Should I include my thesis supervisor as an author for new derived work? I would like to make a variation of one question already answered here.

I have also submitted my Master thesis manuscript to the university library and I have verified that there is no conflict of interest if I publish a summarized version in a journal (in fact, the university urge me to do so to gain visibility). The thesis was based on a previous paper I have published along with my supervisor and one colleague. For that paper  I didn't participate in the creation of the algorithm because my role was testing and finishing paper's drafting. How ever, during the thesis, I added original algorithms to cover some existent deficiencies and the supervisor merely limited himself to check typographical errors and confirm the quality of the results. 

One of the thesis evaluation committee's member suggested me to improve the quality of the evaluation parameters by using a state-of-the-art method I didn't consider before, so I am thinking to add the new method (and the obtained results) to the submission of the next paper.

Since I finished the Master program (some months ago) I haven't mentioned to my supervisor that I am considering to make a new submission, in fact, he is involved with new master candidates and projects, and I am working full-time in industry. Should I still mention him the idea of submiting a new paper or adding him as a contributor?

Note: the first paper was published while I was working as a lab assistant in university A, and I completed the thesis in university B. University A's legal office was fine to let me continue with my thesis as long as I were using a different implementation on a different language (which I did), so I don't see any problem on that aspect. My thesis supervisor is still a professor in both universities.
If he hasn't participated in the new work he isn't really a co-author. Of course you cite the older work as usual and can also acknowledge his help in getting you started. 

However, if you want to continue the work with his participation before publishing then he would naturally be a co-author. 

Just working with you previously doesn't give him, or anyone, authorship on new work.