An Improved Computer Vision Method for White Blood Cells Detection

Algorithm 1

Step 1: Set the DE parameters 𝐹=0.25 and CR = 0.8.

Step 2: Initialize the population of m individuals 𝐄^𝑘={𝐸^𝑘₁,𝐸^𝑘₂,…,𝐸^𝑘_𝑚} where each decision

   variable  𝑝₁, 𝑝₂, 𝑝₃, 𝑝₄  and  𝑝₅ of 𝐸^𝑘_𝑎  is set randomly within the interval [1, 𝑁_𝑝]. All

   values must be integers. Considering that 𝑘=0 and  𝑎∈(1,2,…,𝑚).

Step 3: Evaluate the objective value J(𝐸^𝑘_𝑎) for all m individuals, and determining the 𝐸^best,𝑘  showing

    the best fitness value, such that 𝐸^best,𝑘∈𝐄^𝑘𝐽(𝐸^best,𝑘)=min𝐽(𝐸^𝑘₁),𝐽(𝐸^𝑘₂),…,𝐽(𝐸^𝑘_𝑚).

Step 4: Generate the trial population  𝐓={𝑇₁,𝑇₂,…,𝑇_𝑚}:

   for (𝑖=1; 𝑖<𝑚+1; 𝑖++)

   do 𝑟₁ = floor(rand(0,1)⋅𝑚); while (𝑟₁=𝑖);

   do 𝑟₂ = floor(rand(0,1)⋅𝑚); while ((𝑟₂=𝑖) or (𝑟₂=𝑟₂));

   jrand = floor(5⋅rand(0,1));

       for (𝑗=1; 𝑗<6; 𝑗++) // generate a trial vector

         if (rand(0,1)<=CR or 𝑗 = jrand)

         𝑇_𝑗,𝑖=𝐸^best_𝑗^,𝑘+𝐹⋅(𝐸^𝑘_𝑗,𝑟1−𝐸^𝑘_𝑗,𝑟2);

           else

            𝑇_𝑗,𝑖=𝐸^𝑘_𝑗,𝑖;

         end if

       end for

   end for

Step 5: Evaluate the fitness values  𝐽(𝑇_𝑖) (𝑖∈{1,2,…,𝑚}) of all trial individuals. Check all

   individuals. If a candidate parameter set is not physically plausible, i.e. out of the

   range [1,𝑁_𝑝], then an exaggerated cost function value is returned. This aims to

   eliminate ‘‘unstable” individuals.

Step 6: Select the next population  𝐄^𝑘+1={𝐸₁^𝑘+1,𝐸₂^𝑘+1,…,𝐸_𝑚^𝑘+1}:

   for (𝑖=1; 𝑖<𝑚+1; 𝑖++)

    if (𝐽(𝑇_𝑖)<𝐽(𝐸^𝑘_𝑖))

     𝐸_𝑖^𝑘+1=𝑇_𝑖

      else

      𝐸_𝑖^𝑘+1=𝐸^𝑘_𝑖

    end if

   end for

Step 7: If the iteration number (𝑁_𝐼) is met, then the output 𝐸^best,𝑘  is the solution (an actual

   ellipse contained in the image), otherwise go back to Step 3.