Direct Feature Visualization Using Morse-Smale Complexes

In this paper, we characterize the range of features that can be extracted from an Morse-Smale complex and describe a unified query language to extract them. We provide a visual dictionary to guide users when defining features in terms of these queries. We demonstrate our topology-rich visualization pipeline in a tool that interactively queries the MS complex to extract features at multiple resolutions, assigns rendering attributes, and combines traditional volume visualization with the extracted features. The flexibility and power of this approach is illustrated with examples showing novel features.

1 Introduction

VISUALIZATION of scalar valued volumetric data is a well-studied domain. Traditionally, the underlying technology of these techniques is a mapping from a combination of the scalar value and associated local gradient information to a color and opacity. Some compositing of samples, as in ray casting or slice-based rendering, results in a final image. Such techniques have been successful in producing high-quality images, however, the growing size and complexity of data sets are encouraging development of techniques that incorporate automated analysis. Indeed in many fields, techniques are custom designed to identify and visualize features specific to data from a single application domain. Topology-based analysis methods are an attractive alternative and are especially well suited in this context, since they robustly describe a general feature space that can be queried combinatorially for reproducible and consistent results. The Morse-Smale (MS) complex is a topological representation of a scalar function with characteristics that make it particularly useful in identifying features: the various cells of the complex form the basis of a large feature space; the complex can be simplified to represent the function at multiple scales, for example, to be used in noise removal; and simple and combinatorial algorithms for its computation ensure robustness in the analysis. In particular, recent advances in algorithms for the computation of the MS complex utilizing discrete Morse theory enable, in practice, the analysis of increasingly large and complex data. however, visualization techniques have not yet explored the full potential of this technology. Topological feature identification has traditionally been done by experts on a per-application basis, with custom code being developed to visualize the results of each.