A Hybrid Framework for Shape Registration with Affine and Block-Wise Quadratic Deformations

Most existing Euclidean and affine-based registration methods remain insuffi- cient for modeling complex nonlinear deformations. Building on existing affine registration methods, this paper proposes a hybrid affine-quadratic registration framework that combines affine-invariant global alignment with block-wise quadratic refinements to capture second- order geometric distortions. The approach ensures numerical stability through condition- number minimization of the equi-affine correspondence matrix and employs a closed-form least squares solution for global affine estimation, followed by Tikhonov-regularized least squares for stable quadratic refinements. The number of local deformation blocks is auto- matically selected using BIC. Experiments conducted on MPEG-7, Kimia-99, Kimia-216 and ETH-80 datasets demonstrate the effectiveness of the proposed method in improving registration accuracy under complex shape variations.