Describe the algorithm of statistical models of appearance

I'm trying to create a C# program, which will build, train and fit Active Shape and Active Appearance Models. To do this, I read a few chapters of T.F. Cootes's and C.J. Taylor's article "Statistical Models of Appearance for Computer Vision". From the beginning it was relatively simple and straightforward, but then began to appear some formulas which were very abstract, became not understandable what data is necessary to substitute in formulas and in which form, began to appear inaccuracies(probably, inaccurate to me, as a layman in this kind of data analysis), as well as some of the details began to overlook, because of which meaning became more abstract, ambiguous and confusing. Due to this it became necessary to fully understand the algorithm of building, training and fitting Active Shape and Active Appearance Models. I believe that the right thing is to be done in UML form or other type of algorithm description (this can be your proposal). The main thing is not the form and presentation of this algorithm, but its availability and seamlessly for understanding. Also we need a sample with a few points which will accompany the whole algorithm. P.S. I may be incorrect in terms in some places, due to incomplete understanding of the algorithm of these models, so it will be needed to discuss details. P.P.S Also, if you have any suggestions how to do it better, I'll take it into consideration.