Estimation of Intrinsic Volumes in 2D and test of the random closed set model hypothesis - T. Mrkvicka, T. Kaiser - A new method of estimation of intrinsic volume densities for a stationary random closed set X in 2D 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.
A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set Xi with values in the extended convex ring is introduced. The method is based on the estimating of the intrinsic volumes densities of the epsilon-parallel sets to Xi and comparing them with its envelopes produced from simulations of the model given by the tested hypothesis.
Download the instalation program. Windows
The program allows
1) Estimating intrinsic volumes of pbm files in 2D,
2) Estimating intrinsic volumes of several parallel sets to the pbm files in 2D. Those intrinsic volumes can be used for test of random closed set model hypothesis.
The short manual to the program
[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.
[2] Mrkvicka T.: On testing of general random closed set model hypothesis.

Description of the program for estimating intrinsic volumes.
Set Deltas File (one such is attached in the instalation package) for discretized disk which should be used in the estimation procedure.
Set Epsilon: it is used to change the size of first parallel set to which the closure and complement is applied. The maximum setting (14 for enclosed Deltas file) 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. Maximal setting 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.
If Epsilons file is set then the program computes intrinsic volumes for various first parallel sets. This can be used for testing the random set model hypothesis. Several Epsilons files are enclosed.