Teaching Camera Calibration by a Constructivist Methodology

646 IEEE TRANSACTIONS ON EDUCATION, VOL. 53, NO. 4, NOVEMBER 2010

Teaching Camera Calibration by a ConstructivistMethodology

David Samper, Jorge Santolaria, Jorge Juan Pastor, and Juan José Aguilar

Abstract—This article describes the Metrovisionlab simula-tion software and practical sessions designed to teach the mostimportant machine vision camera calibration aspects in coursesfor senior undergraduate students. By following a constructivistmethodology, having received introductory theoretical classes,students use the Metrovisionlab application to carry out a series ofpractical exercises with the aim of learning in a simple way: 1) thebasic functioning of a camera; 2) how to calibrate a camera; 3) themost important calibration methods and their special characteris-tics; and 4) the generation and use of synthetic calibration points.Evaluations based on student feedback confirm that the use ofMetrovisionlab as a teaching tool facilitates the learning process.

Index Terms—Calibration, cameras, collaborative work, engi-neering education, simulation software.

I. INTRODUCTION

C AMERA calibration is essential for most vision systemsused in dimensional verification and control during

various manufacturing processes. For this reason, the Metro-visionlab [1] application was developed for students studyingthe courses “Further Industrial Processes” and “MeasuringTechniques in Production and Maintenance” to help them learnabout issues relating to camera calibration. Hitherto in thesesubjects, the basics of camera calibration have been taught intheoretical classes describing: 1) the pinhole model camera;2) mathematical models of the various camera calibrationalgorithms; and 3) how to calibrate a camera. These theo-retical classes can be divided into a series of mathematicalaspects that students assimilate easily and another series ofaspects that require intuition to be understood. In general itis much easier for students to assimilate concepts requiringintuition if they are learned actively rather than passively [2].Furthermore, the active participation of students in the learningprocess helps to increase their motivation [3], and this leadsto concepts being assimilated much more effectively [4]. Forthese reasons, the Metrovisionlab simulation software wasdeveloped together with a series of practical problems to besolved by students working in collaboration with each other.By using the simulation software, the students learn conceptswhile following constructivist methodologies and working to-gether to strengthen the learning process [5]. While working on

Manuscript received April 14, 2009; revised December 01, 2009. First pub-lished February 05, 2010; current version published November 03, 2010. Thiswork was supported in part by Universidad de Zaragoza under the “Convocato-rias de Innovación Docente 2008–2009” under Grant 082212.

The authors are with the Design and Manufacturing Engineering Department,Universidad de Zaragoza, Zaragoza 50018, Spain (e-mail: [email protected];[email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TE.2009.2039574

the practical exercises with Metrovisionlab, students activelylearn: 1) the basic workings of a camera; 2) how a camera iscalibrated; 3) the advantages and disadvantages of the variouscalibration methods; and 4) the potential utility of syntheticallygenerated calibration points.

This paper is divided into sections that describe how the sim-ulation software was developed and how it has been used ina series of practical sessions in which the students learn themost important aspects of machine vision camera calibration.Section II describes the teaching environment in which Metro-visionlab has been used and how it has been handled by students.Section III explains the development of the Metrovisionlab sim-ulation software and describes its most important characteris-tics for teaching applications. Section IV shows the results of asurvey given to students who have used Metrovisionlab in orderto check the validity of the method proposed for teaching cameracalibration. Finally, the conclusions are set out in Section V.

II. EDUCATIONAL ASPECTS

A. Courses in Which Metrovisionlab is Used

The Metrovisionlab simulator has been introduced as ateaching tool in two courses taught by the Department ofDesign and Manufacturing Engineering at the Universidad deZaragoza, Spain: 1) Measuring Techniques in Production andMaintenance (20852), an optional subject in the final year ofIndustrial Engineering; and 2) Further Industrial Processes(22522), an optional subject in the final year of Technical In-dustrial Engineering. In the former course, students are taught:a) measuring techniques in manufacturing and maintenancequality control; b) specifications required for measuring; andc) the selection and integration of equipment and systemsfor industrial inspection and maintenance. Topics covered inthe Further Industrial Processes course include: a) computerassisted manufacturing; b) advanced manufacturing methods;and c) vision systems applied to quality control and inverseengineering. The syllabi for these two courses overlap wherethey deal with industrial vision, specifically for measuringor inspection, and it is in this part of the syllabus where theMetrovisionlab simulation software has been introduced.

It was decided to use a constructivistically oriented learningapproach to teach these topics. Therefore, the students were dis-tributed among several work groups, and the teachers createdguidelines for how to carry out several tasks that the studentsmust complete. Various learning-oriented practical activities areperformed, such as solving practical problems in groups of twoor three students followed by an explanation in class, labora-tory sessions, and doing a piece of work as part of the course

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SAMPER et al.: TEACHING CAMERA CALIBRATION BY A CONSTRUCTIVIST METHODOLOGY 647

assessment. These practical problems and laboratory sessionsare planned so that the students, under the teacher’s guidance,can solve their cases actively and interactively using Metrovi-sionlab. The practical problems were designed in such a formthat each group of students has to share its ideas in order to solveseveral questions related to camera calibration, using the knowl-edge acquired during the theoretical classes; later, with the helpof Metrovisionlab, the students had to verify if their answerswere correct. Some of the practical problems that the studentshad to solve can be seen on the Metrovisionlab Web page [1].Using similar techniques, the students also have to solve a realmeasurement problem, offering alternative reasoned and docu-mented solutions, to be carried out in the metrology laboratory.These problems must be solved actively in groups and include anumber of intermediate deliverables, from which the feedbackfrom the students is very useful from the point of view of for-mative evaluation and teaching improvement. On the syllabus,there are two topics concerned with industrial vision applied toquality control. In the first, general concepts of industrial vi-sion are developed, image treatment techniques and algorithmsare introduced, and the types of system usually used in dimen-sional metrology and industrial inspection are described, suchas: 1) 2D systems; 2) laser triangulation systems; and 3) systemsbased on stereovision. The second topic goes more deeply intothe modeling and calibration of cameras and their componentsand precision characterization for their use in metrology and in-dustrial inspection. Hitherto, these topics have been taught inexplanatory sessions complemented by a practical, in which thestudents had to undertake several practical exercises in: 1) imageanalysis using standard images in order to analyze the behaviorof treatment algorithms following the entry parameter values;and 2) calibration of cameras and characterization of their pa-rameters.

The acquisition of skills relating to this part of the course wasevaluated by means of deliverable work and a section in the finalwritten report, in which students have to provide both a specificsolution based on industrial vision to the measurement problemposed and the specifications of the components required for thesolution. Both for this and other parts of the subject, not onlyare the final report and the deliverable work content evaluated,but also the quality of the final presentation that is made to theteachers and fellow students by a set deadline. This also enablesthe general course skills to be evaluated. The final evaluationis thus based on three parts: 1) continuous assessment of eachgroup by the teachers; 2) a final public presentation of the re-sults; and 3) a final written report.

B. Objectives for Metrovisionlab and the Practical Sessions

The specific objectives of the industrial vision part of thecourses, for which the use of the Metrovisionlab simulator isproposed, are that the students should acquire knowledge of:1) the technology, components, and working principles of thevarious systems based on contactless optic sensors used in di-mensional metrology; 2) the different camera calibration tech-niques and algorithms, together with the characteristics of cali-bration objects; and 3) the calibration process of a laser triangu-lation sensor, possible standard specimens, and their influenceon the calibration.

Fig. 1. Scheme followed in the camera calibration practical exercise.

In order for the students reach these objectives, a series ofpractical sessions needs to be organized in which the studentswork together in groups. Students have to do a series of shortexercises with the simulator in these sessions so that they can:1) familiarize themselves with the working environment of theMetrovisionlab simulator; 2) understand the influence of theintrinsic and extrinsic parameters that characterize a camera;3) carry out camera calibrations with the different methodsavailable in the simulator; 4) analyze the influence of the variousparameters against possible errors; and 5) make comparisonsbetween the different calibration methods. At the end of thefirst practical sessions, the students have to use the simulator tocarry out a practical consisting of the calibration of a camera(Fig. 1) following these steps: 1) loading the calibration imagestaken with a camera and defining the basic camera parameters;2) obtaining the screen coordinates of the calibration pointsand linking them with their corresponding global coordinates;3) selecting the calibration method considered the most ap-propriate for the calibration; and 4) analyzing the calibrationresults. During this calibration exercise, the students have tosimulate possible errors both in the image treatment and in thecharacterization of the calibrator in order to be able to evaluatethe sensitivity of the calibration method to these errors.

C. Use of Metrovisionlab in the Theory Classes

The possibility of simulating the workings of a camera, aswell as of modifying the camera parameters in a simple waywhile seeing in graphic form how the modifications affect thesystem, means that the Metrovisionlab simulator is a very effec-tive tool for demonstrating and explaining the most importantconcepts of vision systems in theory classes. During the firsttheory class, the general functioning of the system is explainedto the students in order to familiarize them with it. In the other


Fig. 2. Flowchart of the application Metrovisionlab.

theory classes, the simulator is used as a support so that the stu-dents understand visually and interactively the most importantaspects of camera vision systems.

III. METROVISIONLAB DEVELOPMENT

A. Camera Calibration Software

First, the possibility of using existing camera calibration soft-ware was considered. The notion of using commercial softwarewas quickly discarded because this type of software is focusedon very specific uses and therefore did not have the versatilitythat was needed to be used as an educational tool. Among theopen source and free software tools evaluated, there were sev-eral very interesting alternatives: 1) Tsai Camera CalibrationSoftware [6]; 2) OpenCV and Matlab Camera Calibration Tool-boxes Enhancement [7]; and 3) Camera Calibration Toolboxfor Matlab [8]. These toolboxes and libraries each consider oneunique method of camera calibration, which supposes that thestudents would have to use a different software for each cali-bration method. In addition, these applications have no graph-ical user interface or only a very basic one, which means morelearning time would be needed to use the software. Finally,there was no software that satisfactorily simulated a camera. Itwas therefore decided to develop the appropriate software forteaching camera calibration.

B. Metrovisionlab Architecture

The application was created as a toolbox for the commerciallyavailable Matlab program, thus simplifying the programmingof complex mathematical algorithms and also making it readily

available to the teaching and research communities, giventhe widespread use of Matlab in these areas. In addition tothe Metrovisionlab application, a Web site was created wherestudents can find: 1) documentation for the application; 2) themathematical algorithms of the calibration methods included inthe application; and 3) various examples of its use.

C. Virtual Camera

The basis of Metrovisionlab (Fig. 2) is the simulation of avirtual camera that is defined by the student who sets variousparameters that determine the outcome of the image taken bythe simulated camera. The image will change depending on theparameters of the application. This means that the student canintuitively understand the effect of the various parameters of thecamera on the obtained image.

The interface of the application (Fig. 3) has a wide area thatshows the virtual image taken by the simulated camera fromcalibration points defined by their world coordinates. These co-ordinates can be synthetically generated or loaded from a file.The points appearing in the virtual image are defined by the co-ordinates in the reference image system, which are associatedwith the coordinates in the world reference system of the de-fined calibration points.

The camera’s internal parameters that are configurable by thestudent include those that are most characteristic in camera cal-ibration: 1) the focal length of the lens; 2) the coordinates ofthe optic center in the image reference system; and 3) the hor-izontal and vertical separation between the centers of the ele-ments that make up the camera’s optical sensor. In addition tothese characteristic parameters, the user can also define other pa-rameters to simulate the virtual camera more realistically, such


Fig. 3. Interface of the application.

as: 1) the possible difference between the number of sensor ele-ments of the camera in the direction x and the number of imagepixels captured in the same direction; and 2) the scale uncer-tainty factor that simulates the possible phase lag between theimage acquisition hardware and the optical sensor of the camera.

There are two other factors that, though not normally consid-ered to be intrinsic parameters of the camera, can neverthelesshave a substantial effect on the image obtained. These parame-ters are: 1) distortion caused by the optical lenses themselves;and 2) possible deviations in the optical center of the camera.The distortion simulated by the application is a radial distortioncharacterized by a single factor.

The remaining parameters essential for creating an imagetaken by a virtual camera are the extrinsic parameters. These de-fine the relative position of the camera and the points observedin terms of a rotation matrix and a translation vector . Inorder to make the application more manageable for the student,instead of having to define the nine elements of the rotation ma-trix, it is only necessary to define its equivalent Euler angles.

Students can define other factors that, although not charac-teristics of a camera, are nonetheless useful for simulating theconditions under which a real camera calibration trial would beheld. When calibrating a camera, it is common to use a cali-brator that has a series of easily identifiable marks. Both in the

manufacture of the calibrator and in the measuring of its charac-teristic marks, there can be errors depending on the means usedin the manufacture and measuring processes. To simulate thistype of error, the student can introduce a random deviation insuch a way as to simulate the possible errors that could occur ina real calibration.

D. Synthetic Points Generator

The other indispensable element for obtaining the virtualimage generated by the application is the object captured by thecamera. For the sake of simplicity, it was decided to use groupsof calibration points distributed in matrix form.

Once the camera to be simulated has been characterized, theother essential element for creating a virtual image is havingthe coordinates of the world reference system for the calibra-tion points. The application has a synthetic points generatorthat can create dot matrices, which it uses in order to generatethese coordinates. The generator has options to create a matrixdefining: 1) the number of rows and columns in the dot matrix;2) the number of matrices to be generated in planes parallel tothe length of the axis ; 3) the separations between the matrixrows, columns and planes; and 4) the position with respect tothe origin of the world coordinates of the matrix. The user canalso load the world coordinates of the points from a file.


Fig. 4. (a) Calibration results in numerical form and (b) calibration results in graphical form.

When one of the calibration methods using coplanar pointsis to be used in calibration trials of real cameras, it is usual touse chessboard-type calibrators. In these cases, the coordinatesof the calibration points correspond to the corners of each oneof the chessboards. For this reason, the application included anoption to use a synthetic chessboard as a calibrator.

E. Calibration Methods

One of the most important functions of the application isto calibrate cameras with one of the calibration methods withwhich it is equipped. These include the most important andwidely used methods [9], [10] in the field of camera calibration:1) DLT (Direct Linear Transformation) [11]; 2) Tsai [12];3) Faugeras [13]; and 4) Zhang [14]. Depending on the methodselected, the user can calibrate with different aspects in mind,such as: 1) the use of coplanar or non-coplanar calibrationpoints; or 2) the possibility of making or not making correc-tions to radial distortion caused by the camera lenses. Giventhat the focus of the application is instructional, the focus wasto make the results of the calibrations provided as detailed andcomprehensive as possible.

The results of the application depend on the calibrationmethod used, but there is a series of results common to allmethods, as follows: 1) image coordinates reconstruction error;2) world coordinates reconstruction error; 3) NCE factor (Nor-malized Calibration Error), which is very useful, given that thiserror is independent of the calibration method characteristics[15]; and 4) computation time.

As well as providing results in numerical form [Fig. 4(a)],the application can show in graphical form [Fig. 4(b)] theresults of the reconstruction errors of the calibration points,both in world coordinates and in image coordinates. Thesegraphical representations help the student to better understandthe obtained results.

IV. SURVEY QUESTIONNAIRE

The Metrovisionlab application was used for the first timewith 54 students in the Further Industrial Processes course, di-vided into two different teaching groups of 28 and 26 students;another group of 29 students of the Measuring Techniques inProduction and Maintenance course; and with several studentsworking on the End of Degree Project. The objectives that thestudents were expected to achieve in the part of the coursesrelating to machine vision cameras were: 1) to understand themeaning of the various parameters relating to cameras; 2) tolearn to calibrate cameras with different procedures; 3) toknow how to select the most appropriate calibration methoddepending on the working conditions; 4) to know how to cal-culate the degree of accuracy that can be obtained with specificequipment in given conditions; 5) to learn to do measurementsusing machine vision cameras; 6) to be able to select the appro-priate equipment depending on the measuring conditions; and7) to know whether or not a specific measurement can be doneusing machine vision cameras.

The course was taught actively and collaboratively so that thestudents could achieve the objectives and develop associatedskills. Through project-based learning, the students had to dotasks relating to the calibration of cameras and their use as toolsfor measuring and verification. They were provided with theMetrovisionlab application in order to do these projects. Oncethe exercises were finished, the students were asked to fill outan anonymous survey (Table I) in order to evaluate the useful-ness of Metrovisionlab as a teaching tool. A total of 83 studentstook part in the survey, in which they had to assess a series ofstatements on a scale from 1 to 5 where: 1) 1 represented totaldisagreement; 2) 2 was disagreement; 3) 3 was neutral; 4) 4 wasagreement; and 5) 5 was complete agreement. Fig. 5 shows theresults of analyzing the questionnaires.


Fig. 5. Survey questionnaire results.

TABLE IMETROVISIONLAB SURVEY QUESTIONNAIRE

This survey, besides serving to verify the simulator utility asan educational tool, also has been used to evaluate student pro-files from two different degree programs that will merge intoa single degree program according to the EEES directives thatwill apply to Spanish universities.

Of the total 83 students who took part in the survey, fewerthan 10% thought that learning about the use of cameras was notuseful for their engineering training, while almost 50% thoughtthe opposite. Looking at the results of question A2, it is signifi-cant that 78% of the students who used the application thoughtit easy to work with, while barely 4% did not agree that it wasan easy tool to use. With respect to the usefulness of Metro-visionlab for learning about the use of cameras, the replies tostatements A3, A4, and A5 showed that about 56% of the stu-dents were in agreement or complete agreement that Metrovi-sionlab had helped them, while only 5% thought that it had nothelped their learning. Finally, 25% found the additional materialaccompanying the application in the form of a Web site useful,while 10% did not find it useful.

Besides the results of the survey questionnaire, there is aclearly observed improvement in the quality of students’ finalwritten reports, compared to those from the previous year by

students who did not use Metrovisionlab. The reports by the stu-dents are seen to be more detailed and precise, which suggeststhat the determined objectives have been reached.

V. CONCLUSION AND FUTURE DIRECTIONS

The Metrovisionlab application provides a simple way to un-derstand how various parameters determining the characteris-tics of a camera can affect the image taken with that camera.It also provides knowledge of what factors influence the cali-bration of a camera and to what extent. The application is alsouseful for comparing the various calibration methods to see whatadvantages and disadvantages they have in specific situations.For these reasons, Metrovisionlab is a very useful teaching toolin the area of machine camera calibration, a fact that has beencorroborated by students who have used the application so far.

The implementation of these algorithms (as well as the rest ofthe software) has been performed in Matlab and is available athttp://metrovisionlab.unizar.es to assist other faculty to replicatethe results of the research in a similar education environment.

Future work will concentrate on the potential for broadeningthe scope of the application, for example: 1) implementing new


calibration methods; 2) increasing the complexity of the mod-eling of the lens distortion, taking into account the effects oftangential and prismatic distortions; 3) increasing the functionsof the synthetic points generator; and 4) providing the applica-tion with tools for the extraction of points coordinates from realimages. A focus on all of these questions will make the applica-tion a more powerful teaching tool in the area of machine visioncameras.

REFERENCES

[1] D. Samper, J. Santolaria, J. J. Pastor, and J. J. Aguilar, “Metrovi-sionlab,” 2008 [Online]. Available: http://metrovisionlab.unizar.es

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[5] D. C. Edelson, R. D. Pea, and L. M. Gomez, “Constructivism inthe collaboratory,” in Constructivist Learning Environments: CaseStudies in Instructional Design. Englewood Cliffs, NJ: EducationalTechnology, 1996, ch. 12, pp. 151–164.

[6] R. Willson, “Tsai camera calibration software,” 2009 [Online]. Avail-able: http://www.cs.cmu.edu/~rgw/

[7] V. Vladimir, “OpenCV and Matlab camera calibration toolboxesenhancement,” 2009 [Online]. Available: http://www.graph-icon.ru/oldgr/en/research/calibration/index.html

[8] J. Y. Bouguet, “Camera calibration toolbox for Matlab,” 2009 [Online].Available: http://www.vision.caltech.edu/bouguetj/calib_doc/

[9] F. Remondino and C. B. Fraser, “Digital camera calibration methods:Considerations and comparisons,” in Proc. Int. Archives Photogram-metry, Remote Sens. Spatial Inf. Sci., ISPRS Commission V Symp.,2006, vol. 36, no. 5, pp. 266–272.

[10] H. Zollner and R. Sablatnig, “Comparison of methods for geometriccamera calibration using planar calibration targets,” in Proc. 28thWorkshop Austrian Assoc. Pattern Recog. (OAGM/AAPR) DigitalImag. Media Educ., 2004, pp. 237–245.

[11] Y. I. Abdel-Aziz and H. M. Karara, “Direct linear transformation fromcomparator coordinates into object space coordinates in close-rangephotogrammetry,” in Proc. ASP/UI Symp. Close-Range Photogram-metry, 1971, pp. 1–18.

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[13] O. Faugeras, Three-Dimensional Computer Vision: A Geometric View-point. Cambridge, MA: MIT Press, 1993.

[14] Z. Zhang, “Flexible camera calibration by viewing a plane fromunknown orientations,” in Proc. 7th IEEE Int. Conf. Comput. Vision,1999, vol. 1, pp. 666–673.

[15] J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distor-tion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach.Intell., vol. 14, no. 10, pp. 965–980, Oct. 1992.

David Samper received the B.S. and M.S. degrees in industrial engineeringfrom the Universidad de Zaragoza, Zaragoza, Spain, in 2005 and 2007, respec-tively.

He is currently an Assistant Researcher with the Department of Design andManufacturing Engineering, Universidad de Zaragoza. He is with the Manu-facturing Engineering and Advanced Metrology Group (GIFMA), which is amember of the Aragón Institute of Engineering Research (I3A) at the university.His research interests include 3D stereo measurement, noncontact measurementsystems, and camera calibration.

Jorge Santolaria received the B.S., M.S., and Ph.D. degrees in mechanical en-gineering from the Universidad de Zaragoza, Zaragoza, Spain, in 1998, 2000,and 2007, respectively.

He is currently an Associate Professor of Mechanical Engineering withthe Department of Design and Manufacturing Engineering, Universidad deZaragoza. He is with the Manufacturing Engineering and Advanced MetrologyGroup (GIFMA), which is a member of the Aragón Institute of EngineeringResearch (I3A) at the university. His research interest includes precisionengineering, modeling and calibration of coordinate measuring systems,laser-based and noncontact measurement systems, and optimization and errorcorrection computational methods.

Jorge Juan Pastor received the B.S., M.S., and Ph.D. degrees in mechanicalengineering from the Universidad de Zaragoza, Zaragoza, Spain, and a post-graduate certificate in robotics and computer vision from Universidad de Ali-cante, Alicante, Spain, in 2001, 2003, 2009, and 2007, respectively.

He is currently an Associate Professor of Mechanical Engineering withthe Department of Design and Manufacturing Engineering, Universidad deZaragoza. He is with the Manufacturing Engineering and Advanced MetrologyGroup (GIFMA), which is a member of the Aragón Institute of EngineeringResearch (I3A) at the university. His research interests include 3D robotics andgeometric vision, manufacturing processes optimization and automation, 3Dstereo measurement, and developments in precision mechanics and microtech-nology.

Juan José Aguilar received the B.S., M.S., and Ph.D. degrees in industrial en-gineering from the Universidad de Zaragoza, Zaragoza, Spain, in 1988, 1990,and 1994, respectively.

He is currently an Associate Professor with the Department of Designand Manufacturing Engineering, Universidad de Zaragoza. He is the groupcoordinator of the Manufacturing Engineering and Advanced Metrology Group(GIFMA), which is a member of the Aragón Institute of Engineering Research(I3A) at the university. His research interests include manufacturing processesoptimization and automation and developments in precision mechanics andmicrotechnology.

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Teaching Camera Calibration by a Constructivist Methodology