next up previous contents
Next: Unbundling the Software Distribution Up: Medial Axis Analysis of Previous: Contents

Introduction

 

The 3DMA software package is designed to provide a convenient tool for analyzing the geometry of a randomly shaped object in 2- and 3-dimensional images. Specific data sets analyzed with this software include:

The input to the package is a 2 or 3D digitized, grey-scale, image of the object. Specifically it is assumed that the image consists of two populations of voxels, object and background. A wide variety of input formats for the image are currently supported, either in volume or slice-wise form. Formats currently supported are listed in §6.2. Typically the images are produced either by synchrotron computed microtomography, laser scanning confocal microscopy or visual microscopy.

Geometric analysis of the object in such a grey-scale image typically requires three major steps:

Segmentation

Segmentation is the process of converting the grey-scale image into a `black and white' image by determining the population assignment (object or background) for each voxel in the image. Typically the object/background boundary in the image is fuzzy due to finite voxel resolution and possible collection noise (e.g. tomographic reconstruction artifacts). 3DMA provides four segmentation algorithms:

In support of image segmentation, 3DMA also offers the ability to produce 2- and 3D graphical images of the input data set, as well as histogram(s) of the image intensity. Image graphics is provided through output files for postprocessing viewing. Graphical formats currently supported are described in §7. Threshold values required in all 4 segmentation algorithms are based upon knowledge of the image intensity histogram. Additionally, 3DMA also offers the ability to produce 2- and 3D graphical images of the resultant segmented data set.

Dimensional Reduction

Analysis of the geometry of a three dimensional object, especially one of random shape is very difficult. More extensive analysis of the object's geometry is based upon determining and characterizing its one dimensional skeleton (medial axis). The skeleton of a digitized object is efficiently obtained by erosion-based algorithms; the 3DMA code uses the algorithm of Lee-Kashyap and Chu, (T.-C. Lee, R.L. Kashyap and C.-N. Chu, Building skeleton models via 3-D medial surface/axis thinning algorithms, CVGIP: Graph. Models Image Process., 56 (1994) pp. 462-478.) As long as the object contains no embedded (background phase) cavities, its skeleton is one dimensional preserving the fundamental topology of the object. The digitized skeleton consists of curve segments (voxel paths) which meet at branch clusters. Since the skeleton also retains a strict geometric position within the object, it also preserves much of the fundamental geometry of the object. In addition to its characterization properties, the skeleton provides a useful means of searching the object for specific attributes. These attributes depend somewhat on the type of object being analysed.

Statistical Analysis

As 3DMA was developed to analyze the geometry of objects of "random" shape, the majority of the analysis consists of determining the spatial distribution of characterizing attributes.

3DMA provides the following analyses of the three dimensional object:

During the erosion process, the distance from each voxel in the object to the closest object surface voxel is computed and stored. This provides another characteristic distribution of the three dimensional object:

The following analyses of the skeleton are provided:

Currently, for rock images, 3DMA uses the skeleton to determine the following:

Currently, for neuron images, 3DMA uses the skeleton to determine the following:

Currently, for fiber network images, 3DMA uses the skeleton to determine the following:

Note: As this is a research code undergoing extension of its capabilities, recently developed/developing capabilities may not be included in the latest released verion of 3DMA


next up previous contents
Next: Unbundling the Software Distribution Up: Medial Axis Analysis of Previous: Contents

Brent Lindquist
Thu Sep 30 12:33:54 EDT 1999