Two-Dimensional Gaussian Surface Fitting with MATLAB Code Implementation

To perform two-dimensional Gaussian surface fitting in MATLAB using a copy-and-execute approach, several critical steps require careful implementation. The process begins with defining the Gaussian function model, typically implemented using the formula: f(x,y) = A*exp(-((x-x₀)²/(2σ_x²) + (y-y₀)²/(2σ_y²))), where A represents amplitude, (x₀,y₀) denotes the center coordinates, and σ_x, σ_y control the spread along respective axes. The fitting algorithm commonly employs nonlinear least-squares optimization through MATLAB's lsqcurvefit function or the Curve Fitting Toolbox. Key implementation steps include: initial parameter estimation from input data peaks, setting appropriate bounds for convergence, and configuring optimization tolerances. The code typically requires preprocessing of 2D coordinate matrices using meshgrid and reshaping data into column vectors for the fitting function. After algorithm execution, validation involves analyzing residual plots and goodness-of-fit metrics like R-squared values. For suboptimal results, parameter constraints may need adjustment or robust fitting methods should be considered. The final fitted surface can be visualized using surf or contour plots, with applications ranging from image processing to scientific data analysis. While the copy-paste approach simplifies initial setup, understanding the underlying optimization mechanics ensures proper parameter tuning for different datasets.