Least Squares Image Matching

Least squares image matching is an image registration method based on mathematical optimization theory, which achieves precise alignment by minimizing the sum of squared grayscale differences between two images. The core concept transforms the image matching problem into a nonlinear optimization problem, solved through iterative computations to find the optimal solution.

Algorithm implementation typically involves these key steps: First, establishing geometric deformation and radiometric distortion models to describe transformation relationships between images; then constructing the sum of squared grayscale differences as the objective function; finally employing optimization algorithms like Gauss-Newton or Levenberg-Marquardt for iterative solving. During iteration, gradient information must be computed and normal equations established for parameter resolution. In code implementation, this requires functions for gradient calculation using Sobel or Scharr operators, and matrix operations for solving linear systems.

In practical applications, this method achieves subpixel matching accuracy, making it particularly suitable for high-precision measurement tasks. However, it has specific requirements for initial value selection and image quality - excessive initial deviation or insufficient texture features may cause non-convergence. Program implementation must pay special attention to numerical stability through techniques like regularization, and carefully set iteration termination conditions using thresholds for parameter changes or residual norms.

From an engineering perspective, complete solutions should incorporate pyramid hierarchical strategies to expand convergence ranges, and reliable coarse matching methods to provide good initial values. These techniques significantly enhance algorithm robustness and practicality when implemented together. Code implementation would typically involve building image pyramids with Gaussian blurring and downsampling, and combining with feature-based matching algorithms for initialization.