Computing with Biologically Inspired Neural Oscillators: Application to Colour Image Segmentation

Algorithm 1

1. Initialisation

- set 𝑧(0)=0 and calculate the connecting weights

𝑊_𝑖𝑘=𝐼_𝑚/(1+|𝐼_𝑖−𝐼_𝑘|); where 𝐼_𝑚 is the maximum gray scale value, 𝐼_𝑖 and 𝐼_𝑘 represent the pixel

value corresponding to neuron 𝑖 and 𝑘.

- find leaders: 𝑝_𝑖=𝐻(∑_{𝑘∈𝑁𝑖}𝑊_𝑖𝑘−𝜃_𝑝) and randomly start all the oscillators on the left branch

(i.e., set the value of their units 𝑥 to a random value in the interval [LC𝑥, LK𝑥], the points LC and LK

has already been shown in Figure 2).

2. Selection

- Find the closest leader 𝑗 to left knee (LK).

- Jump the found leader to right branch (RB), the other oscillators move towards LK

𝑥_𝑗(𝑡+1)=RK;𝑧(𝑡+1)=1           {jumpup};

𝑥_𝑘(𝑡+1)=𝑥_𝑘(𝑡)+(LK−𝑥_𝑗(𝑡));for𝑘≠𝑗

3. Jumping

Iterate until stop

If  𝑥_𝑖(𝑡)=RK and 𝑧(𝑡)>𝑧(𝑡−1)

    𝑥_𝑖(𝑡+1)=𝑥_𝑖(𝑡);          {stayontheRB}

elseif    𝑥_𝑖(𝑡)=RK and 𝑧(𝑡)<=𝑧(𝑡−1)

    𝑥_𝑖(𝑡+1)=LC;𝑧(𝑡+1)=𝑧(𝑡)−1; {jumpdown}

    if 𝑧(𝑡+1)=0 go to Selection.

else      

    {calculateinputtoneuron}

    𝑆_𝑖 (𝑡+1)=sum(𝑤_𝑖𝑘⋅𝐻(𝑥_𝑘(𝑡)−LK))−𝑊_𝑧𝐻(𝑧(𝑡)−𝜃_𝑧);

    If 𝑆_𝑖(𝑡+1)>0

      𝑥_𝑗(𝑡+1)=RK;𝑧(𝑡+1)=𝑧(𝑡)+1   {jumpup};

    else

        𝑥_𝑗(𝑡+1)=𝑥_𝑗(𝑡);     {stayonLB}