Deformable Transformation

Deformable transformations are mathematical models used to represent and analyze the warping and bending of shapes or images, aiming to align or register data across different instances or viewpoints. Current research focuses on developing efficient and robust algorithms, often employing neural networks (e.g., deformation networks, Gaussian splatting) or closed-form solutions (e.g., Procrustes analysis extensions) to handle complex deformations in various applications. These advancements are significantly impacting fields like medical image analysis (improving segmentation and augmentation), computer vision (enhancing image registration and 3D reconstruction), and graph analysis (providing new tools for handling directed and signed graphs). The ability to accurately model and manipulate deformable transformations is crucial for numerous applications requiring precise shape or image alignment.