Question

What is the Euler number of a region with polygonal network containing V,Q and F as the number of vertices, edges and faces respectively?

(a) V+Q+F

(b) V-Q+F

(c) V+Q-F

(d) V-Q-F

The question was asked at a job interview.

Enquiry is from Regional Descriptors topic in chapter Representation and Description of Digital Image Processing

Answer 1

The correct answer is (b) V-Q+F

To explain: It is very important to classify the polygonal network. Let V,Q and F denote the number of vertices, edges and faces respectively. Then,

  V-Q+F=C-H

Where C,H represents the number of connected components and number of holes in the region respectively. So, the Euler number E is given by V-Q+F.