Algorithm 1: Improved Genetic Algorithm

Input: population_size = 100; max_generations = 50; mutation_rate = 0.1; crossover_rate = 0.8; trans_x_offset = 30; trans_y_offset = 10; angle = 0; angle_offset = 5. Output: The best transformation parameters.

1. If The area of the current image$>0.4,$ 2. Template = select the most recent image with area greater than 0.8; 3. Else Template = the next frame; 4. End. 5. Based on Equation (2), calculate the relative displacement of the centroids of the current image and the template to obtain the relative displacement values: trans_x, trans_y. 6. Set initialization parameters and initialize the population based on the initial parameters: 7. trans_x_range = [trans_x − trans_x_offset, trans_x + trans_x_offset]; 8. trans_y_range = [trans_y − trans_y_offset, trans_y + trans_y_offset]; 9. angle_range = [angle − angle_offset, angle + angle_offset]; 10. While (the number of iterations $\le$ max_generations) 11. Initialize the population. 10. For each individual, calculate the fitness according to Equation (3). 11. In each generation: 12. Tournament selection involves selecting the individual with high fitness as the parent. 13. Generate new offspring through two-point crossover and site mutation [24,39]. 14. Perform elitism to ensure the best individuals are preserved. 15. end while 16. output the fitness of these solutions.