OPTIMIZATION STRATEGIES FOR IMAGE REGISTRATION USING RIGID AND MÖBIUS GROUPS

*Aizaz Hussain; Ali Riaz; Muhammad Anas Jawaid; Zafarullah Mangi; Adnan Shehzad

Authors

*Aizaz Hussain
Ali Riaz
Muhammad Anas Jawaid
Zafarullah Mangi
Adnan Shehzad

Abstract

Image registration is an important technique used to align two or more images by minimizing the mismatch between their visual appearances. It has wide applications in areas such as medical imaging, computer vision, remote sensing, and biological shape analysis. In this study, optimization strategies for two-dimensional image registration are investigated using rigid and Möbius transformations. The rigid transformation model consists of scaling, rotation, and translation parameters, while the Möbius transformation provides a more flexible framework for handling complex geometric deformations. The registration process is formulated through a discretized least-squares objective function based on the sum of squared differences between pixel intensities of the source and target images. To obtain accurate alignment, different optimization strategies are explored, including coarse search, gradient descent, and landmark-based initialization. Coarse search is used to explore the transformation space and provide an approximate solution, whereas gradient descent refines the transformation parameters to achieve improved registration accuracy. In addition, landmark initialization is incorporated to generate reliable initial estimates for difficult registration cases and to reduce the possibility of convergence toward local minima. The proposed framework is theoretically analyzed to evaluate the effectiveness of the optimization strategies. The analysis demonstrates that the combined use of coarse search, landmark initialization, and gradient-based refinement improves image alignment and optimization performance. This study highlights the effectiveness of combining rigid and Möbius transformation frameworks within a unified optimization-based image registration approach.

Keywords : Image Registration, Rigid Transformation, Möbius Transformation, Optimization Techniques, Gradient Descent, Coarse Search, Landmark Initialization, Least Squares Optimization.