Adaptive reconstruction of freeform objects with 3D SOM neural network grids

Abstract

Reverse engineering is an important process in CAD systems today. Yet several open problems lead to a bottleneck in the reverse engineering process. First, because the topology of the object to be reconstructed is unknown, point connectivity relations are undefined. Second, the fitted surface must satisfy global and local shape preservation criteria that are undefined explicitly. In reverse engineering, object reconstruction is based both on parameterization and on fitting. Nevertheless, the above problems are influenced mainly by parameterization. In order to overcome the above problems, the paper proposes a neural network, Self Organizing Map (SOM) method, for creating a 3D parametric grid. The main advantage of the proposed SOM method is that it detects both the orientation of the grid and the position of the sub-boundaries. The neural network grid converges to the sampled shape through an adaptive learning process. The SOM method is applied directly on 3D sampled data and avoids the projection anomalies common to other methods. The paper also presents boundary correction and growing grid extensions to the SOM method. In the surface fitting stage, an RSEC (Random Surface Error Correction) fitting method based on the SOM method was developed and implemented.