Modified Dendrogram of High-dimensional Feature Space for Transfer Function Design

We introduce a modified dendrogram (MD) (with sub-trees to represent the feature space clusters) and display it in continuous space for multi-dimensional transfer function (TF) design and modification. Such a TF for direct volume rendering often employs a multi-dimensional feature space. In an n-dimensional (nD) feature space, each voxel is described using n attributes and represented by a vector of n values. The MD reveals the hierarchical structure information of the high-dimensional feature space clusters. Using the MD user interface (UI), the user can design and modify the TF in 2D in an intuitive and informative manner instead of designing it directly in multi-dimensional space where it is complicated and harder to understand the relationship of the feature space vectors. In addition, we provide the capability to interactively change the granularity of the MD. The coarse-grained MD shows primarily the global information of the feature space while the fine-grained MD reveals the finer details, and the separation ability of the high-dimensional feature space is completely preserved in the finest granularity. With the so called multi-grained method, the user can efficiently create a TF using the coarse-grained MD, then fine tune it with the finer-grained MDs to improve the quality of the volume rendering. Furthermore, we propose a fast interactive hierarchical clustering (FIHC) algorithm for accelerating the MD computation and supporting the interactive multi-grained TF design. In the FIHC, the finest-grained MD is established by linking the feature space vectors, then the feature space vectors being the leaves of this tree are clustered using a hierarchical leaf clustering (HLC) algorithm forming a leaf vector hierarchical tree (LVHT). The granularity of the MD can be changed by setting the precision of the LVHT. Our method is independent on the type of the attributes and supports arbitrary-dimension feature space.