I'm building a segmentation algorithm. I'm segmenting pieces of paper in a book that have been slightly crumpled. Imagine taking a piece of paper, crumpling it into a ball, and then trying to straighten it back out.
The piece of paper is an actually 3D object, but I want to segment a 2D plane running through the geometrical center of the 3D object. Is this a center of mass problem?
I have a 3D matrix of binary values -- 1 being on the piece of paper, and 0 not on the piece of paper.
What kind of algorithm can I run to find the 2D plane?
For volumes the "geometric center" usually refers to the medial axis; for algorithms to compute it see for instance this paper. However note that the medial axis of 3D volume can be topologically complex (consisting of sheets and curves glued together) and you will require significant post-processing to get anything resembling a developable surface from the medial axis of a page-shaped volume.
You're probably better off trying to fit a surface through the point cloud representing your page, rather than computing any kind of center. If you post a picture of the input mesh, I can give you more specific advice.