Point-set Data Fitting By Optimizing Global Relations

To solve the regularly encountered challenging problem of recovering real objects' exact geometry from noisy and incomplete data-set, the paper introduced an algorithm to simultaneously extract local fitting primitives and their mutual global relations. Under the basic assumption of man-made objects normally composed of primitives grouped together to form regular repeating structures as basic building units, which satisfy various mutual global relations, the algorithm directly couple primitives'data fitting error function and global constraints to formulate a constraint non-linear optimization problem, which leads to data-set's best reconstruction result while getting the optimum solution.The algorithm first applied state-of-the-art RANSAC technique to extract initial local fitting primitive from date-set, then used two global relation extraction and optimization stages to process these primitives, and finally output optimal primitives which strictly con-forming to initial data-set's inherent structural characteristics. In the first pre-processing stage, the pipeline applied orientation and placement optimization algorithm in this paper's preliminary work to normalize each input primitives' parameters, which provides stable in-puts to the next stage. In the following processing stage, the pipeline computed possible rotational symmetry transformations among primitives and used respective results to vote for corresponding transformation's confidence, which guided the extraction of spatial orbit information implied in the underlying initial data-set for positional optimization.The paper tested the algorithm's robustness on a series of synthesized and scanned date, which obviously shows the algorithm is both highly stable and broadly applicable, and the efficiency evaluation can also show the algorithm operates effectively. The paper also discussed possible future directions, and listed several typical applications in the hope of inspiring other related in-depth researches and developments.