If
this plugin aids your investigations, please cite the
following abstract.  I am currently finalizing this paper for
submission and will update the citation at a later date.

Invest Ophthalmol
Vis Sci.
ARVO Meeting Abstracts April 22, 2011 52:5470
Topical
Neuroprotectin D1 Attenuates Experimental CNV and Induces Activated
Microglia Redistribution.
Sheets
KG,
Bokkyoo J, Zhou Y,
Winkler J, Zhu M, Petasis N, Gordon WC, Bazan NG.
Neuroscience
Center of Excellence, Louisiana State University Health Sciences
Center, New Orleans, LA 70112, USA.

This
plugin calculates the 3D shape descriptors
Solidity3d & Convexity3d based upon a convex hull constructed
from
an 8-bit or 16-bit grayscale image stack.  Users
can define thresholds prior to executing or the plugin will assume a
dark background and auto threshold the stack using the IsoData method
and the stack histogram. Pixels within the threshold values will be
gathered
into a point cloud for subsequent construction of the convex hull.

Due
to necessary calculations, this plugin can also measure the surface
area, voxels, and volume for the point cloud and
the convex hull.  Surface
area and Volume use the image calibration and report values in units^2
and units^3, respectively. 

The
plugin can also visualize the convex hull vertices by generating a new
image stack containing only white pixels at location of vertices.  A
future version will be able to generate an entire convex hull in the
image stack.

From
The Image Processing Handbook, 5th Ed. by John C. Russ: 

• Solidity
  =  Area / Convex Area
• Convexity
  = Convex Perimeter / Perimeter

The
3D equivalent of Area is Volume, and the 3D equivalent of Perimeter is
Surface Area.  Thus
this plugin defines:

• Solidity3d
  = Volume / Convex Volume
• Convexity3d
  = Convex Surface Area / Surface Area

Analyze>3D
Convex Hull>Convex
Measures>

•  Measure
  Convex Volume…
•  Measure
  Convex Voxels…
•  Measure
  Convex Surface Area…

Analyze>3D
Convex Hull>Object
Measures>

•  Measure
  Volume…
•  Measure
  Voxels…
•  Measure
  Surface Area…

Analyze>3D
Convex Hull>Shape Descriptors>

•  Measure
  Solidity3D…
•  Measure
  Convexity3D…
•  Measure
  All… 

The
plugin can also visualize the convex hull vertices

•  Plugins>3D
  Convex Hull>Make Convex Hull Vertices Stack…

•  Plugins>3D
  Convex Hull>Make Convex Hull Stack…

Generate
multi-point selections from convex hull vertices and store in the roi
manager

• Edit>Selection>3D
  Convex Hull>Select Vertices…

Generate
z-plane cross section polygon selections from the convex hull and store
in the roi manager

• Edit>Selection>3D
  Convex Hull>Select Hull…

Determination of the convex hull is done using a
modified version of  the
quickhull3d package.  For
specific modifications to the quickhull3d package, see the annotations
within the source code. The quickhull3d package was written by

Copyright, 2004.
John E. Lloyd, Ph. D.
Research Engineer, CS and
Electrical and Computer Engineering
University of British
Columbia
lloyd at cs.ubc.ca
Available at  QuickHull3D:
A Robust 3D Convex Hull Algorithm in Java

This
package is a 3D implementation of QuickHull for Java, based on the
original paper by Barber, Dobkin, and Huhdanpaa and the C
implementation known as qhull. The algorithm has O(n log(n))
complexity, works with double precision numbers, is fairly robust with
respect to degenerate situations, and allows the merging of co-planar
faces.

Barber, C. B., D.P.
Dobkin, and H.T. Huhdanpaa, “The Quickhull
Algorithm for Convex Hulls,” ACM Transactions on Mathematical Software,
22(4):469-483, Dec 1996, www.qhull.org

Gathering
the point cloud data necessary to build the convex hull is modeled on
the approach used in the Point_Cloud plugin written by 

Jonathan B. Glass, 2010
jbglassij
at gmail.com
Available on the ImageJ
Plugins site Export
Point Cloud

• LearnImageJ
• QuickHull3D:
  A Robust 3D Convex Hull Algorithm in Java
• Export
  Point Cloud
• QHull