access icon free Soft shape registration under Lie group frame

In this study, the authors address a two-dimensional (2D) shape registration problem on data with anisotropic-scale deformation and noise. First, the model is formulated under the iterative closest point (ICP) framework, which is one of the most popular methods for shape registration. To overcome the effect of noise, the expectation maximisation algorithm is used to improve the model. Then, the structure of Lie groups is adopted to parameterise the proposed model, which provides a unified framework to deal with the shape registration problems. Such representation makes it possible to introduce some suitable constraints to the model, which improves the robustness of the algorithm. Thereby, the 2D shape registration problem is turned to an optimisation problem on the matrix Lie group. Furthermore, a sequence of quadratic programming is designed to approximate the solution for the model. Finally, several comparative experiments are carried out to validate that the authors’ algorithm performs well in terms of robustness, especially in the presence of outliers.

Inspec keywords: quadratic programming; expectation-maximisation algorithm; Lie groups; image registration

Other keywords: matrix Lie group; Lie group frame; optimisation problem; anisotropic-scale deformation; ICP framework; soft shape registration; noise; 2D shape registration problem; iterative closest point; expectation maximisation algorithm; quadratic programming

Subjects: Optimisation techniques; Other topics in statistics; Other topics in statistics; Optimisation techniques; Optical, image and video signal processing; Computer vision and image processing techniques

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