As posted above, ImageJ or CellProfiler are preferred options. Whether you get useful results, however, depends on your raw data and the way you use the softwares. For cell counting, try to segment features that can be spatially separated easily. Typically, that would mean using object counting options applied to images of nuclear stains. If you go ahead with your analysis you will probably notice yourself that the seemingly simple task you have could turn out as a non-trivial problem. In fact, image segmentation and object identification is a big research focus in the area of 'computer vision'.
One final tool for image registration - give ilastik a go (http://www.ilastik.org/).. very easy to use and to train, and you can export the images to be counted in another package (eg imageJ or CellProfiler) very easily. Also, if you've never used ImageJ before, perhaps you might want to start with Fiji (http://fiji.sc/Fiji) which is just ImageJ but is tailored to image analysis. Good luck :)
I would also recommend ImageJ if you do not have the money for a commercial package. I routinely use the Fiji distribution of ImageJ (www.fiji.sc) and also regularly run workshops on using it. You can download the notes and demo images relevant to cell counting and segmentation from the following links. Cheers. Cam
I am sorry if this is no longer relevant, but I would strongly recommend you take a look at MIPAR at http://MIPAR.us. It is new, and very user friendly software we have just released as an extended free trial that has proven extremely capable at solving nearly any segmentation problem/image analysis problem we have faced. I am available any time to make a recipe file for you to jump start your analysis. Several tutorials are also available on the site. Very powerful for large batch processing as well. Hope we can help!
I use Image Pro Plus V7.0. Its an old version of the software but the newer versions are more reliable and more easy to use. Overall, it's necessary to find out which method of staining would be better to use for staining the intended cells. I think, making the cells distinguishable is more important than the software that you are going to use.
When you analise the Figure 12 in the referenced article (Corneal Endothelium: Histology, Physiology and In-vivo Examination with Specular Microscope) which can be found at the link below.
What is important is the lack of specific microscope manufacturers' concern with this problem, solved only by methodology that considers one more image to analyze the endothelial mosaic in a personal way, this can only be solved by computerized resource, I worked for it in my lab, the software called Cell Analyzer.