Video analysis helps students to connect physical, mathematical, and graphical models with the phenomena that the models represent and improves student kinematic graph interpretation skills. The widespread availability of easy to use software packages like Logger Pro (Vernier), Capstone (PASCO), and Tracker have led to many introductory physics courses adopting video analysis techniques in the classroom. Such uses include high-speed cameras to study rocket launches and other innovative applications. In this paper, we will look at ways in which some common systematic errors can affect outcomes

Frisch, Kayt E.

Martin, Tim

Zwart, John

English

Video analysis helps students to connect physical, mathematical, and graphical models with the phenomena that the models represent and improves student kinematic graph interpretation skills. The wide-spread availability of easy to use software packages like Logger Pro (Vernier), Capstone (PASCO), and Tracker have led to many introductory physics courses adopting video analysis techniques in the classroom. Such uses include high-speed cameras to study rocket launches and other innovative applications. In this paper, we will look at ways in which some common systematic errors can affect outcomes

Frisch, Kayt

Dordt College

Digital Collections @ Dordt Faculty Work Comprehensive List 3-2020 Systematic Errors in Video Analysis Tim Martin Kayt Frisch John Zwart Dordt University, john.zwart@dordt.edu Follow this and additional works at: https://digitalcollections.dordt.edu/faculty_work  Part of the Physics Commons, and the Science and Mathematics Education Commons Recommended Citation Martin, T., Frisch, K., & Zwart, J. (2020). Systematic Errors in Video Analysis. The Physics Teacher, 58 (3), 195. https://doi.org/10.1119/1.5145415 This Article is brought to you for free and open access by Digital Collections @ Dordt. It has been accepted for inclusion in Faculty Work Comprehensive List by an authorized administrator of Digital Collections @ Dordt. For more information, please contact ingrid.mulder@dordt.edu. Systematic Errors in Video Analysis Abstract Video analysis helps students to connect physical, mathematical, and graphical models with the phenomena that the models represent and improves student kinematic graph interpretation skills. The wide-spread availability of easy to use software packages like Logger Pro (Vernier), Capstone (PASCO), and Tracker have led to many introductory physics courses adopting video analysis techniques in the classroom. Such uses include high-speed cameras to study rocket launches and other innovative applications. In this paper, we will look at ways in which some common systematic errors can affect outcomes. Keywords cameras, parallax, errors, video recordings, students Disciplines Physics | Science and Mathematics Education Comments Online access to article: https://aapt.scitation.org/doi/full/10.1119/1.5145415 This article is available at Digital Collections @ Dordt: https://digitalcollections.dordt.edu/faculty_work/1204 Phys. Teach. 58, 195 (2020); https://doi.org/10.1119/1.5145415 58, 195© 2020 American Association of Physics Teachers.Systematic Errors in Video AnalysisCite as: Phys. Teach. 58, 195 (2020); https://doi.org/10.1119/1.5145415Published Online: 19 February 2020Tim Martin, Kayt Frisch, and John ZwartARTICLES YOU MAY BE INTERESTED INA Measurement of Gravitational Acceleration Using a Metal Ball, a Ruler, and aSmartphoneThe Physics Teacher 58, 192 (2020); https://doi.org/10.1119/1.5145414Rainbows: A Graphical ApproachThe Physics Teacher 58, 152 (2020); https://doi.org/10.1119/1.5145401Video-Based Analysis of the Transition from Slipping to RollingThe Physics Teacher 58, 170 (2020); https://doi.org/10.1119/1.5145407    DOI:  10.1119/1.5145415      THE PHYSICS TEACHER ◆ Vol. 58, March 2020                 195 What, then, are the factors that lead to these non-realistic values in an experiment like the two-dimensional tossed ball experiment? Systematic errors in video analysisTwo variations in the way that students set up and execute the 2D ball toss experiment suggest sources of systematic error that might adversely affect the results of the experi-ment. One common experimental setup places the reference meterstick and the tossed ball different distances from the camera (referred to below as reference length misplacement). A second experimental setup has the ball toss in a plane that is not parallel to the camera’s lens plane (referred to as incorrect camera angle). While avoiding these problems is commonly recommended in places such as Vernier’s Tech Info Library, we wanted to make systematic measurements to determine the size of the errors introduced.4 In addition to these two common setup errors, we wanted to consider the effect of fo-cal length choice for our zoom lens cameras, recognizing that images taken with extreme wide-angle focal length lenses can show significant distortion effects.  As described below, we have made measurements to determine the level of systematic errors that these introduce. These are not an exhaustive set of systematic error sources, and it should be noted that the be-havior of the digital shutter has been observed to play a role in measurement error as well.5 Experimental setup: Camera settingsFor all measurements, we recorded video clips using a Canon PowerShot A1200 digital point and shoot camera. This camera has a modest 4x optical zoom, with a lens effective focal length range of 5.0 mm to 20.0 mm. In each experiment, we used three different focal lengths: wide angle, normal, and telephoto. In keeping with the language used in photography, the 5.0-mm focal length is considered wide angle due to the field of view being wider than that normally seen by the eye, and the 20.0-mm focal length is a telephoto setting,  and a normal setting midway between these two, which yields  an image close to what the eye sees. It should also be noted that whether the lens is considered wide angle or not depends both on the focal length of the lens as well as sensor/film size. The equivalent focal length range for a 35-mm film camera would be 28 mm to 112 mm. All video clips were analyzed using Logger Pro 3.8.6 (Vernier). Reference length misplacementMisplacing the reference length is effectively a parallax problem, since apparent object size is relative to its distance from the camera. For example, if the meterstick was placed closer (than the tossed object) to the camera, the tossed ob-ject would appear to travel a shorter distance than it actually did. We simulated this effect by creating an array of hori-zontal metersticks, with each meterstick an additional 0.2 m Systematic Errors in Video AnalysisTim Martin, Kayt Frisch, and John Zwart, Dordt University, Sioux Center, IAVideo analysis helps students to connect physical, mathematical, and graphical models with the  phenomena that the models represent and improves student kinematic graph interpretation skills.1 The wide-spread availability of easy to use software packages like Log- ger Pro (Vernier), Capstone (PASCO), and Tracker have led to many introductory physics courses adopting video analysis techniques in the classroom. Such uses include high-speed cameras to study rocket launches and other innovative appli-cations.2,3 In this paper, we will look at ways in which some common systematic errors can affect outcomes.A common problem using video analysisWhen performing numerical fits to data to extract phys-ically significant values, we have had mixed results. Video analysis in carefully conducted experiments can result in reasonable parameter values. However, students frequent-ly find substantially different values than expected, even when least-squares fitting measures are good. For example, a two-dimensional ball toss might have a good quadratic fit for the vertical position as a function of time, yet the value of the acceleration due to the gravitational force g from the curve fit can be far from the accepted value. For example, in Fig. 1(a), we have a value of g = 11.74  0.02 m/s2. This value is not only too high, but its uncertainty is too small to explain this high value. A second example [Fig. 1(b)] is a case where the vertical position curve fit yields a value for g that is 12.2  0.3 m/s2, but the horizontal position data show a non-zero acceleration. (a)(b)Fig. 1. Screenshots of two projectile motion video capture and analysis results.196 THE PHYSICS TEACHER ◆ Vol. 58, March 2020different method. Our results are consistent with theirs.6Incorrect camera angleWe simulated the effect of a ball toss that has a motion component away from the camera by rotating the camera a known amount relative to a fixed target (Fig. 4). The target is a rectangle containing an array of black line segments, each 0.250 m in length. The camera was placed on a tripod and set to be at the same height as the center of the target. For each of the three focal lengths, the camera-target distance was adjusted so that the target filled the frame vertically and was centered horizontally when the camera was at 0° from normal incidence. As shown in Fig. 4(b), we then moved the camera to the side so that the angle from the normal increased in 5° steps up to 20°, taking a video clip at each position. In each case the angle is changed such that the left side of the target is further from the camera than the right side. This mimics the variation in apparent distance traveled if an object moves with a component away from the camera.The center horizontal line was used as the reference length, and the apparent length of each of the segments was measured with respect to it. We normalized the measured lengths for all segments by finding the percent difference from the reference length. The most extreme effects occur for the horizontal bars in the corners, with the lower horizontal bars’ results being very close to the upper horizontal bars’ results. Figures 5 through 7 are the plots of apparent length of the upper hor-izontal bars (right and left) vs. angle from normal incidence for the three focal length settings that we used. As Fig. 5 shows, there is little variation in apparent length when the camera is carefully placed so that the target plane is parallel to the camera independent of focal length setting. The farther away from the camera with a slight vertical offset to make them all visible to the camera (Fig. 2). Video clips were recorded with the camera set at wide angle, normal, and tele-photo settings. For each focal length setting, the distance from the camera to the array of metersticks was adjusted to produce an image of the sticks that nearly filled the viewfinder.  The center stick was used as our reference length, meaning that it was selected as 1 m using the set scale tool. The apparent length of each of the other metersticks was measured using the measurement tool. Metersticks that were closer (than the reference) to the camera appeared larger than one meter (Fig. 3), while metersticks that were farther from the camera ap-peared shorter. A reference length offset of 0.2 m in either di-rection affects the apparent length by approximately 5% when using either the normal or telephoto settings and by more than 10% with the wide angle setting. In the ball toss experi-ment presented at the beginning of this paper, this would re-sult in a value of g that was off by 0.5 m/s2 (normal or telepho-to) to 1.0 m/s2 (wide angle). The error becomes much more pronounced with the reference lengths that are offset by 0.4 m from the center length, with the wide angle view showing an error of as much as 40%. This is the effect that is responsible for the large value of g in the experiment shown in Fig. 1(a). It is interesting to note that the results are much more sensitive (i.e., greater errors occur) when the camera is at wide angle, which is the default focal length when the camera is first turned on. Very recently others studied parallax errors by a Fig. 2.  Meterstick array used to study parallax.Fig. 3. Apparent length change due to distance from the camera. Negative distances refer to metersticks that were closer than the reference to the camera.(a)Target(b)Fig. 4.  (a) Target used to study variations in apparent length of segments located in different parts of the field of view. (b) Angle variations.                THE PHYSICS TEACHER ◆ Vol. 58, March 2020                 197 scatter seen at 0° on each of the plots is consistent with the re-peatability of length measurements when using the computer mouse to select segments. As the camera is moved from nor-mal incidence, systematic errors in apparent length become significant. At its most extreme for the camera at its wide an-gle setting and 20° from normal, apparent length varies from –15% to +20% from the left side to the right side at the top or bottom of the field of view. An object moving with constant velocity horizontally across the field of view would appear to have a significant acceleration due to this effect.  Telephoto and normal settings are better behaved. While not graphically displayed, other parts of the target show less variation in ap-parent length but roughly follow the trend shown in Fig. 5.  As these measurements show, care must be taken to min-imize systematic errors that can result if an object’s distance from the camera changes significantly or if the reference length is at a different distance than the object from the cam-era. If one is using a camera with a zoom lens, both problems can be reduced by using a longer focal length lens setting.  When using a wide angle lens, such as that used in most cell phone cameras, particular care is needed when setting up the shot.References1.  R. Beichner, “The impact of video motion analysis on kine-matics graph interpretation skills,” Am. J. Phys. 64, 1272–1277 (Oct. 1996).2.  D. Desbien, “High-speed video analysis in a conceptual physics class,” Phys. Teach. 49, 332–323 (Sept. 2011).3.  D. Brown and A. Cox, “Innovative uses of video analysis,” Phys. Teach. 47, 145–150 (March 2009).4. Vernier Tech Tip, https://www.vernier.com/til/1464/.5.  R. Teese “The Effect of Rolling Shutter on Video Analysis,” pre-sented at the AAPT 2015 Summer Meeting, http://www.aapt.org/Conferences/sm2015/session.cfm?type=other&sort=code.6.  J. Stephens, M. Bostjancic, and T. Koskulitz, “A study on par-allax error in video analysis,” Phys. Teach. 57, 193–195 (March 2019).Tim Martin graduated with his undergraduate physics degree and contin-ued his studies at Knox Seminary in Florida. Tim is currently the pastor at Fron Lutheran Church in South Dakota. He has a passion for seeing how God has revealed Himself through His marvelous work in creation.Kayt Frisch currently serves as an associate professor of biomedical  engineering at George Fox University in the Portland, OR area. Her research interests include using video motion capture to study the dynam-ics of the body during volleyball hitting and the creation and assessment of active, project-based learning experiences in undergraduate physics and engineering classrooms.John Zwart is now professor of physics emeritus. He remains interested in physics pedagogy, especially in the design of lab activities for introduc-tory physics courses. Dordt University, Sioux Center, IA; John.Zwart@dordt.eduFig. 5. Apparent length as a function of angle from normal incidence to the target with the camera lens at its wide angle setting.Fig. 6.  Apparent length as a function of angle from normal incidence to the target with the camera lens at its normal setting.Fig. 7.  Apparent length as a function of angle from normal incidence to the target with the camera lens at its telephoto setting.

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