Computational Topology Codes

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I am working on a project with a PI that thinks could be solved with computational topology tools. For this project, we will be looking at the persistent homology of objects in 3D images.

I tried to install Javaplex, but I was having difficulties getting it to work. It requires Matlab (which I don't have a license for), and I was unsuccessful in porting it to Octave. Basically, there were issues getting octave-java from macports, and installing it from source is a PITA.

Since I am completely unfamiliar with computational topology (and so is the PI), I was hoping that someone could point me towards codes that is relatively easy to get started with. Yes this is a subjective question, but I would prefer to avoid banging my head against a wall trying getting something (and all of its dependencies) installed, only to find out that it isn't what I need or that it has a very high barrier to entry.

I am particularly interested in open source codes that are relatively easy to use, install and output files that can be visualized using Gnuplot or some other open source plotting program. Also, I would like to run this on a remote cluster, so being able to do my visualization over X11 would be wonderful.