Error analysis in reconstruction of a line in 3-D from two arbitrary perspective views. (English) Zbl 1009.65013
Summary: The process of reconstruction of a line in 3-D space from a pair of arbitrary perspective views obtains the set of parameters representing the line. This method is widely used in many applications of 3-D object recognition and machine inspection. 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 we derive a set of inverse perspective equations for reconstruction of a line in 3-D space based on coplanarity equations. We assume the correspondence between the pair of projections of the line on the image planes. Simulation studies were conducted to observe the effect of noise on errors in the process of reconstruction. We present this performance analysis illustrating the effect of noise and parameters of imaging setup, on errors in reconstruction. Smaller resolution of the image, certain geometric conditions of the line 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.
In this paper we derive a set of inverse perspective equations for reconstruction of a line in 3-D space based on coplanarity equations. We assume the correspondence between the pair of projections of the line on the image planes. Simulation studies were conducted to observe the effect of noise on errors in the process of reconstruction. We present this performance analysis illustrating the effect of noise and parameters of imaging setup, on errors in reconstruction. Smaller resolution of the image, certain geometric conditions of the line 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.
MSC:
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
| 51N05 | Descriptive geometry |
Keywords:
perspective views; reconstruction; stereo vision; least squares regression; error analysis; inverse perspective equations; object recognition; machine inspection; performance analysisReferences:
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