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An innovative method for remote measurement of minimum vertical underclearancein routine bridge inspection

B. Riveiro a,, D.V. Jauregui b, P. Arias c, J. Armesto c, R. Jiang d

a Department of Materials Engineering, Applied Mechanics and Construction, School of Industrial Engineering, University of Vigo, C.P. 36208, Vigo, Spainb Department of Civil Engineering, College of Engineering, New Mexico State University, Las Cruces, NM, USAc Department of Natural Resources and Environmental Engineering, School of Mining Engineering, University of Vigo, C.P. 36310, Vigo, Spaind Department of Engineering Technology and Surveying Engineering, College of Engineering, New Mexico State University, Las Cruces, NM, USA

a b s t r a c ta r t i c l e i n f o

Article history:

Accepted 18 April 2012

Available online 17 May 2012

Keywords:

Bridge inspection

Close range photogrammetry

Vertical underclearance

This paper presents an innovative and low cost procedure for the complete and accurate measurement ofminimum vertical underclearance in a safe environment foroperators. This procedure draws on the principles

of terrestrial convergentphotogrammetry which makes possible the reconstruction of the bridge components

and surrounding features in 3D space. Using the measured 3D coordinates, an algorithm was developed in theMatlab software to calculate the vertical underclearance. Furthermore, a procedure based on 3D curve ttingwasdeveloped to estimate the mathematicalexpression of thebeam curve.The resultingmethodologyis suit-

able and advantageous for implementation in routine bridge inspection because it provides a more extensive

and accurate measurement of vertical underclearance under much safer conditions. In addition, the estimateof the beam equation can be used not only for clearance measurement but also for periodic monitoring of thebeam shape over time.

2012 Elsevier B.V. All rights reserved.

1. Introduction

It is true that extensive knowledge of the functional and conserva-tion states of a structure is needed in order to properly schedule itsmaintenance and ultimately, ensure its preservation. Periodic monitor-ing of geometry usually plays a key role in the detection of structural

anomalies, and in some cases such as stone arch bridges, can aid inpreventing collapse due to problems with equilibrium andstability [1,2].

In the case of modern bridges (mainly composed of concrete orsteel), although the diagnosis of their condition state is assessed

based primarily on the physical condition of the structural elements,the external shape and geometry also plays a very important role inthe overall evaluation. The presence of deterioration, defects, and/ordamages (e.g., impact damage caused by truck collisions, concrete

spalls or delaminations, fatigue or shear cracks, section loss) and evi-dence of irregular movement are the most important parametersconsidered during a routine bridge inspection, and move advancedtools for their detection and quantication need to be investigated.

Bridge inspection is a key factor in the maintenance and preserva-tion of the civil infrastructure of a country. Many parameters haveto be periodically evaluated in order to determine the physical condi-

tion of the structure [35]. In the bridge management protocol oftransportation agencies, there usually exists an initial phase focused

on routine inspection, where, by means of quick and simple docu-mentation, the rst diagnosis of the current state of the structure is

obtained[68]. When some evidence of distress about the physicalcondition or stability of the structure is found in this initial stepsuchas excessive beam sag or support settlement, a special inspectionplan should be initiated to perform an in-depth evaluation of the

bridge. Currently, there are several basic techniques available to mea-sure irregular bridge movement such as plumb bobs, laser levels,theodolites, and total stations.

Horizontaland vertical clearances are important geometric parame-

ters that must be measured to a high level of accuracy during a routinebridge inspection. The acquisition of these dimensions is traditionallyaccomplished by means of basic contact tools such as tape measuresand range poles that lack metric accuracy, and which also require the

operators to perform the clearance measurements under dangeroustrafc conditions.Fig. 1illustrates the use of a range pole to measurethe minimum vertical underclearance which is the distance from theroadway or railroad track beneath the bridge to the underside of the

superstructure [3]. As shown in the gure, measurements are usuallytaken at discrete points on the bottom surface of the beam to savetime and also due to safety concerns. Furthermore, it is difcult to

keep the range pole perfectly vertical to obtain an accurate measure-ment particularly for higher clearances. Consequently, it is possiblethat the minimum vertical underclearance is not measured accuratelyat the correct location.

There are 116 items of bridge data used by the FHWA to monitorand manage the National Bridge Inventory (NBI) in the United States

Automation in Construction 25 (2012) 3440

Corresponding author. Tel.: +34 986 813 499; fax: +34 986 811 924.

E-mail address:[email protected](B. Riveiro).

0926-5805/$ see front matter 2012 Elsevier B.V. All rights reserved.

doi:10.1016/j.autcon.2012.04.008

Contents lists available at SciVerse ScienceDirect

Automation in Construction

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a u t c o n
http://dx.doi.org/10.1016/j.autcon.2012.04.008http://dx.doi.org/10.1016/j.autcon.2012.04.008http://dx.doi.org/10.1016/j.autcon.2012.04.008mailto:[email protected]://dx.doi.org/10.1016/j.autcon.2012.04.008http://www.sciencedirect.com/science/journal/09265805http://www.sciencedirect.com/science/journal/09265805http://dx.doi.org/10.1016/j.autcon.2012.04.008mailto:[email protected]://dx.doi.org/10.1016/j.autcon.2012.04.008

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as given in the Structure Inventory and Appraisal (SI&P) sheet. Thedata are divided between inventory items that pertain to the perma-nent conditions of the bridge and appraisal items that pertain to thecondition of the bridge component in comparison to current stan-dards[3]. In the SI&P sheet, geometric data are considered inventory

items under which the minimum vertical underclearance is item 54.This particular item is coded with 5 digits; the rst digit representsthe reference feature (highway or railroad beneath structure) and theremaining four digits represent the minimum vertical underclearance

(in feet and inches).Underclearance information is used by personnel involved with

the permitting of oversize/overweight vehicles and is used in evaluat-ing the sufciency of a bridge to remain in service (i.e., sufciency

rating). Four separate factors are determined (using 19 of the 116items reported in the SI&A sheet) to arrive at the sufciency rating:(1) structural adequacy and safety; (2) serviceability and functional

obsolescence; (3) essentiality for public use; and (4) special reduc-tions. Horizontal and vertical underclearances and the deck conditionaffect the second factor while the superstructure and substructureconditions affect the rst factor. The sufciency rating ranges from

0 to 100% with the latter percentage representing an entirely suf-cient bridge. Bridges qualify for replacement when the rating fallsbelow 50% and rehabilitation when the rating falls below 80% [3].

In spite of the simplicity and rapidity in using traditional instru-

ments, the quality of metric results is poor. Surveying techniquesoffer better quality results in terms of accuracy, but these methodshave important limitations for regular use in relation to handling of

equipment and the amount of data collected. Terrestrial photogram-metry and laser scanning are two geomatic techniques which havesignicantly evolved, being more and more used in diverse eldsincluding architecture [9,10]; civil engineering [1114]; industry[15,16];and archaeology[17,18]. Many investigations show the po-

tential of these new technologies in the eld of bridge engineering[19]. From the captured precise 3D geometry of bridges, for example,an improved assessment of the structure can be made [20]. Laserscanning is gaining popularity due to its simplicity in usage and

speed of acquisition[21]. A few studies of damage detection in con-crete bridges using terrestrial laser scanner data can be found in[2224]. Similar to traditional surveying equipment, laser scanningpresents important limitations for routine inspection work including

cost of equipment, necessity for trained operators, and amount of

data stored during the bridge survey.

Consequently, low cost technologies capable of collecting mean-ingfuland accurate metric data without the needfor overly complicat-ed equipment operation and extensive data processing are needed.Close range photogrammetry has several strengths that make it a

suitable method for measuring bridge features during a routine in-spection such as it utilizes low cost equipment, it is relatively easy touse, and it provides high metric precision. An extensive review ofthe application of this technique in bridge engineering can be found

in [19]. Gonzalez-Aguilera and Gmez-Lahoz[25] present a novel pho-togrammetric system based on a singleimage for obtainingthe overallgeometry of bridges by means of dimensional analysis. Other studiesrelated to bridge monitoring based on photogrammetric methodsincluded those performed by Chang and Ji[26]and Hang et al.[27].

Before new technologies are included in the protocols for metricdocumentation, they must rst be validated. In this context, method-

ologies of surveying need to be adapted to overcome the existingdifculties in routine bridge inspection. This paper presents an inno-vative andlow cost procedure forthe complete andaccurate measure-ment of minimum vertical underclearance in a safe environmentfor operators. This procedure draws on the principles of terrestrial

convergent photogrammetry which makes possible the reconstruc-tion of the bridge components and surrounding features in 3D space.Using the measured 3D coordinates, an algorithm was developed inthe Matlab software to calculate the vertical underclearance. Further-

more, a procedure based on 3D curve tting was developed to esti-mate the mathematical expression of the beam curve. The resultingmethodology is suitable and advantageous for implementation inroutine bridge inspection because it provides a more extensive andaccurate measurement of vertical underclearance under much safer

conditions. In addition, the estimate of the beam equation can beused not only for clearance measurement but also for periodic moni-toring of the beam shape over time.

2. Theoretical backgrounds

2.1. Photogrammetric process

Close range photogrammetry is a non-destructive geomatic tech-nique which allows the 3D shape of objects to be reconstructed

from photographic images. The conversion from 2D information ofimages to 3D models is achieved by means of the photogrammetricprocess. Two main steps contribute to this process: inner orientationand external orientation.

The inner orientation reconstructs the internal geometry of theimaging system, which denes the perspective system, by meansof the camera calibration process. The metric parameters obtainedfrom the camera calibration include the 3D position of the perspec-

tive centre in the image space (focal length and principal point onthe sensor), sensor dimensions, and lens distortions. The lens distor-tions are sources of errors during the image recording and must becompensated for to obtain the most accurate reconstruction of the

3D model. The symmetric radial distortion signicantly inuencesthe photogrammetric reconstruction as shown in [28,29]. There aretwo common formulations for radial distortion: balanced and unbal-anced models. Although these models can be mathematically equiva-

lent, the balanced model results in smaller apparent distortions so iscommonly used by camera and lens manufacturers[3032].

The external orientation locates the relative position of eachcamera used in the 3D reconstruction process at the time images

were taken. Hence, if the position of one camera is known, the rela-tive external orientation is done using the positions (X, Y, Z) andorientations (, , ) of the other cameras. For a given point in an ob-

ject space, the coplanarity condition requires that the point's position

in two overlapped images and the camera's perspective centre aresituated in the same plane. As shown by Krauss in [33], the relative

orientation of images is achieved when the image coordinates of

Fig. 1. Measurement of minimum vertical underclearance during a routine bridge

inspection.

35B. Riveiro et al. / Automation in Construction 25 (2012) 34 40

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ve points are known. The external orientation is completed whenthe model is scaled and placed in the absolute coordinate system.When the relative camera position is solved, the camera perspectivecentre Oi, a point in the image (xi, y i), and the position of this point

over the surface of the object (X,Y,Z) are located in the same straightlinebased on the collinearity equation. It is then possible to obtainthe 3D position of a point on the object surface from measurements

in the image. The mathematical principles of this process are further

explained in[34]and[35].

2.2. 3D tting algorithm

The shape of object surfaces can be usually modelled by meansof parametric surfaces. When a set of data points dening the objectsurface is available, a function of two independent variables (x and

y) can be determined to best t a parametric surface to the data. For

3D curve tting, a dependent variable f can be modelled from twoindependent variables x and y, where data are a set of n3D points(xi,yi,fi), fori = 1:n,nN.

In this case, object points with three spatial coordinates (xi,yi,zi)

are obtained from the photogrammetric process. Xi and Yi compo-nents of space points are initially aligned according to transversaland longitudinal bridge's directions, respectively. Zi corresponds tothe vertical component (clearance direction).

This 3D information provides the two independent variables(x and y) as well as a third component zi for the minimization ofthe following expression (1),

ni1 f xi;yi zi

21

3. Methodology

3.1. Instrumentation

To be feasible, an important aspect to consider in the effort toenhance routine bridge inspection work is maintaining the simplicity

of equipments used for basic inspection tasks while providing betterdocumentation. For this reason, the measurement procedure devel-

oped in this study was based on simple eld setups and the usageof digital cameras which do not require advanced knowledge ofdigital image recording by operators. A digital, semi-metric camera(Canon EOS 10D) equipped with a CCD sensor, RGM matrix resolution

of 6.29 million pixels and a Canon EF 20 mm f/2,8 lens was used forimage acquisition.

External information with real dimensions of a reference body isrequired in order to get the 3D model scaled. In this sense, during

the execution of this project a reference distance was obtained bymeans of measuring coordinates of two control points.

To validate the photogrammetric results, separate measurementsusing topographic equipment were made. A total station (Leica model

TCR 1203+) was used to measure a set of points dening the lowerprole of the beam and control points. The technical features of theinstrument include long-range coverage (up to 400 m); 2 mm+2 ppm accuracy; 10 cc angular accuracy (1 cc typical average measure-

ment in angles deviation);and 6/2 mm sensitivity of levels.

3.2. Camera calibration

The cameras are calibrated under xed imaging parameters inthe laboratory prior to the eld work. Consequently, operators onlyhave to acquire a few photographs during the actual bridge survey(eld calibration requires signicantly more photographs). The

camera calibration process is performed in the Calibration moduleof the Photomodeler Pro software using a scaled planar grid of

points which is captured by means of several images from different

points of view. The calibration images are marked and importedinto the photogrammetric platform where the geometric parametersof the camera are almost automatically obtained. The parametersrepresenting the inner orientation of the camera used in this study

are presented inTable 1, as well as the components of the mathemat-ical polynomials that model the radial (K1 and K2) and tangential(P1and P2) lens distortions.

Based on the sensor dimensions given in the table, the pixel size

amounts to 7.3 m, which together with the principal distance of theimage system, determines the maximum perceived detail of objectscaptured in a digital image. The spatial resolution of an image overthe object surface can be calculated as the pixel size projection orGSD (ground sample distance) by means of the following expression

(2),

GSDAsx

f 2

where,Ais the mean distance to the object, fis the principal distance

of the calibrated camera and sx is the pixel size calculated from theCCD size of the camera sensor and image resolution. Based on thecomputed values of pixel size and principal distance, for instance,

the pixel size projection expected is 11 mm if an operator is workingwith averaged object distances of 30 m. Consequently, the minimumerror of measurement from images will exceed this value.

3.3. Data acquisition

Once the cameras are calibrated, they can be directly used in the

eld. For the measurement of vertical clearance, as well as other geo-

metric features, the methodology for data acquisition consists of thefollowing steps:

Selection of camera parameters according to the internal congura-tion determined from camera calibration.

Denition of camera stations. According to the principles of con-vergent photogrammetry, cameras should maintain convergence

angles of 90 degrees. This angle is dened by the maximumangle between the main directions of the cameras from the vertexto the same point on the object surface. Fig. 2illustrates the rec-

ommended geometry of the camera network. Reference system has to be established. For this purpose, a refer-

ence distance has to be known in the object space, preferably mea-sured around the imaginary plane where vertical clearance is going

to be measured. Adequate framing. It is important to ensure that the structure en-

tirely ts into the image and that the structure takes up the mostpossible space in the photo area. This image conguration optimizes

the spatial resolution over the bridge surface, since it correspondsto the minimum operative distance between camera and object

Table 1

Calibration parameters of Canon EOS 10D+20 mm lens, and standard deviation of

values.

Parameter Value Standard deviation

Focal distance [mm] 20.339 0.001

Principal point position (x) [mm] 11.180 0.001

Principal point position (y) [mm] 7.467 0.001

Sensor width [pix] 3072 Sensor height [pix] 2048 Format width [mm] 22.6643 3.5104

Format height [mm] 15.1130 K1 [] 2.140104 7.3107

K2 [] 4.24107 5.8109

P1 [] 3.53105 8.2107

P2 [] 1.1105 1.1106

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and, consequently, the minimum GSD value achievable. Further-more, overlap between convergent images should always be higherthan 60% of the photo area, otherwise external orientation of theimages cannot be realized.

Image acquisition. Images must be captured ensuring adequate ex-posure levels and thus, it is important to use a tripod when naturallight is not sufcient and the shutter speed required is longerthan 1/30 s. Lighting conditions are very important during imageacquisition because underexposed images or images with excess

brightness and reections may lead to mistakes during image resti-tution, and consequently, a reduction of the measurement accuracy.

Data storage. Most digital cameras directly store the data intoportable memory devices which subsequently may be downloaded

to a PC or workstation. An advantage of digital cameras is the capa-bility to control the image acquisition process via a camera controlsoftware installed on a PDA or tablet PC.

3.4. Data processing

Following the eld work, the images previously stored in thecamera's digital media are downloaded to the workstation in thelaboratory. The photogrammetric process starts when the parametersof camera calibration are imported and the perspective geometry of

the rays from the image points is modelled. Next, the location and ori-entation of images in the reference system may be found. It is rstnecessary to provide the information needed for the bundle adjust-ment. As mentioned previously, six common points (ve plus a proof

point) between convergent images produces a determinate system ofequations, the solution of which gives the relative external orientationsof the images. The model is scaled in real space via the reference dis-tance used during image acquisition. This reference distance was accu-

rately measured by surveying methods, with the same accuracy ofthe truth data of the experiment. Optionally, the operator can denethe orientation of the project coordinate system, for example, usingthe main vertical plane of the structure as the YZ plane. Extraction

of the point clouds is then achieved during the process of restitution(reconstruction of 3D point positions) on the pavement and bottomcontour of the beam. Once the 3D position of the object points is calcu-lated they are exported to text les. These les are then imported into

the algorithm developed in the Matlab software where the calculationof the minimum vertical underclearance is performed.

3.5. Minimum vertical clearance algorithm

To estimate the minimum vertical underclearance, an algorithm

based in 3D curve tting was developed using the Matlab software.

The input data is composed of two les that contain: the coordinates

of the 3D points measured on the pavement, and those measured onthe bottom beam contour, respectively. The rst point cloud is ttedto a plane, whose normal vector denes the vertical line of the sys-tem. Once the verticality is dened, the points of the pavement are

readjusted to a 3D surface that best ts the road shape on the basisof least squared tting.

On the other hand, the points of the beam contour are tted to afourth degree polynomial curve to estimate the beam camber. The

vector in longitudinal direction of the 3D tted curve, and the verticalvector dened by the pavement surface result in a plane from whichthe minimum vertical underclearance is measured. This inspectionvalue is calculated as the difference between the beam curve and

the vertical projection of the curve over the pavement surface.It is important to note that the vertical clearance is measured

along the beam length and consequently, the minimum under-clearance can be calculated as well as its relative longitudinal position

on the beam. This position is also located in the photograph of thebridge structure so it is possible to monitor any changes in the verticalclearance between consecutive inspections. Additionally, this algo-

rithm calculates the equation of the beam camber so it is possible tomonitor the beam deection and consequently, this parameter canbe used to evaluate potential problems such as excessive prestresslosses.

4. Results

The methodology developed in this article was applied to a pres-

tressed concrete highway bridge, whose beams are the structuralelements which dene the minimum vertical underclearance of thebridge. The bridge evaluated is named the Dr. C. Quentin FordBridge

(hereafter referred to as the Ford Bridge) and carries the I-25 inter-state highway in Las Cruces, New Mexico, USA.

The validation of the methodology was done through comparisonof the measurements obtained with the photogrammetry and topo-

graphic equipment described earlier and shown inFig. 3. The totalstation provided an independent check of the photogrammetric mea-surements of vertical clearance and beam camber.

4.1. Photogrammetric results

Three different sets of points were obtained from the photogram-metric analysis: points restituted on the pavement surface; points

dening the lower beam prole; and a set of control points locatedthroughout the bridge area. Control points were measured to quantify

the accuracy of the photogrammetric measurement system.Table 2

Fig. 2.Recommended geometry of camera network for image acquisition during routine bridge inspection.

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shows the precision of the restituted points calculated as the standarddeviation of each point after the bundle adjustment. As shown by the

table values, the level of precision of the three data sets (beam, pave-ment and control points) is similar.

4.2. Point-to-point measurement

The control points were measured with the total station with the

aim of checking the accuracy of the 3D restitution of single points.As shown in Table 3, the precision of photogrammetric points issignicantly lower than the point precision attained by the total sta-tion. Thus, the topographic measurements were taken as the true

values of the control points by which the accuracy of the photogram-metric results were evaluated.

Since both measurements belong to different coordinate systems,a 3D conformal transformation[36]was applied to the photogram-

metric measurements to correlate with the coordinate system denedby the total station. The residuals of the transformation representthe accuracy of each control point and were calculated as the vectordistance between the real point position and the position of the

transformed photogrammetric points. Table 3 presents the photo-grammetric and topographic precisions and the transformation resid-uals for each control point.

As can be seen, precision values inXcomponent (direction parallel

to camera's principal length) are signicantly lower than those in theother directions, because in that direction the depth of spatial data isvery low compared with the other directions.

4.3. 3Dtting algorithm

For the vertical underclearance measurement, the 3D coordinatesof the beam and pavement points were exported in ascii format.

These les were subsequently imported into the 3D tting algorithmdeveloped in the Matlab software and the automatic clearance mea-surement was carried out separately using the photogrammetricand topographic data.

Fig. 4 shows the vertical underclearance values along the beam

principal direction obtained from both sources of data as well as theaccuracy for each point (computed as the vertical difference vectorbetween measured and tted points). The average precision in thepolynomial tting was 0.026 m for the photogrammetric data and

0.002 m for the total station data. As expected, the error of the adjust-ed point cloud is better than the average precision of single points forboth measurement systems[37].

4.4. Minimum vertical clearance and defection curve parameterization

As shown in Fig. 5, the minimum vertical underclearance was

measured at the left end of the beam with a real (topographic) valueof 5.247 m and an estimated photogrammetric value of 5.222 m.According to the proposed methodology, the user can measure thevertical underclearance at any position along the beam so it will be

possible to monitor the same position during successive routine in-spections of the structure. In addition, the beam camber can be moni-tored by comparison of the deection curves, whose mathematicalrepresentation is also provided by the algorithm developed.

5. Conclusions

This article presents a novel methodology for the measurement ofminimum vertical underclearance during routine bridge inspections.The methodology is based on the principles of 3D measurement byterrestrial photogrammetry which provides a high level of metric

precision. To automate the clearance measurement process, an algo-rithm basedon 3D curve tting was developed in the Matlab softwarewhose data entry are the 3D information obtained from the photo-grammetric analysis.

The proposed methodology was validated by means of compari-son with topographic data. Averaged vertical clearance difference, be-tween the photogrammetric results and the real data, was 0.008 m;and the average precision of the adjustment achieved were 0.017 m

Fig. 3.Photogrammetric and topographic equipment used for Ford Bridge Measurement.

Table 2

Averaged results of 3D single point position for control points and restituted pointclouds.

X precision (m) Y precision (m) Z precision (m) RMS (m)

Beam 0.024 0.014 0.007 0.028

Pavement 0.036 0.014 0.007 0.039Control Points 0.026 0.019 0.011 0.035

Table 3

Precision of photogrammetric and topographic measurements and photogrammetric accuracy of each control point.

Control point name Photogrammetric precision Total station

precision (m)

Accuracy of

photogrammetric

data (m)X Precision Y Precision Z Precision RMS

(m) (m) (m) (m)

1 0.045 0.036 0.013 0.059 0.0032 0.0094

2 0.04 0.034 0.016 0.054 0.0032 0.0175

3 0.023 0.017 0.01 0.030 0.0031 0.01074 0.021 0.011 0.009 0.025 0.0031 0.0130

5 0.021 0.005 0.01 0.024 0.0031 0.0142

6 0.021 0.01 0.01 0.025 0.0031 0.0037

7 0.02 0.016 0.011 0.028 0.0031 0.0060

8 0.02 0.021 0.011 0.032 0.0031 0.0130

9 0.023 0.023 0.007 0.034 0.0031 0.0092

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and 0.0013 m for photogrammetric and topographic data respectively.Both systems of measurement found the minimum value of verticalunderclearance at the same location along the beam, which equaled

5.222 0.025 m based on the photogrammetric method. These resultssupport the implementation of photogrammetry in the protocols ofroutine bridge inspections due to its high level of accuracy.

In summary, this investigation showed that photogrammetryis suitable for use in routine bridge inspections because it providesan accurate measurement technique for minimum vertical under-clearance. One of the most important advantages of this procedure

is that it provides a safe environment for operators, particularly inhigh capacity roads, since operators do not need access to the road-

way or rail to perform the measurement. In addition, the estimateof the mathematical expression of the beam curve can be used not

only for clearance measurement but also for periodic monitoring ofthe beam camber over time.

It is important to note that the specic equipment used in thisstudy only permitted identifying objects whose size was bigger than

0.011 m (spatial resolution of camera system due to experimentconguration). For the same average range of measurement and thesame focal length, a camera with a pixel size smaller than 4mwould provide us with a spatial resolution of 6 mm. Additionally, if

a great angular lens of, for example, 50 mm is mounted on the camerainstead of a 20 mm focal length one the achievable spatial resolutioncould be approximately 2.5 mm. Hence, future research should befocused towards the validation of different camera systems to maxi-

mize the level of accuracy of the proposed methodology.

Acknowledgments

The nancial support of the Ministry of Science and Education

(Spain) for Scientic Research under Grant No. BIA2009-08012, theSpanish Centre for Technological and Industrial Development (GrantNo., IDI-20101770) and Human Resources Program of the Ministry of

Science and Education (AP2006-04663) is gratefully acknowledged.

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Fig. 5.Superposition of vertical underclearance values obtained from photogrammetric and topographic methods.

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http://dx.doi.org/10.1016/j.isprsjprs.2010.06.003http://dx.doi.org/10.1016/j.isprsjprs.2010.06.003http://dx.doi.org/10.1016/j.isprsjprs.2010.06.003http://dx.doi.org/10.1111/j.1475-4754.2010.00566.xhttp://dx.doi.org/10.1111/j.1475-4754.2010.00566.xhttp://dx.doi.org/10.1111/j.1475-4754.2010.00566.xhttp://dx.doi.org/10.1016/j.isprsjprs.2010.06.003http://dx.doi.org/10.1016/j.isprsjprs.2010.06.003

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