Estimation of Intrinsic Volumes in 3D - T. Mrkvicka, T. Kaiser - A new method of estimation of intrinsic volume densities for a stationary random closed set X in 3D with values in the extended convex ring is introduced. The local Steiner formula is applied to the closure of the complement of the parallel set for n different radii and, by solving a linear regression model, estimates of the intrinsic volume densities of the parallel set are obtained, which are used as approximations of those of X itself.

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Download the instalation program. Windows
The package contains two programs.
In GenBool you can simulate your own 3D boolean model of balls. The WinEiv3d is the estimation program itself. The data must be given in 2D slices of format pbm. The program is easy to use, but there are several things good to know. When you set your data directories, you must choose Epsilon and Discretized balls file.
Epsilon is used to change the size of first parallel set to which the closure and complement is applied. Setting 22 gives you the basic estimation method. Setting 1 gives you the method that reduces the bias of the estimator. This method will be described in forthcoming paper. Setting 22 is best to apply when the image is larger, so the bias is small. Setting 1 is better to apply in other cases when the reduction of the bias is needed and we are ready to pay for this reduction with a small decrease of the accurancy.
Discretized balls file Set here the file which contais the discretized balls and its radii. One of such file is added in the setup.zip file. You can change the number of balls and its radii.
[1] Mrkvicka T., Rataj J.: On estimation of intrinsic volume densities of stationary random closed sets. {\it Stochastic Process.\ Appl.} (2007), doi:10.1016/j.spa.2007.04.004.