Sparse-plus-dense-RANSAC for estimation of multiple complex curvilinear models in 2D and 3D

The detection of multiple complex structures in noisy, outlier-rich two- and three-dimensional data is a challenging model estimation problem. In this paper, we build on the RANSAC method to select multiple model instances, focusing especially on curve estimation. Estimation of complex curves such as splines has so far received little attention in the context of model estimation, but has primarily been considered as a segmentation problem. Our proposed curve estimation is based on Sparse-Plus-Dense RANSAC, a framework in which estimation is performed on sparse points, guided by dense image data. This approach is extended to complex curvilinear models, in two- and three-dimensional data. The estimation is hierarchical, based on a merging step that uses an intuitive cost function. Results are presented on synthetic and real X-ray data, showing that the proposed approach performs comparably to state-of-the-art multiple model estimation in the synthetic data, while it significantly outperforms state-of-the-art in the real X-ray sequences. It also achieves correct localization of the model endpoints, which is a crucial aspect in the context of the clinical application.