Non-invasive Subpixel Method for Frequency Measurements Based on Image

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1 11th European Conference on Non-Destructive Testing (ECNDT 2014), October 6-10, 2014, Prague, Czech Republic More Info at Open Access Database Non-invasive Subpixel Method for Frequency Measurements Based on Image Julian ESPINOSA 1,2, Belen FERRER 3, Ana B ROIG 1, Jorge PEREZ 1,2, Pablo ACEVEDO 2, David MAS 1,2 1 Dept Óptica, Farmacología y Anatomía, Universidad de Alicante; Alicante, Spain julian.espinosa@ua.es, anabelen.roig@ua.es, jorge.perez@ua.es, david.mas@ua.es 2 IUFACyT, Universidad de Alicante; Alicante, Spain; pablo.acevedo@ua.es 3 Dept Ingeniería Civil, Universidad de Alicante; Alicante, Spain; belen.ferrer@ua.es Abstract We present a non-contact technique to measure object vibrations of small amplitude. The method is based on image acquisition and multilevel thresholding. Just using a video camera with high enough acquisition rate, the technique allows non-invasive measuring of object vibration frequencies. The technique has been successfully implemented with a standard consumer camera and validated through different experiments. Keywords: structural health monitoring, civil engineering, image processing, Vibration analysis 1. Introduction Accelerometers are usually preferred though the methods existing for measuring vibrations. These devices register the local acceleration of the specific point of the specimen where they are attached. However, they are difficult to use when the specimen is not accessible due to the object itself or the surrounding conditions [1]. Alternatively, Doppler vibrometers are used as non-contact devices but they result expensive for many applications [2]. An additional drawback for both methods is that they are only capable of taking measurement from a single point. Image based methods are becoming a reliable alternative to non-contact measurement of movement and vibrations. Most are based in object recognition and tracking through digital image correlation [3]. They are easy to implement but they require of high-resolution cameras. This handicap is overcome by the sub-pixel methods [4], which improve the physical resolution of the acquiring device, theoretically up to more than 50 times [5]. Additionally, these systems capture a relatively large area and not only a single point so multipoint measurement at any location within this area is theoretically possible. Unfortunately, many of the existing methods need a target attached to the specimen. The target is then recognized and tracked through a video sequence. Although the attachment is done with soft adhesives and measurements are taken from a distance, the method cannot be considered non invasive, since access to the object is needed. Additionally, many objects to be measured may be delicate and any object cannot be attached on them. In this paper, we propose a targetless sub-pixel technique for measuring frequency vibrations of standard objects. From a captured frame, our method consists of taking a small region of interest (ROI) where light intensity variation due to object vibration is expected to happen. Instead of considering small variations of intensity, the analysis is done at different thresholded levels so only binary information is considered. Variation in the number of white pixels inside the region is tracked in order to obtain the frequency of the vibration movement. The method can be applied on one or multiples ROIs simultaneously, thus giving complete information about the object movement.

2 2. Methods Binary thresholding on a digital image provides the number of pixels whose luminance value is equal or lower than a selected value. The result of this operation is directly connected with the object geometry and the illumination structure. A subtle change in the illumination slightly modifies the appearance of the object. Although this change may not be noticeable when looking the whole scene a binary threshold in the proper level will show this information as a change in the active pixels. Therefore, changes of a single pixel at one specific level can be found and tracked even if it is produced at a sub-pixel scale [6]. Standard objects usually present complex profiles and a relatively wide dynamic range. By simplicity, we will consider gray scale images (figure 1a), although the concepts can be easily extended to color scenes. The first approach to gray scale images consist of reducing them to binary images by selecting a proper thresholding level (figure 1b) according to the histogram, statistical values (maximum, minimum, median...) or any other criterion. We propose here to explore pixel changes at different levels simultaneously. Therefore, if the object moves or vibrates, it is very likely that several brightness levels are affected. For example, figure 1c shows the result of a 0.25 px displacement to the right. One can see clear differences respect to figure 1b in the thresholded levels. Figure 1. a) Gray scale image. b) Thresholded and discretized image. c) Thresholded and discretized image displaced 0.25 px Changes in the image can be due to the illumination or to the object itself. If the object is moving, a specific pixel in the image will change due to the object displacement. If the object is vibrating, these changes will be periodic and easy to detect In case of vibration, pixel changes are periodic so information about the movement frequency can be obtained from them. By counting the pixel variations in a single level we obtain a signal whose Fourier transform will provide the frequency of the movement. Of course the movement can affect to more than one level, so the information of the different levels can be combined an take advantage of the redundancy to increase the signal to noise ratio. Some considerations must be done before showing the real performance of the method. The first one concerns the number of grey levels to be analysed. If we consider an eight bits gray image, although all 256 levels are available a full analysis is impractical and will take a high computational time. Light changes will only affect to few levels and adding more of them will result in a more noisy result. Thus a small number of levels will suffice the frequency analysis. We also do not need to consider to whole image, but only a small region of interest

3 where the movement is expected to be more evident. We also must select the area with the highest contrast, so the probability of finding a light change is increased [7]. In summary, the method will be applied as follows: first, one (or multiple) ROI in the video sequence must be selected. All frames are binary thresholded to a predetermined number of levels. In all our experiments, we always used eight levels. The pixel variations in each level are accounted through all the sequence and a Fourier analysis is performed on the obtained vector, thus obtaining eight Fourier spectra per ROI. These spectra are then averaged so all the information is gathered together and analysed at once. 3. Results We have applied the method to measure the frequencies of different objects. In the first example, we have measured the vibration of a tuning fork designed for 440 Hz. The ROI was selected in the point with the higher expected amplitude movement. The binarization of the image was done at 8 different threshold levels. Fig. 3 shows the result of binarization in 8 different levels. For each one of these level there is a temporal series of images in which some pixels periodically changes from active to non-active. Fourier transform for each one of these series is shown in fig. 4. For all levels, a 441 Hz frequency was clearly obtained. In this case, all information from the different levels was clear and redundant, but it has to be taken into account that this is a very particular case in which a unique and very clear frequency appears in the object, and it is not the general case that can be found in real world. Fig. 3: Binarized image for 8 different thresholds in the ROI taken for the tuning fork. Fig. 4: Fourier transform of signals obtained for 8 different thresholds for the tuning fork.

4 In Figure 3, we show the case of a vibrating bar. In this case, we applied our method to ROIs covering the entire image. We can see that the method detects all points in the image vibrating at the same frequency and we found that the bar was vibrating at a frequency of 260 Hz. Figure 3. Vibrating bar. Points vibrating at 260 Hz are highlighted. We would like to underline here that in the two examples shown, sequences have been acquired at 1000 fps with a Casio EX-ZR1000, a pocket camera that can be found in the market at around 300. Output of the camera is coded as an AVI-JPEG file, so one can see a small degradation in the borders due to the lossy compression. Although this noise also degrades our signal and adds some noise to the Fourier spectrum, the method is able to find the frequency peaks of the main vibration modes Last experiment is a real application outside of the laboratory. In 2011, an earthquake of 5.1 moment magnitude scale happened in Lorca, a small city in Spain [8]. The town hall of this city is a building in which the slabs are held to the wall by some tension bars, as it is shown in fig. 7. After the earthquake, some tension bars were apparently loosened and that caused fear to the users of the building. Therefore, the task was to determine the tension in the bars, to compare with the expected one and obtain a security factor for the building. As the frequency of a bar is related with the tension that it is supporting, measuring the vibration frequency of the tension bars can solve the problem. On the one hand, the frequency of a metallic bar can be measured using accelerometers. These devices have to be glued to the bars in order to measure acceleration. Fourier analysis of accelerometer gives the frequency. However, on this case the use of accelerometers was very complicated, because the bars were not reachable from each slab and therefore it was needed the use of an elevator platform. Additionally, the building is opened to the public and it is just below the bars to be analysed, as it can be seen in fig. 7. All this made very difficult the use of accelerometer; even in the highest slab it was impossible to use it because the elevator platform could not reach that slab. On the other hand, the frequency also can be measured using our method. The only needed setup is one tripod holding the camera located in the slab. The movement of the bars was imposed just hitting them with a rubber mallet while a camera recorded it. Once the sequence is recorded, the analysis can be done to every point in the scene, which is another big

5 advantage of this method. On fig. 8(a), four different ROI are allocated in four different bars in the scene. For all these ROI, the frequency obtained is shown in fig. 8(b). The frequencies obtained for all bars were between 20 and 24 Hz. Taking into account the section of the bars, the tension could be determined and it could be concluded that the structure is safe. Fig. 7: Tension bars holding the slabs in the Town Hall of Lorca (Spain) Fig. 8: Frequencies obtained in four different bars by image processing in Town Hall of Lorca (Spain) 4. Conclusions In this communication, we have presented a method for measuring vibration frequencies of moving objects with a low cost camera and with subpixel resolution [7]. With a camera we obtain a high-speed sequence of a moving object. Then, by selecting a convenient region of interest, the frames are thresholded and the number of pixel variation within this region for each frame is accounted for all the sequence. With this we obtain different one-dimensional signals whose frequency spectra are obtained through the Fourier transform. The spectra are then averaged and a single measurement is obtained for each ROI.

6 The experiments show that the method is robust and allows simultaneous measurement of different regions within the same sequence. It is even possible to obtain a color vibration map that describes the movement of an object at a glance [9] Acknowledgements The authors acknowledge the support of the Spanish Ministerio de Economía y Competitividad through the project BIA , the Generalitat Valenciana through the project PROMETEO/2011/021 and GV/2013/009 and the University of Alicante through the project GRE A.B. Roig acknowledges the financial support from CajaMurcia References 1. J J Lee, Y Fukuda M. Shinozuka, S Cho and C Yun, 'Development and application of a vision-based displacement measurement system for structural health monitoring of civil structures', Smart Struct. Syst. Vol 3, No 3, pp , H N Nassif, M Gindy and J Davis, 'Comparison of laser Doppler vibrometer with contact sensors for monitoring bridge deflection and vibration', NDT Int. Vol 38, No 3, pp , F Hild and S Roux, 'Digital Image Correlation: from displacement Measurement to identification of elastic properties a review', Strain Vol 42, No 2, pp 69 80, J C Trinder, J Jansa and Y Huang, 'An assessment of the precision and accuracy of methods of digital target localization', ISPRS J. Photogramm. Vol 50, No 2, pp 12 20, D Mas, J Espinosa, A B Roig, B Ferrer, J Perez and C Illueca, 'Measurement of wide frequency range structural microvibrations with a pocket digital camera and sub-pixel techniques', Appl. Opt. Vol 51, No 14, pp , D Mas, B Ferrer, J T Sheridan and J Espinosa, 'Resolution limits to object tracking with subpixel accuracy', Opt. Lett. Vol. 37, No 23, pp , Ferrer B, Espinosa J, Roig AB, Perez J, Mas D Vibration frequency measurement using a local multithreshold technique Opt. Express, vol 21, nº 22 pp , Lorca earthquake at (last visited on 08/07/2014). 9. J Espinosa, B Ferrer, D Mas, J Perez and A B Roig, 'Method and system for measuring vibrations', Patent pending nº P ( ).