Table 1 Steps involved in the Proposed Face Image Enhancement Technique

1. The face image is acquired, resized, and converted to gray scale as f(i, j)

2. The values of the lower and upper constraints for each parameter in the transformation function (see Eq. 1) are defined.

3. The CSO algorithm is initiated as follows:

 3.1. Let the number of nests be n, and the dimension of each particle be D, which corresponds to the number of variables to be optimized in our algorithm. In this case, D = 4, representing the four different parameters to be optimized in Eq. (1). The probability of discovering an alien egg or solution in a nest is given as P_a, while the number of iterations of the CSO algorithm is given as S.

 3.2. The random and initial solutions (nests) for each parameter are generated

 3.3. For every CSO iteration, until S, do

 3.4. Use Levy flights to obtain a new solution for each nest

 3.5. Evaluate each solution (nest) using Eq. (8)

 3.6. The best value among all the nests is obtained as Ε_max

 3.7. If \( {E}_{S+1}^{\mathrm{max}}>{E}_S^{\mathrm{max}} \)

 3.8. Update the new global best

 3.9. End if

 3.10. Empty a fraction of the worst nests based on P_a

 3.11. Update each new solution using Eq. (9)

 3.12. Keep the best nests

 3.13. Return to step 3.4 until S is completed

4. Obtain the optimized values of each parameter after the CSO iterations are completed

5. Use the optimized values in Eq. (1) to obtain a final enhanced image, g(i, j)