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Chapter 1

Introduction

Volume data is defined by a three-dimensional grid of scalar values or tuples. Each
point on the grid is called a voxel. (The two-dimensional version of volume data
is a grey-scale or colored image). Volume data can be generated for simulations
or generated through imaging technology such as computed tomography (CT) in
medicine and electron microscopy (EM) in bio-molecular imaging. The most intuitive
analysis of a 3D volume map is through visualizing the data. For example, given a CT
scan of a hand, we can reconstruct a 3D model of the hand that allows for interactive
visual manipulation such as rotation, translation, and magnification. In addition to
visualizing the entire volume, sometimes it is useful to visualize the components that
reside within a volume map. (In the case of the hand CT, it would be useful if we can
separate out the bones from the flesh). To visualize components within a volume, the
first step is to separate out regions of interest within the data set. This separation
is called segmentation. Besides bone∕flesh separation in medicine, segmentation also
corresponds to other high-level semantics such as locating symmetric subunits from a
reconstructed image of a protein (see Figure 1.5(b)) and identifying individual parts
of a mechanical object like an engine (see Figure 1.5(d)).

Our work addresses the specific problem of visualizing segmented volumes. We
focus on reducing the jagged boundary associated with binary classification of seg-
mented volumes. In addition to visualization, we also develop a semi-automatic seg-
mentation interface and demonstrate that this interface is an intuitive and efficient
method for segmentation.

In the rest of this chapter, we will discuss the background and motivation of our

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