The main task of this activity was to perform the feasibility study  of the contactless measurement of  eccentricity  of pipes. This activity has been carried out following two different approaches. 

 The former is aimed at developing a 2D vision method, and at assessing the measurement performance of suitably developed 2D imaging procedures. The latter is aimed at implementing a 3D technique, using four optical 3D heads, based on the projection of laser stripes.

The 2D vision approach is sketched in Fig. 1.

Fig. 1: set-up for 2D measurement of the eccentricity.

In this set-up, a videocamera captures the transversal section of the pipe. Then, the  inner and the outer profiles of the pipe are segmented and, by suitable fitting, the radius and the centre coordinates of the outer and of the inner circles are estimated. The distance between the two points is a measure of the pipe eccentricity (see Fig. 2). This apprach has been implemented in the demonstrators shown in  Fig. 3.

Fig. 2: Principle of measurement. Points Co and Ci are the centres of the outer profile and of the inner profile respectively. Eccentricity is measured as the distance between them.	Fig. 3: Photograph of the 2D demonstrators. Two stations have been implemented to comply with the large range of the diameters of the pipes under test. The demonstrator on the left is used to acquire pipes with diameters larger than 75mm.

Suitable procedures have been developed to perform the acquisition and the measurement tasks. Fig. 4 shows an example of the software front panel (LabView 7).

Fig.4: Front panel of the measurement software

The measurement performances have been evaluated with respect to the eccentricity values measured by using a caliper as the reference. The results show that the measurement uncertaintiy in correspondence with drawed pipes is below 0,02mm. In this case, the profiles are very regular, and the quality of the images is good (see. Fig. 5 as an example). In contrast, when the elaboration is applied to pipes before the bar-drawing, image quality decreases, due to the presence of irregularities in the borders, and to  unequal reflectivity of the surface in correspondece with the acquired section (see. Fig. 6). In this case, the uncertainties are between 0.05mm and 0.64mm, depending on the quality of the surface.

Fig.5: Image of the transversal section of a pipe after bar-drawing	Fig. 6: Image of the same pipe before bar-drawwing

The 3D vision approach is sketched in Fig. 7.

Fig. 7: principle of measurement

Four optical heads, each using a laser stripe and a video-camera, have been positioned as shown in the figure. Their orientation allowes the acquisition of object points which do not belong to the pipe border, and, hence, are not affected by distrurbances. Each head projects on the corresponding portion of the pipe a laser stripe which is acquired at an angle by the camera. The object shape deforms the pattern, as shown in Fig. 7. The deformed pattern is acquired by the camera, and elaborated to calculate the coordinates of the stripe. These are then mapped from the pixel plane to the real world coordinates, by using suitable calibration of the camera-projector pair. Fig. 8 shows an example of the profiles obtained by using this procedure.

Fig. 8: Example of the profiles acquired by the optical heads.

These profiles are corrected for the distortion induced by the oblique projection direction of each laser stripe. Then the four profiles are registered into a single reference, as shown in Fig. 9. The profiles are used to feed the fitting algorithm that estimates the centre coordinates of the two circles. From these coordinates we can get the eccentricity measurement.

Fig. 9: registration of the profiles and estimate of the eccentricity.

The demonstrator implemented to perform this procedure is shown in Fig. 10.

Fig. 10: 3D demonstrator

The experiments performed at the laboratory showed that the achievable uncertainties were in the rage between 0.1mm and 0.3mm, which was unacceptable. However, the study of the error sources, showed that the main problem was in the control of the geometrical parameters related to the position of each optical head with respect to the others.  Hence,  we developed a dedicated platform to simulate these error sources, and understood that the method could lead to the required specifications, provided that proper mechanical mounting was used to finely control these parameters. This solution is obviously very expensive. For this reason we continued the research, independently on the Commissioner, and focused our study on alternative ways to calibrate and register the profiles.