Error analysis in the reconstruction of a parabola in 3D from two arbitrary perspective views

摘要

The process of reconstruction of a parabola in 3-D space from a pair of arbitrary perspective views obtains the set of parameters which represent the parabola. This method is widely used in many applications of 3-D object recognition, machine inspection and trajectory tracing. However in certain applications which require a large degree of accuracy, a study of errors in the process of reconstruction, with the help of a rigorous performance analysis is necessary. In this paper, the reconstruction of a 3D parabola from two perspective projections is described. In this process, the two end points and the vertex of the two pair of projections of the parabola are considered as feature points to reconstruct the parabola in 3-D. Simulation studies have been conducted to observe the effect of noise on errors in the process of reconstruction. The performance analysis illustrating the effect of noise, loss of accuracy due to mathematical calculations and parameters of imaging setup, on errors in reconstruction are presented. The angle between the reconstructed and original parabola in 3-D space has been used as a one of the criterion for the measurement of error. Smaller resolution of the image, certain geometric conditions and imaging setup produce poor performance in reconstruction. Results of this study are useful for the design of an optimal stereo-based imaging system, for best reconstruction with minimum error.