Application and validation of profile-image method for measuring deformation of tunnel wall

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Application and validation of proﬁle–image method for measuring deformation

of tunnel wall

Tai-Tien Wang

a,*

, Jen-Jer Jaw

b

, Yo-Ho Chang

c

, Fu-Shu Jeng

b a

Department of Materials and Mineral Resources Engineering, National Taipei University of Technology, Taipei, Taiwan

b_{Department of Civil Engineering, National Taiwan University, Taipei, Taiwan} c_{Institute of Earth Sciences, National Hualien University of Education, Hualien, Taiwan}

a r t i c l e

i n f o

Article history:

Received 10 August 2007

Received in revised form 30 April 2008 Accepted 27 May 2008 Available online xxxx Keywords: Safety inspection Tunnel wall Deformation Proﬁle–image method Laser

a b s t r a c t

The deformation of a tunnel is one of the major phenomena that indicate the safety of a tunnel under operation. Yet, the deformation of tunnel profiles so far cannot be effectively obtained, as confined by the long time required when using conventional geodetic surveying and the insufficient precision pro-vided by other devices. The profile–image method, by which the profile of a tunnel can be determined by laser-lit profile in an image is tested in this study to validate its applicability. The methodology, including superimposing of images, and the results of validations are presented. The results indicate that the profile–image method has a precision of 4 mm for medium size tunnel. Meanwhile, the factors affect-ing the precision of measurements are highlighted, includaffect-ing distortion of lens, number of calibration points, types of lasers, and contrast of profile to the background. The influences of these factors are also presented.

1. Introduction 1.1. Background

Since the deformation of an operating tunnel may serve as a di-rect indicator regarding the variation of safety, the deformation is of major concern especially when conducting maintenance inspec-tion for such a tunnel. The subsequent deformainspec-tion of a tunnel after construction inherently is a result of ambient stress changes, which will also affect the state of safety of the tunnel. This defor-mation can also be used for back analysis to reveal what condi-tions, e.g. ambient stress changes and existence of cavity, have occurred. Therefore, it is possible that the deformation of tunnel (or its inner lining) can be adopted as a criterion for evaluating the current state of safety, and for providing precaution for upcom-ing disasters (Japanese Society of Civil Engineers, 2002, 2003; Wang et al., 2005, 2007a). From the viewpoint of maintenance, it is preferable to well quantify the quantities and the pattern of deformation of tunnel lining, and to observe deformation on a reg-ular basis.

However, to measure the deformation of a tunnel currently is not a common practice owing to the time and cost required by this operation. Especially, for an operating tunnel, e.g. a highway

tun-nel, the trafﬁc must be stopped when conducting surveying pro-ﬁles so that the time allowed for survey is really limited.

Many methods have been developed to measure the profiles of a tunnel, and the deformation of a profile can be accordingly ob-tained by comparing the previous profile and the current profile. Conventionally, a profile can be precisely yet rather slowly point-by-point measured by geodetic devices. Laser devices capable of automatically scanning an entire section of a tunnel, resulting in tens of thousands of points with their spatial coordinates, the so-called ‘‘cloud of points”, are also available (Langer et al., 2000; Wang et al., 2007b). The third method, direct laser beam measur-ing the relative position of a point at tunnel wall to the laser device has been also utilized. If the trace of such a laser device is recorded, the spatial coordinate of each measured point can then be deter-mined. By doing this, the profile can be accordingly obtained.

However, conventional geodetic survey is rather time consum-ing and thus is difﬁcult to meet the requirement of limited time al-lowed. On the other hand, both the automatic laser scanning and the direct measurement using laser beam can be conducted rather fast but require further validation on the precision of the measurements.

Further strategies have been adopted by researchers to cope with these difﬁculties (Lichti et al., 2000; Boehler et al., 2001; Boehler and Marbs, 2002). One popular approach is the laser range technology on the basis of traveling time of laser beam, which usu-ally integrates a rotating mirror with a laser ranger to get all-round angle of data. The accuracy of this approach depends on the errors

* Corresponding author. Tel.: +886 2 2771 2171x2773; fax: +886 2 2731 7185. E-mail address:ttwang@ntut.edu.tw(T.-T. Wang).

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of measured distance and gauged angle, and is usually limited to 10 mm or worse (Chao, 2006; Chiu, 2007). Another possibility is to use the stereo images technology based on the triangulation, which analyzes stereo pairs taken from various positions to obtain the 3D coordinates of lining surface. Its precision is restricted by the resolution of the images, the geometry of intersected rays of conjugated points, and the orientation parameters of the images. In general, the conﬁguration of stereo images is rather troublesome due to the space limitation in a tunnel.

Finally, a third strategy is also founded on the triangulation, but only a single image is used. The line connecting the illuminating la-ser and the camera is adopted as a base, which correlates the line connecting the object and the camera with the angle in-betweens to form a triangulation. An intelligent alternative of the third strat-egy is to specify some points with known coordinates, which are referred as ‘‘calibration points” or ‘‘control points”, within an image so that these points can be used to determine the coordinates of any particular points within the image. The coordinate of these cal-ibration points is precisely determined using geodetic device be-fore an image is taken. This method is referred as ‘‘proﬁle–image method” herein. This method has been successfully used in small scale laboratory tests for ﬂow surface measurement (Capart et al., 2002; Douxchamps et al., 2005).

As such, it is of interest to extend this method to measure the profile of any section of a tunnel. Many questions may follow this extension: How can this method be extended to measure the pro-file of a tunnel? What is the precision? How fast is the measuring operation? etc. The study also aims at finding the answers for these questions.

1.2. Basics of proﬁle–image method

As depicted inFig. 1, the fundamental concept of imaging meth-od is to find coordinates of any specified points from 6 points with known coordinates. All the specified points and the 6 points with

known coordinates, referred as ‘‘calibration points” herein (Ni, 2005), should be first taken into one image by camera. If the profile of an object is desired, a line laser can be used to beam the surface of the object so that the connection of all the illuminated points on the surface in fact constitutes a profile. As shown inFig. 1, the cam-era is located at point P, the coordinates of points alone line (or profile) S are to be determined, and these specified points are in-cluded in the image.

After the speciﬁed points are included in one image, they can be readily related to the local coordinate of the image, as shown by the image inFig. 1. The next task is to ﬁnd the transformation rela-tionship of the global 3D coordinates and the local 2D coordinates. This transformation of coordinates can be found using perspective projection method (Faugeras and Luong, 2001). The following notations are adopted throughout this paper: lower-case letters denote 2D coordinates measured in the image taken; upper-case letters denote the global 3D coordinates in real space. For both cases, vectors are indicated in bold face.

Fig. 1illustrates that the position vector S of an arbitrary point S in global coordinate system can be described by the position vector P of projection centre and the ray direction q, respectively. The 3D coordinates S are related to the 2D coordinates q as

S ¼ P þ kq ð1Þ

where k is a scalar parameter. The vector q can be directly measured from the image, at any speciﬁed point on s, and indicated as (xs_{, y}s_).

Given a line parallel to X–Z plane, the global coordinates of S = (XS_{, Y}S_{, Z}S_{) can be determined by projection centre P = (X}P_{, Y}P_{, Z}P₎

and the image position (xs_{, y}s_{). Accordingly, the following relation}

can be established:

ðXS; YS_; _ZS

ÞT¼ ðXP; YP_; _ZP

ÞTþ kMðxs; ys_; _1ÞT

ð2Þ

where the superscript T represents transpose of raw vectors and M is a 3 3 transformation matrix corresponding to the orientation and position of the image.

Fig. 1. Illustration of imaging geometry of proﬁle–image method used in laboratory for ﬂow surface measurement. The global 3D coordinates S are related to the local 2D coordinates q. Their transformation relationship can be determined by means of at least six calibration points with known coordinates in the image taken (afterNi, 2005).

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By rearranging Eq.(2), we have

ðkxs_; _kys_; _kÞT

¼ AðXS;YS; ZSÞTþ B ð3Þ

where A is the inverse matrices of M, and B = M1_(XP_{, Y}P_{, Z}P₎T_{. As a}

result, there are 11 unknown coefﬁcients in matrix A and B, and thus 11 equations are required to determine them. On the other hand, each calibration point provides two equations, in x-direction and in y-direction, for solving those unknowns (Capart et al., 2002). Accordingly, the transformation would be accomplished if no less than six calibration points are provided and included in the image. If more than six calibration points are provided within an image, then the precision can be further improved, taking advantages of the special information provided by these surplus calibration points.

With reference to Fig. 1, the points, forming a proﬁle S, to be surveyed are highlighted by a line laser and acquired by a digital camera. A laser light-pot, although it may look fairly small in the taken image, in fact is constituted by more than one pixel. The next task, referred as ‘‘particle identiﬁcation”, is to identify a represen-tative pixel, which best represents the position of the laser spot. Therefore, image processing method should be undertaken to pin-point position of a laser spot from the image in order to precisely retrieve its 2D location, which ensures a better 3D coordinates to be converted.

The techniques regarding image processing and the particle identiﬁcation have been discussed in detail byJähne (1995), Capart et al. (2002)and Spinewine et al. (2003). In general, three main steps are involved: (1) to increase the contrast of the laser light-spots by assigning different degrees of grey-scale colors to the spots and to the background; (2) to eliminate noises by applying low-pass and high-pass ﬁlters; and (3) to identify the representa-tive pixel, which is brightest in the spot, for each individual laser point. As a result, the 2D coordinates of laser points, measured in laboratory, can be determined with fairly well precision (Veber et al., 1997; Capart et al., 2002; Ni, 2005).

1.3. Scope of this study

This work aims to extend the application of the profile–image method, from laboratory scale to field scale, to measure the profile of tunnel wall. By doing this, the profiles of a same section mea-sured at different investigations can be compared and the defor-mation, if it does occur, can be identified. A few questions follow this extension of application: (1) How is the precision? (2) What are the factors affecting the results of measurement and the degree of influences? and (3) Will the field conditions, e.g. background illumination of a tunnel, affect the precision? On the basis of labo-ratory-scale image method, some technological transformations have been implemented in order to match the requirement for sur-vey task in real tunnel-scale. Therefore, a series of tests are desig-nated to validate these technological transformations. The precision and the efficiency of field work are the main items to be observed during the validation process. Finally, the factors affecting the results of the profile–image method are discussed. 2. Framework of research

The original profile–image method was applied to measure the profile of a movable object so that the line laser was fixed in space and the object moved through the line laser to obtain profiles for different sections, as shown inFig. 1. As such, the six calibration points and camera are also fixed in space. When extending pro-file–image method to tunnels, the tunnel cannot move through the line laser and, instead, the entire measuring system must move along the course of tunnel, as shown inFig. 2. Since at least six

cal-ibration points should be included in an image, many calcal-ibration points, with their 3D coordinates measured by geodetic device, should be set up within the tunnel. Therefore, the procedures for applying proﬁle–image method to tunnels should be slightly mod-iﬁed from the original method, and are summarized inFig. 3.

Owing to the nature of profile–image method, the coordinates of the points along a profile are determined by the six calibration points, and the location (or coordinates) of camera is not needed. Therefore, the positions of the camera inside the tunnel are not measured. Remarkably, the planes of the image (the CCD of cam-era) and the profile should be parallel, as shown inFig. 2.

The 3D coordinates of the calibration points can be selected to be relative to a ﬁxed point, which is often located at tunnel portal. If the global coordinates of this ﬁxed point, referred as ‘‘reference point” herein, are measured, then the global coordinates of all cal-ibration points can also be determined.

The conditions of a tunnel can be different from the ones in the laboratory, for instance, the size for a tunnel survey is much larger than the object measured in laboratory scale. Since the tunnel is much larger, the power of line laser adopted for laboratory mea-surements is no longer sufﬁcient and a laser device with much stronger power should be employed. On the other hand, the in situ conditions of a tunnel can also be different, e.g. the background illumination. Too strong illumination lowers the contrast of laser line; yet too dim background may prevent correct focusing of the camera.

In the situations that the tunnel is quite large so that the laser power is not sufﬁcient to yield a bright enough proﬁle shown in

Fig. 2. Illustration of imaging geometry of proﬁle–image method for the survey of tunnel wall. Laser device is used to beam the proﬁle to be measured. The calibration points have to be set up within the tunnel and taken into the image.

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the taken image, a special technique is thus used, as in this study. Multi-images using the same calibration points, sometimes up to 200 images or more, were taken for the same profile and are then superimposed so that the contrast of the profile can be significantly improved, and points along the profile can be reliably extracted by the later image processing procedures as a result.

Keeping the above-mentioned concerns in mind, the validations are set to have two stages, as shown inFig. 4: (1) Stage I – small-scale tunnel (Fig. 5); and (2) Stage II – medium size tunnel (Fig. 6). The small and the medium model tunnels are 1.0 0.7 1.0 m (length width height) and 5.0 1.9 3.3 m, and are made of stainless thin-sheet and wood, respectively. The small tunnel, de-noted as Model Tunnel I herein, is chosen for two reasons: (1) all the coordinates within it can be more precisely measured; and (2) the tunnel wall is flexible so that deformation with pre-speci-fied magnitude can be applied. Therefore, the profile–image meth-od can be further tested by checking the profiles before and after deformation. The medium size tunnel, denoted as Model Tunnel II, is chosen since its size, although being quite small indeed, is closer to that of the actual tunnel. Accordingly, for medium model tunnel, stronger laser should be employed and only geodetic device can be used for determining the coordinate of calibration points and pro-files. The effect of image superimposed method is to be validated as well.

Concerning the later application for tunnel inspection, the equipments adopted should be simple and commonly available. Therefore, an ordinary digital camera, Canon EOS 350D with EF ser-ies 18–55 mm lens, is adopted for taking the photos. Both point la-ser and line lala-ser were used to beam proﬁles inside a tunnel. These laser devices have a wavelength of 650

l

m, respectively, with 12 and 5 mW powers for line laser and point laser. To determine the global 3D coordinates of the calibration points, a geodetic device of total station type is utilized. The adopted total station, Leica TCR 705, has a nominal angle precision of 5”, 1.5 mgon and dis-tance precision of 3 mm + 2 ppm in 170 m without target reflector. And for comparison purposes, a 3D terrestrial laser scanner RIEGL LMS-Z360i is also paralleley used to obtain tunnel profiles. Later on, the profiles obtained by the proposed profile–image method and terrestrial laser scanner will be compared to highlight the characteristics of these two methods.

The actual profiles of Model Tunnels I and II are, respectively, measured by a ruler and a total station. Several repetitions of mea-surements have been carried out to ensure the accuracy of the ac-tual profiles of these two tunnels, which will serve as the basis for justifying the precision of other measuring methods. The coordi-nates of calibration points, highlighted by the brighter spots shown inFig. 5b and by the numbered crosses shown inFig. 6, are deter-mined by the same ways. There are 105 calibration points arranged for Model Tunnel I and the other 36 points for Model Tunnel II. To enhance the precision of profile–image method, more than six cal-ibration points, usually up to 10–15 points nearer to the profile are used for determining the profile to be measured.

3. Results of validation

There are 10 profiles scanned by line laser and each of them is pictured by one single image, which will be further processed to determine their coordinates of each profile. A typical result, com-paring to the actual profile, is depicted inFig. 7a. These two profiles are so close to one another and are difficult to distinguish the dis-crepancies between them. Accordingly, a measure of mean discrep-ancy based on root mean square errors (RMSE) method is adopted to represent these discrepancies:

R ¼1 n Xn i¼1 R2i ¼ 1 n Xn i¼1 ðRm RaÞ2 ð4Þ

where Rmand Raare the measured and the actual distance to a

pre-set reference point, as shown inFig. 7b; Riis then the error of an

individual point along the profile to be measured, and is denoted as a function of an angle h measured from left spring line clockwise; and R represents the overall, mean error for the entire profile con-stituted by the deduced n points.Fig. 7b illustrates the definition and configuration of Rm, Ra, Riand pre-set reference point

corre-sponding to an actual proﬁle. 3.1. Model Tunnel I

A typical variation of Rialong a measured proﬁle is shown inFig.

8. The Ri’s are less than 2 mm for the particular proﬁle shown in

Fig. 8. It has been observed that the error near the middle part of the crown (h = 50–130°) is less than the ones outside this range, as shown inFig. 8. The majority of the calibration points are ar-ranged in the middle part of the crown of the Model Tunnel I (h = 50–130°) accounting for the less error. The calibration points also have closer spacing near the middle crown, yet being far spaced around the side walls (h = 14–50°, and 130–166°), as shown inFigs. 5b and 7a. As shown inTable 1, a smaller proﬁle (h = 45– 135°), which is deduced based on closer spaced calibration points, tends to have a better precision than the one (h = 14–166°) with

Fig. 3. The procedures for applying proﬁle–image method to the survey of tunnel wall.

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far-spaced calibration points included in deduction process, as shown in the fourth and the third columns ofTable 1, respectively. As a result, the overall R for each proﬁle conspicuously decreases to below 1.25 mm in most cases, if close-spaced calibration points are utilized.

Based on the Riof each measured proﬁle, the mean error of this

profile, R, can then be calculated using Eq.(4), and the R’s for the 10 measured profiles are summarized in Table 1. The profiles are numbered to according their distance to the tunnel end nearer the camera; a close profile has a smaller number, that is, Profile #1 is closest to the camera. Being closest to the camera, the upper profile is thus located at the upper end of the image, where greater

lens distortion can be expected. This phenomenon may account for the greatest R (=1.69 mm) among the 10 proﬁles. Meanwhile, the calibration points are not located right on Proﬁle #1, which may further worsen the results of deduction.

For a same profile, more than one photo were taken and com-pared. Ideally, these images are supposed to be exactly the same and so is the deduced profile. These images are further superim-posed and the deduced profile is then compared to the actual pro-file, as shown inFig. 9. Accordingly, all the R’s for the measured profiles (based on superimposed images) are calculated and sum-marized in the fifth column ofTable 1. The R’s deduced from super-imposed line laser images, with an average of 1.20 mm and a

Fig. 4. The frame of this present work and main efforts. First, minor adjustments of the profile–image method are implemented to extend its use from laboratory scale to field scale. Two model tunnel tests are then carried out to validate their applicability. Finally, the factors affecting the measure precision are discussed and field tunnel measurements are addressed.

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standard deviation of 0.68 mm, are both similar to those deduced from single line laser image, which have an average of 1.15 mm and a standard deviation of 0.22 mm. As such, superimposing of images is acceptable and will be used for a larger tunnel to empha-size the contrast of the laser illumination.

For a larger tunnel, the illumination of line laser is not sufficient to illuminate a detectable profile; therefore, a point laser must be used. By rotating the point laser, taking photos for the points along a profile and superimposing the images, an image containing all the points can be obtained and the profile can then be deduced. The number of images to be superimposed can be up to 250 for each profile. The precision of point laser should be tested using Model Tunnel I before applying it to a larger tunnel. The typical var-iation of Rialong a profile is shown inFig. 10, which has a

maxi-mum Riof 2.72 mm. Furthermore, all the R’s for the six measured

proﬁles are calculated and summarized inTable 2. In general, by comparingTable 2withTable 1, the proﬁles deduced from point la-ser have somewhat greater, yet acceptable error.

The variation of R for distinct proﬁles obtained by previously mentioned three methods (single image and superimposed image using line laser and point laser) is compared and illustrated in

Fig. 11. For these proﬁles of Model Tunnel I, the measured results are rather stable and seem to be less than 2 mm in most cases, which is acceptable for safety inspection of tunnel, although better precision is still wished. Overall, the results deduced from single image are better than those from superimposed images, and the re-sults obtained by line laser are better than those obtained by point laser.

Fig. 5. The setup proﬁle–image method for survey of Model Tunnel I: (a) the Model Tunnel I as well as the layout of line laser device and the camera and (b) the proﬁles illuminated by laser and the arranged 105 calibration points.

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3.2. Model Tunnel II

Since Model Tunnel II is larger than Model Tunnel I, the illumina-tion of line laser is not sufficient to provide a clear image for deduc-ing the profile. A trial was made to rotate a point laser to yield an illuminated profile, and it was found that the illumination is still not sufficient. Finally, superimpose of images, whether obtained by line laser or point laser, must be used for the Model Tunnel II. Therefore, the coordinates of profiles deduced from superimposed images by line laser and by point laser are discussed as follows.

When utilizing the superimposed image technique, there are 12 profiles illuminated by line laser and another 10 profiles by point laser conducted. Among which two typical results, compared to their correspondingly actual profiles, are illustrated in Figs. 12a and 13a. While taking a photo, a minor vibration may be caused while shutting the picture. Unfortunately, line laser is very sensi-tive to such shutting vibration such that interlacing of illuminated

profiles can be found within a superimposed image. Therefore, some pixels, outside the range of profile, are removed to avoid mis-take when conducting point identification. As a result, the distribu-tion of points determined from line laser (Fig. 12a) is less uniform than the cases obtained by point laser (Fig. 13a).

The typical variations of Rialong a measured proﬁle, using line

laser and point laser, are, respectively, shown inFigs. 12b and 13b. All the R’s for these measured proﬁles are then calculated and sum-marized inTable 3. The proﬁles illuminated by point laser, with R’s ranging 2.50–4.16 mm and an average of 3.25 mm, are better than those obtained by line laser, having the R’s ranging 3.35–7.33 mm and an average of 4.86 mm. The relative strong illumination of point laser may account for the better precision.

The measured results for Model Tunnel II show that the R’s of proﬁle–image method are 3–5 mm in most cases, as shown in Ta-ble 3. It is seen that a larger tunnel tends to have larger R’s, com-paring Table 3(Model Tunnel II) toTables 1 and 2(Model Tunnel

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I). These results validate the proﬁle–image method for measuring tunnel wall. If the deformation of tunnel has the order of cm’s, then the precision of 3–5 mm seems to be acceptable.

For comparison purposes, the profile obtained by laser scanner is also conducted, as shown inFig. 14a. Since the points scanned by laser scanner are not necessarily located on one profile, the profile is obtained by treating the points, located within 10 mm distance to the measured profile, to be on the same profile.Fig. 14b displays the corresponding variation of Rialong the profile. The R’s of the

proﬁle determined from laser scanner, ranging 10.02–13.68 mm

and with an average of 11.79 mm, are greater than those obtained from the proposed proﬁle–image method, as summarized inTable 4. This 10–13 mm error is in fact the precision of the adopted laser

Fig. 10. A typical variation of Ri along a measured proﬁle, deduced from

superimposed point laser image, of Model Tunnel I. Fig. 7. A typical result of Model Tunnel I deduced from proﬁle–image method,

profile illuminated by line laser and pictured by one single image, is compared to the actual profile (Fig. 7a). These two profiles are too close to distinguish the discrepancies in between. Therefore, additional definition and configuration of Rm,

Ra, Riand pre-set reference point corresponding to an actual proﬁle are used for

comparison propose (Fig. 7b).

Fig. 8. A typical variation of Rialong a measured proﬁle, deduced from single line

laser image, of Model Tunnel I.

Table 1

Root mean square error for survey of Model Tunnel I, proﬁles illuminated by line laser

Proﬁle no. Ya

(mm) Rb

(mm)

h= 14–166° h= 45–135°

Single image Single image Superimposed image 1 5.9 1.94 1.69 2.76 2 30.4 1.82 1.01 1.42 3 50.9 1.52 1.24 1.66 4 70.5 1.79 1.04 0.63 5 90.2 1.39 1.08 1.01 6 110.2 1.54 0.98 1.02 7 130.5 1.56 1.20 0.86 8 148.9 1.63 1.25 0.83 9 171.1 1.25 1.08 0.64 10 204.3 1.67 0.90 – Average 1.61 1.15 1.20 Standard dev. 0.21 0.22 0.68 a

Y is the distance of the proﬁle to the portal. The camera is located outside the tunnel.

b_{R is the mean error, represented by the root mean square error (RMSE) as}

deﬁned by Eq.(4), of the measured distance from the actual distance for all points along a proﬁle.

Fig. 9. A typical variation of Rialong a measured proﬁle, deduced from

superim-posed line laser image, of Model Tunnel I.

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scanner. Therefore, a better precision can be made if a more precise laser scanner is used.

4. Discussion

As perceived from the previous tests, the factors influencing the precision of the proposed profile–image method may at least in-clude distortion of lens, point identification, numbers of calibration points, types of lasers as well as contrast of profile to the background.

Lens distortion, often possessed by ordinary digital camera, makes a point to be deviated from the correct point in an image and leads to incorrect deduced coordinates. In this study, the inﬂu-ence of lens distortion has been minimized by adjusting the taken image to a less distorted image. The adjustment was based on the distortion nature of the lens used, and was conducted using the software provided by Caltech (Savarese et al., 2005). Without using this adjustment process, the error can increase from 12 to 26 mm for the proﬁles of Model Tunnel I.

Given a laser-illuminated point in an image, there can be a group of pixels in the image, and the selection of right pixel inher-ently affects the precision of the coordinates deduced.

To properly determine the location of a ‘‘point” within a group of pixels, the technique proposed byVeber et al. (1997)is adopted: The obscured laser spots on the image can be reﬁned to sub-pixel by ﬁtting a second-degree interpolation surface around the spot. As a result, the expected RMSE on the (xs_{, y}s_{) image coordinates}

ob-tained by this technique has the order of 0.25 pixel. The laser spots in an image usually have the size of 4–7 pixels. Each pixel repre-sents a distance of 0.5–0.75 mm in tunnel according to the resolu-tion of image taken. Based on the adopted image processing

technology, the accuracy for pinpointing is about of the order of 0.25 pixel. Therefore, the theoretical accuracy in determining the coordinates, induced by locating the pixel alone, is about the order of 0.25–0.56 mm. The measured R’s for Model Tunnel I (1.53 mm), with other sources of error involved, are about 2–6 times of the theoretical accuracy.

The rest of the three issues affecting the precision of imaging method are discussed as follows.

4.1. Number of calibration points

As previously mentioned, at least six calibration points are re-quired to determine the proﬁle. It is of interest to know (1) Will the precision be improved by increasing the number of calibration points? (2) How many calibration points are needed to yield a reli-able proﬁle?

To evaluate the inﬂuence of the number of calibration points on the precision, three points within a proﬁle are selected for further comparison. These three points are located at the positions of h= 45°, 60° and 90°, respectively. They are chosen because rela-tively greater Ri’s are observed, as shown in Fig. 13. In addition

to the proﬁle obtained using six calibration points, 7, 10, 14, 21, 28 and 36 calibration points around the measured points are used to determine their coordinates. As a result, the variations of Riof

the three points with the number of calibration points are ob-tained, as illustrated inFig. 15. If the error on the plane of proﬁle is concerned, namely 2D situation, the Rireduces to a constant

le-vel when more than 7 points are used (Fig. 15a). When the error in 3D space is of concern, it takes 10–14 points to reduce the error to a low, constant level, as shown inFig. 15b. This test also highlights

Fig. 11. The variation of R for distinct proﬁles, deduced from single images and superimposed images using line laser and point laser, of Model Tunnel I. The results obtained by proﬁle–image method are rather stable and seem to be less than 2 mm

in most cases Fig. 12. A typical result of Model Tunnel II deduced from superimposed line laser image: (a) the measured profile and the correspondingly actual profile and (b) the variation of Rialong the profile.

Table 2

Root mean square error for survey on middle crown (h = 45–135°) of Model Tunnel I, proﬁles illuminated by rotating point laser and composed of superimposed images

Proﬁle no. Y (mm) R (mm) 1 15.6 2.22 2 28.6 1.63 3 44.4 1.64 4 79.3 1.57 5 98.2 1.31 6 116.8 0.79 Average 1.53 Standard dev. 0.47

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that (1) 3D situation requires more calibration points than 2D sit-uation; (2) Too many calibration points do not help increasing the precision.

4.2. Types of lasers

Although line laser and point laser have about the same preci-sion for Model tunnel I, point laser seems to have much better pre-cision for a greater tunnel (Model Tunnel II), as shown inFig. 16.

The interlaced phenomenon existing in superimposed line laser images obstructs proper image processing and evidently reduces

its precision. Consequently, conjunction use of point laser and superimpose of images are found to be more feasible in practice. 4.3. Contrast of proﬁle to the background

Laser-lit spots with relatively high contrast to the background, which can be acquired by prolonging the exposure time while tak-ing images, are ideal for proﬁle–image method to pinpoint their positions. Nevertheless, prolonging the exposure time may have some disadvantages, including (1) the dim corona around a spot can be made brighter so that the size of spot can be increased,

Table 3

Root mean square error for survey of Model Tunnel II, proﬁles composed of superimposed images

Profile illuminated by line laser Profile illuminated by point laser Profile no. Y (mm) R (mm) Profile no. Y (mm) R (mm) 1 51.7 4.22 1 45.3 3.29 2 103.4 3.92 2 75.7 2.98 3 148.5 3.98 3 103.3 2.83 4 195.0 3.35 4 159.9 2.50 5 251.6 3.40 5 232.2 2.73 6 302.7 5.19 6 282.0 3.44 7 352.1 5.72 7 333.5 3.97 8 393.7 4.67 8 394.0 2.74 9 448.9 5.27 9 465.8 3.88 10 498.5 5.48 10 495.6 4.16 11 553.4 5.80 12 607.6 7.33 Average 4.86 3.25 Standard dev. 1.16 0.59

Fig. 14. A typical result of Model Tunnel II obtained from laser scanner: (a) the measured proﬁle and the correspondingly actual proﬁle and (b) the variation of Ri

along the proﬁle.

Table 4

Root mean square error for survey of Model Tunnel II, deduced from results obtained by RIEGL LMS-Z360i Proﬁle no. Y (mm) R (mm) 1 45.3 10.10 2 75.7 10.02 3 103.3 10.14 4 159.9 10.30 5 232.2 10.80 6 282.0 12.81 7 333.5 13.68 8 394.0 12.81 9 465.8 12.72 10 495.6 12.66 11 553.4 12.67 12 607.6 12.77 Average 11.79 Standard dev. 1.38

Fig. 13. A typical result of Model Tunnel II deduced from superimposed point laser image: (a) the measured profile and the correspondingly actual profile and (b) the variation of Rialong the profile.

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and (2) the undesirable spots, caused by scattering reflection of laser or background light sources, are also enhanced simulta-neously. These unfavorable effects may lead to a lower precision, or, even worse, mistaking of points. Therefore, the factors affecting the contrast to the background, such as the exposure time and background illumination, are further studied to reveal their influ-ence on the precision of profile.

The influence of exposure time is illustrated inFig. 17. Since smaller laser spots with sufficient contrasts are provided, the R’s for various profiles of Model Tunnel II (superimposed images using point laser) obtained from the exposure time of 1/200 s are consis-tently less than those of 1/4. The most appropriate exposure time is not necessarily the same for different tunnels; therefore, the expo-sure time should be properly determined before conducting safety inspection so that the best precision can be achieved.

The R’s obtained from totally dark condition in nighttime and from dim lit condition at nightfall are compared inFig. 18. Suppos-edly, since there is no background illumination in the totally dark condition and no interference would happen, better precision should be obtained for totally dark condition. However, about the same orders of precision were obtained for both cases. For the to-tally dark condition, longer exposure time is required owing to the totally dark background, the laser-lit spot is broadened, and the precision is accordingly reduced, that is, the effect of better back-ground condition (totally dark) is compensated by the longer co-exposure time.

4.4. Application to the survey of tunnel wall

Given the precision of about 1.2 mm for Model Tunnel I, it is of interest to know whether the deformation and the correspond-ing precision of tunnel wall can be detected. For this purpose, an

Fig. 15. The variations of Riof three pre-set points with the number of calibration

points which are used to deduce their coordinates: (a) the Rireduces to a constant

level when more than 7 points are used in case the error on the plane of proﬁle (2D) is concerned and (b) the Rireduces to a low, constant level as 10–15 points are used

in case the error in 3D space is concerned.

Fig. 16. The variation of R for distinct proﬁles, deduced from superimposed images using line laser and point laser, of Model Tunnel II. Contrasting toFig. 11, proﬁles illuminated by point laser seem to have much better precision for a greater tunnel.

Fig. 17. The inﬂuence of exposure time. The R’s for various proﬁles obtained from exposure time of 1/200 s are consistently less than those of 1/4.

Fig. 18. The inﬂuence of background illumination. Since the effect of background illumination is compensated by the exposure time, the results obtained for totally dark condition are about the same order of precision to those for dim light condition.

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intentional bulge with thickness of only approximately 3 mm is designed to provide a slight deformation of tunnel wall. The resulted proﬁle and the original proﬁle are compared, as shown inFig. 19. It can be seen that the proposed imaging method has effectively showed the deformation of tunnel wall, even the defor-mation is rather small.

Furthermore, the Model Tunnel I is forced to deform with max-imum horizontal displacement of about 15 mm on its right side. One of the measured profiles is compared with its original profile, as illustrated in Fig. 20. The deformation pattern has been suc-cessfully revealed by the two profiles measured. Such information can be very helpful for identifying deformation mechanism later. Moreover, the data points on the deformed segment are about 250, which are much more than those provided by geodetic sur-vey. Therefore, the profile–image method shows merits, both in the precision and in the numbers of points along a profile, in char-acterizing the whole deformed pattern of the profile, when com-pared to methods using conventional geodetic survey or laser scanner.

The proposed profile–image method has also been tested in two real, full size tunnels. For the first tunnel, a double-lane highway tunnel, it took about half day to survey six profiles with all proce-dures included. For the second tunnel, a single-lane railway tunnel, it took about 2.5 h to measure three profiles. Most of the time was used for surveying the coordinates of calibration points. In fact, the time needed for measuring a particular profile is just about 15– 20 min.

5. Conclusive remarks

Profile–image method has been developed for measuring pro-files of moving objects in small, laboratorial scale. This study ex-tends this method and tests its applicability for measuring the profile of a tunnel. The superimposed image technique is conjunc-tively utilized to enhance the insufficient contrast of the laser-lit profile as the tunnel size became larger. And results from experi-ments with small and medium scales prove that the proposed pro-file–image method exhibits merits in providing good precision, sufficient data points along a profile and fastness in time survey. Consequently, especially for tunnels in operation, the profile–im-age method can serve as a feasible and efficient way for safety inspection and for continuously monitoring the tunnel deforma-tion. It is found that the precision of the proposed profile–image method can be influenced by the lens distortion, image resolution, types of lasers and contrast of profile to the background. This also highlights the key issues to be improved in the future.

Acknowledgements

The authors acknowledge the contribution of Mr. Chun-Wei Chao and Ms. Ya-Chu Chiu in completion of this work. The authors also thank two anonymous reviewers for their valuable sugges-tions to make this paper in the present form.

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Fig. 20. The application of deformation detection. The deformation pattern has been successful revealed by the two successfully measured proﬁles.

Fig. 19. The application of local tiny deformation detection. The proposed proﬁle– image method has effectively showed the deformation of tunnel wall, even the deformation is rather small.