MATLAB Implementation of Affine Transformation Based on Least Squares Method

In this article, we will demonstrate how to implement affine transformations using the least squares method. Affine transformation is a crucial technique in computer vision applications, enabling image operations such as rotation, translation, and scaling. This implementation will be carried out in the MATLAB environment with detailed code walkthroughs for each step. The discussion covers fundamental principles including point set selection strategies, affine matrix construction methodologies, and error minimization techniques. Key implementation aspects include using MATLAB's matrix operations to solve the linear system A*X = B through the pseudoinverse (pinv function) for optimal parameter estimation. Through this tutorial, you will gain practical understanding of least-squares-based affine transformations and enhance your MATLAB programming skills for computer vision applications. The code implementation will specifically show how to handle coordinate mapping between source and target points while maintaining transformation matrix invertibility conditions.