Image Matching Using Dimensionally Reduced Embedded Earth Mover’s Distance

Pseudocode 1

function Calculate_𝐿₁(image)

begin

 Scale image to 64 × 64

 Initialize an image matrix, original_img, of 64 × 64

 Initialize an image matrix, imageMtrx, of (2 × 64) × (2 × 64)

 Set imageMtrx to original_img

 Initialize 𝑈₁, a random number between 0 and 64

 Initialize 𝑉₁, a random number between 0 and 64

 Shift each position in imageMtrx to position (𝑈₁, 𝑉₁)

 Set 𝐺₁ array to pixels of imageMtrx

 //Create 𝐿₁_vector of image matrix including 𝐺₁ array followed by 𝐺₂ array,…,

   followed by 𝐺_𝑛 array (as in Figure 3)

 Initialize 𝐿₁_vector to null

 𝐿₁_vector = 𝐺₁

 for  𝑖=1 to 6

   Set 𝐺_𝑖+1 to sum of each 4-neighbour elements of 𝐺_𝑖 multiplied by side length

    𝐿₁_vector = 𝐿₁_vector + 𝐺_𝑖+1

 end for

 return 𝐿₁_vector

end

function Calculate_Embedded EMD(image 1, image 2)

begin

 Initialize 𝐿₁_vector 1

 Initialize 𝐿₁_vector 2

 Initialize EEMD

 Set 𝐿₁_vector 1 to Calculate_𝐿₁(image 1)

 Set 𝐿₁_vector 2 to Calculate_𝐿₁(image 2)

 Subtract each pair of corresponding elements of 𝐿₁_vector 1 and 𝐿₁_vector 2

 Add all subtractions into EEMD and display it

end