Would you explain the formula for me?

[yingma111]

In paper: CANNYLINES: A PARAMETER-FREE LINE SEGMENT DETECTOR
at 2.1.1. Helmholtz Principle on Edge Detection writes: For each edge segment with the length , the number of connected pieces of is .
Would you explain for me?

[Gofinge]

I am not the writer of the paper, I am also trying to figure out the problem. But I think “Edge detection by Helmholtz principle” might be helpful. Most of the thoughts of CannyLine came from the paper.

[SueeH]

In paper: CANNYLINES: A PARAMETER-FREE LINE SEGMENT DETECTOR
at 2.1.1. Helmholtz Principle on Edge Detection writes: For each edge segment with the length , the number of connected pieces of is .
Would you explain for me?

I read this paper recently, I think it means the links between every point in a line.
For example a line with 5point (p1,p2,p3,p4,p5),the possible connection to p1 is(p1,p2,p3,p4,p5),the possible connection to p2 is(p2,p3,p4,p5)... since we set connection without direction, so the sum connection is as formula.