Volumetric Attribute Filtering and Interactive Visualization Using the Max-Tree Representation

Abstract

The Max-Tree designed for morphological attribute filtering in image processing, is a data structure in which the nodes represent connected components for all threshold levels in a data set. Attribute filters compute some attribute describing the shape or size of each connected component and then decide which components to keep or to discard. In this paper, we augment the basic Max-Tree data structure such that interactive volumetric filtering and visualization becomes possible. We introduce extensions that allow (1) direct, splatting-based, volume rendering; (2) representation of the Max-Tree on graphics hardware; and (3) fast active cell selection for isosurface generation. In all three cases, we can use the Max-Tree representation for visualization directly, without needing to reconstruct the volumetric data explicitly. We show that both filtering and visualization can be performed at interactive frame rates, ranging between 2.4 and 32 frames per seconds. In contrast, a standard texture-based volume visualization method manages only between 0.5 and 1.8 frames per second. For isovalue browsing, the experimental results show that the performance is comparable to the performance of an interval tree, where our method has the advantage that both filter threshold browsing and isolevel browsing are fast. It is shown that the methods using graphics hardware can be extended to other connected filters.

Component-Trees and Multivalued Images: Structural Properties

“…Most of them are devoted to filtering or segmentation [8], [14], [15], [16], [17]. Other applications have also been considered, for instance, image registration [7], [18], image retrieval [19], [20], image classification [21], interactive visualisation [22], multithresholding [23] or document binarisation [24].…”

Mathematical Morphology in Computer Graphics, Scientific Visualization and Visual Exploration

“…The basic Max-tree data structure can be augmented by extensions that allow (i) direct volume rendering, (ii) representation of the Max-tree on graphics hardware, and (iii) fast active cell selection for isosurface generation. In all three cases, the Max-tree representation can be used to change filter parameters interactively and visualize the result at interactive rates [51]; see Figure 4 for an example.…”

Global gray‐level thresholding based on object size

“…We use the component tree (8), which is a quasi-linear algorithm based on Tarjan's union-find procedure (9), making the computations fast. Component trees have been used for adaptive segmentation (10)(11)(12)(13)(14), and at least some of the global threshold methods mentioned above (e.g., Refs. 4,5,7) could be implemented in an efficient way using component trees.…”