on the contour tree, and especially focus on effective uses of the contour tree in depicting structural relationships in volume rendering, as well as uses of topological information of the contour tree in generation of transfer functions.

---

People

Motivation

Topology provides insight into the fundamental structure of a data set, independently of the application domain. Topology considers connected components in a relatively intuitive fashion that can be used for a wide variety of applications. A contour tree has been used as an abstract representation of scalar fields, where properties such as isosurface area, enclosed volume, and the contour tree were plotted alongside isosurfaces to provide user with additional cues to interesting isovalues. It has also been used for fast isosurface extraction, mesh simplification, and other isosurface processing. The roles of contour tree in volume rendering can be categorized into following groups:

• Depict topological relationships

One of the most important contributionsof the contour tree to volume rendering is that it introduces topological and positional information (because the contour tree can be used to index different regions in the data set, it provides positional information) into the rendering pipeline. In this way, the topological relationships of objects in the data set can be depicted in the rendering scene explicitly. It is possible to visualize inner structures occluded by outside structures based on the contour tree.

• Contour tree defined segmentation and transfer function specification

Since each contour in a data set corresponds one-to-one with a point on a branch in the contour tree and a branch corresponds one region in the data set, it is possible to use the contour tree as an index for a volume data set to identify different regions. In other words, the data set is segmented based on the contour tree. This is useful in volume rendering to specify different transfer functions for differentregions.

So the project focuses on how to effectively use the contour tree in volume rendering, for example, to simplify the contour tree more effectively, to represent various relationship described in the contour tree in volume rendering, and to generate transfer functions for various regions automatically.

Theory

For a scalar field f, the level set of an isovalue h is the set L (h) = {(p) |f (p) = h}. A connected component of a level set represents a region/volume. A contour is a set of connected components all of which are at the boundary of the region(volume). As h increases, contours appear at local minima, join or split at saddles, and disappear at local maxima of f. Data points, at which the topology of the level sets change (local minima, saddles, or local maxima), are called critical points. All points other than critical points are called regular points. The contour tree can be obtained by representing the critical points with nodes, and regular points, which belong to a same region/volume with edges connecting the critical points. It represents the transitions of topological changes.

The contour tree is a structure that captures the topological evolution of a level set as the isovalue varies. Its nodes are critical points of the data set. Nodes of degree one (leaves of the tree) are minima and maxima where contours are created or destroyed. Interior nodes of degree three or higher are saddles where two or more contours merge or a single contour separates into multiple disconnected contours. Arcs of the contour tree represent contoursbetween critical points, i.e., contours which do not change topology (with the exception of genus changes) as the isovalue varies between critical values.

Publications

• Jianlong Zhou and Masahiro Takatsuka. Automatic transfer function generation using contour tree controlled residue flow model and color harmonics. IEEE Transactions on Visualization and Computer Graphics, 15(6):1481–1488, November-December 2009. (DOI), (BibTex)
• Jianlong Zhou and Masahiro Takatsuka. Structural Relationship Preservation in Volume Rendering. In Computer and Information Science 2009, R. Lee, G. Hu, and H. Miao (Eds.), Chapter 21, pp. 229-238, June 2009, Springer. (Link), (BibTex)
• Jianlong Zhou and Masahiro Takatsuka. Contour Tree Simplification Based on a Combined Approach. Technical Report TR 624. School of Information Engineering, The University of Sydney, Australia. June 2008. ISBN 9781742100593. (Link), (BibTex)

Repository