I am new to this wonderful site. I searched around a bit but I couldn't find any well-discussed posts on applications of differential geometry to artificial intelligence, or more generally to computer science.
I came across Riemannian Geometry a few months back via YouTube(lol) and have been hooked on it since. I even bought a textbook and started learning from there. I am an engineer and I have sufficient math skills to make sense of the book, but it hardly has any real life applications. Almost everything is "Prove this" or "Theorem that". So I wanted to know if there are any real-life implementable applications for CS. More specifically, in the field of AI and Machine Learning.
From what I have understood, differential geometry allows us to "see","understand" and "analyze" curves in higher dimensional spaces. Is this accurate? And can this help in AI and Machine Learning? In subtopics like Natural Language Processing, Robotics, Computer Vision, Data analysis?
I would sure like to start off with a simple project which helps me understand differential geometry better.
Thanks
PS: Sorry if I have not framed this question well, it is my first question.
Best Answer
For applications of Differential Geometry in Computer Science, the following link is very useful: http://stat.fsu.edu/~anuj/CVPR_Tutorial/ShortCourse.htm
It talks about : "Differential Geometric Methods for Shape Analysis and Activity Recognition"
One of the contributors of the above is Dr.Anuj Srivastava (http://stat.fsu.edu/~anuj/index.php). I liked the following line from his research areas page- "This technology is needed in many applications -- medical diagnosis, biometrics, video surveillance, undersea imaging, terrain mapping, and satellite image analysis."
Hope it helps !