Two-Dimensional Gaussian Surface Fitting Code

The two-dimensional Gaussian surface fitting code discussed in this article represents a significant algorithm widely employed in numerous applications. This implementation utilizes two distinct methodological approaches, each possessing unique advantages and limitations. The first method employs gradient descent optimization, characterized by rapid convergence toward optimal solutions through iterative parameter adjustments based on the negative gradient direction. The second approach leverages Newton's iterative method, which typically demonstrates superior stability through second-derivative Hessian matrix computations, though potentially requiring more iterations to achieve convergence. Both implementations incorporate key functions for Gaussian parameter initialization, residual calculation, and convergence monitoring. Regardless of the selected methodology, this algorithm serves as a powerful tool for addressing various practical problems involving surface approximation and pattern recognition.