Материал: [2.1] 3D Imaging, Analysis and Applications-Springer-Verlag London (2012)

3.11 Further Reading

One of the earliest papers on triangulation-based spot scanning for the capture and recording of 3D data was published by Forsen in 1968 [36]. Kanade presents a collection of chapters from different authors that describe a number of close-range active 3D imaging systems [44]. Many survey papers that review range sensors have been published [7, 16]. The geometric description of the point and profile based system presented a simple scanner. Mirrors can be used to fold the baseline such that the baseline of a system is larger than the physical scanner and where the mirrors dynamically modify the field of view of the camera such that the sensor only sees a small area around the laser spot [54]. The calibration of point-based triangulation scanner is discussed in [12, 13, 25].

An article published by Salvi et al. [57] presents an in-depth classification of different types of structured light patterns. Davis et al. [29] present a unifying framework within which one can categorize 3D triangulation sensors, for example on the basis of their coding within the spatial and temporal domains. Moreover, an analysis of the uncertainty of a white light fringe projection based on Gray codes is presented in [63]. Many analyses of the impact of random noise on phase shift methods have been conducted [31, 40, 53, 62].

The two authoritative texts on the matter of uncertainty and vocabulary related to metrology are the Guide to the Expression of Uncertainty in Measurement (GUM) and the International Vocabulary of Metrology (VIM) [1, 5]. The document designated E 2544 from the American Society for Testing and Materials (ASTM) provides the definition and description of terms for 3D imaging systems [6]. Moreover, the VDI 2634 is a document from a standardization body that addresses the characterization of optical distance sensors [2]. Error propagation in the context of multiple-view geometry is discussed in [28]. The characterization of active 3D imaging systems is discussed in [19, 24, 26, 27, 35, 38, 45–47].

3.12 Questions

1.Name and explain three categories of triangulation scanner, based on different methods of scene illumination.

2.In recent years, the resolution of cameras has significantly increased. What are the impacts of this on each type of triangulation scanner?

3.What are the impacts on the 3D data of varying the baseline of a laser stripe scanner without recalibrating the system?

4.What are the impacts on the 3D data of varying the distance, d (the distance between the camera center and image plane) of a laser stripe scanner without recalibrating the system?

5.What are the values of Rp , Tp , x1, y1 and x2 for which the three constraints in Eq. (3.30) are not linearly independent?

6.What are the elements that can limit the lateral resolution of a stripe scanner? Classify those elements as belonging to the spatial or structural resolution.

3.13 Exercises

1.Using a programming environment of your choice, develop a 2D simulator of a phase shift fringe projection scanner that can reproduce the intensity artifact shown in Fig. 3.15. Assume that optical-induced blurring is only present in the camera images and that the camera has an infinite spatial resolution. Repeat the experiment for a fringe projection system that uses a Gray code.

2.Modify the previously developed prototype in order to apply it to a stripe scanner. Plot a graph that shows the variation of error due to the width of the stripe.

3.For a stripe-based scanner, an occlusion occurs when the linear detector does not see the laser spot. However, since the spot size is not infinitesimal, there are intermediate situations where only a fraction of the spot is seen by the detector. Using a prototyping environment, develop a model to evaluate the impact of this on the recovered geometry.

4.Perform the error propagation computation for a stripe scanner that includes uncertainty on the angles α.

5.Using Fig. 3.17, trigonometry and the thin lens equation, give the derivation of Eq. (3.46).

6.Modify the camera model presented in Sect. 3.3.1 to incorporate a Scheimpflug condition.

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