Employing Nelder-Mead Method in Point Clouds Registration Process and Comparison of the Results with Singular Value Decomposition and Genetic Algorithm

In reverse engineering it may be required to perform multiple measurements due to the size and part complexity limitations of the physical equipment CMM / Optical Scanner and / or settings. To model the whole part it is required to bring different point sets obtained during different scans to a common coordinate system. Registration process for point clouds is to find the geometric transform between them in which all point clouds are transformed into a single absolute coordinate system. Theoretically، it is very straight forward to perform registration by finding the six components of transformation matrix (3 angles plus 3 displacements) and this can be mathematically determined if three non-linear points are known in both global and local coordinate systems. The process of registration is strongly affected by inaccurate data and may fail in the case of noisy data، hence other methods are usually sought to find the transformation matrix. This paper tries to solve the problem in practical applications. The Nelder-Mead method was employ for point clouds registration for the first time. The registration was also performed using Singular value decomposition and Genetic Algorithm methods. The three methods were compared in terms of convergence، accuracy and computation time.