Robust point matching by l1 regularization

We propose a new method to solve the point matching problem by l₁ regularization. The non-rigid transformation function based on compact support radial basis functions (CSRBF) is represented by the linear system with respect to its coefficients. The transformation function is estimated by the proposed sparse optimization model with regularizing the CSRBF coefficients by l₁ norm and the affine coefficients by the square of l₂ norm. The optimization model for linear problem of transformation function can be efficiently solved by a fast iterative shrinkage-thresholding algorithm (FISTA) to accelerate the convergence speed of iterative procedure. Experiments on simulated point sets and lung datasets show that our method by l₁ regularization obtains accurate registration results and is robust to estimate the correspondence and the transformation between two point sets in the presence of noise and outlier.