Fitting 2D Gaussian Surfaces

Fitting 2D Gaussian surfaces in MATLAB is a common task in image processing and data analysis, applicable to scenarios such as peak detection and surface modeling. The 2D Gaussian surface is defined by six key parameters: center coordinates in x/y directions, amplitude, standard deviations, and rotation angle.

The typical implementation begins by preparing a 2D data matrix, which could be experimental measurement data or simulated test data. For the fitting process, nonlinear least squares methods are generally employed, where MATLAB provides functions like lsqcurvefit or fit for implementation. Prior to fitting, appropriate initial parameter estimates must be set, as they directly impact the convergence of the fitting algorithm. The lsqcurvefit function requires specifying an objective function that calculates the Gaussian surface values based on the parameters, while the fit function can use predefined model types like 'gauss2'.

For surface visualization, after completing the fitting, functions like mesh or surf can be used to create comparison plots between original data points and the fitted surface. To evaluate fitting quality, residuals or the coefficient of determination R² can be calculated. If convergence issues occur, adjustments to initial parameters or consideration of data noise handling may be necessary. The mesh function displays the surface as a wireframe mesh, while surf creates a colored surface plot with lighting effects for better visual distinction.

In practical applications, this technique is commonly used in microscopy image analysis, optical measurements, and other fields requiring precise localization of 2D peak positions. Through fitting, accurate peak center coordinates and distribution characteristic parameters can be obtained, enabling quantitative analysis of spatial patterns in scientific data.