First- and Second-Order Full-Differential in Edge Analysis of Images

Algorithm 1

Edge Detection with First and Second Differential.

Input: Images 𝐷={𝐈₁,𝐈₂,𝐈₃,…,𝐈_𝑁},𝐈_𝑖∈ℝ^𝑚×𝑛 and 𝑐₁,𝑐₂;

Output: Edges of 𝐷, 𝑉={𝐄₁,𝐄₂,𝐄₃,…,𝐄_𝑁},

   where 𝐄_𝑖∈ℝ^𝑚×𝑛;

Step  1. Boundary processing 𝐷;

Step  2. Pre-processing 𝐷 with rgb2gray (or rgb2hsv);

Step  3. Differential computing according to (7);

Step  4. Differential computing according to (15);

Step  5. Edge image according to (9);

Step  6. Edge image according to (16);

Step  7. End.