Geometric Analysis, Visualization, and Conceptualization of 3D Image Data

William Johnston and Wing Nip
Imaging and Distributed Computing Group
Information and Computing Sciences Division
Lawrence Berkeley Laboratory
Berkeley, CA 94720

Publication number: LBL-35329

Credits

CONTENTS

Introduction

The acquisition and study of image-like data from throughout the volume of an object permits us to represent and explore the internal three-dimensional structure of that object exactly as it exists in the undisturbed object. This unit will explore how such image data is obtained, and the kinds of analysis and visualization that can be done with the data by using computer based imaging and visualization. This work introduces concepts in 3D geometry, 2D and 3D image processing and display, computer graphics and visualization, and the exciting ability of imaging and computer systems to explore the frequently complex and invisible world of the "insides" of a plant, animal, machine, etc.

In general terms the steps involved in this exploration are as follows, and we will examine each of them in detail in the course of this study unit.

(1) Acquire information about the inside of an object, and generate a 3D image data set:

The image of the inside of an object can arise from:

The resulting 3D image is a discrete scalar field, that is, it is a 3D grid with values given at each point of the grid. This type of 3D image is frequently called a voxel data set. (The word "voxel" is derived from "volume pixel"). The numeric values of the voxels must, of course, be interpreted according to the nature of the imaging process (they might represent material density, concentration of hydrogen, electron density, color, etc.) Figure 1 ( ) shows part of a 3D data set of an NMR (MRI) scan of an orange. The image values (quantity of magnetically excitable hydrogen, which is typically different in different type of biological tissues) are represented as shades of gray. Figure 2 ( ) use optical density to represent the 3D nature of the data. In other words, each grid point is assigned a gray value and opacity based on the magnitude of the data value ("0" is transparent and black, while the highest value is completely opaque, and white). When this representation is carefully designed, the voxel data set is seen in a "cloud like" appearance.

(2) Define the regions (geometric structures) of interest:

This process (called segmentation) can be done automatically if the regions are well separated in terms of data values. Normally, however, a human has to give "hints" as to where the boundaries are located because imperfect imaging techniques loose or modify the information needed for unambiguous interpretation. These hints are really the incorporation of auxiliary knowledge (what we know about the object from other types of studies). For example, a human can say "I know because of other imaging studies, and because I have cut this object open and looked at it, that this boundary which appears to fade away in this part of the image, really continues and reconnects over here. The artifact arises from problems in acquiring the 3D image. To correct for this I will draw in the boundary to reflect what I know is really the case." These hints are usually provided in the form of "masks" defined in planes that are 2D slices through the 3D data set. These slices may, or may not, correspond to any physical aspect of the original imaging. The actual process entails using a "paint-brush" like program to mark boundaries. This process has to be done separately for each structure of interest. Figure 3 ( ) shows one of the 3D masks for each of the six structures defined for the orange:

A mask is defined for every slice that intersects the structure of interest. In the case of the outer skin, this means that 64 masks are needed to define the structure since the outer skin intersects all 64 slices of the volume data. ( Figure 3 shows one typical mask for each of the six structures (at slice 32, which is about the middle of the orange).

(3) Create a geometric model for each of the structures of interest:

By "geometric" model we mean a collection of geometric primitives (points, lines, polygons, etc.) that accurately represent the shape of the surface. These geometric descriptions are used to enhance the visualization of the object and to provide for quantitative analysis (the surface area, volume, mean curvature, topology, etc.).

When we started, the surfaces of the structures were represented only implicitly by differences in color. There are a number of ways to convert the color changes into geometry. Conceptually most of the methods involve some sort of contouring. Consider a 2D slice of the volume image, and we draw lines through that slice along pixels of constant value (color). This operation effectively defines the boundary between areas of different color. The masks mentioned above are human supplied hints as to where to draw these contour lines in the areas where the color difference fades away.

By effectively stacking the masks, and covering the surfaces with a tightly fitting, fishnet like mesh (a process called tessellation) we generate 3D polygons that do not overlap each other, and do not leave holes in the mesh. This mesh of small polygons is now a "geometric" definition of the surface of the structure of interest. Such a geometric model is built for each structure of interest. Figure 4 ( ) shows both the inner skin model, and the model for the seeds.

(4) Use computer graphics to visualize the results:

The next step is to present the models in a way that allows people to understand the spatial features and relationships in the interior of the object. This is done by using a collection of computer graphics techniques called visualization.

(5) Exploration and discovery:

When the modeling process is complete, students may explore and manipulate the invisible geometry of the object. Figure 8 ( ) is the result of a high school student using a commercial 3D animation program to make the "exploded" view of the orange model produced the process described above. What this student really wants to do is to make an exploded view of a frog, not like anatomy books where inside parts are pulled apart to expose what is underneath, but by leaving everything in it's correct 3D relationship, and "fading out" the parts that obscure the areas of interest, etc.




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Page last modified: 01/09/05
Contacts: Bill Johnston, David Robertson