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Oen Archive Toulouse Archive Ouverte (OATAO) OATAO is an oen access reository that collects the work of Toulouse researchers and makes it freely available over the web where ossible.

1 Oen Archive Toulouse Archive Ouverte (OATAO) OATAO is an oen access reository that collects the work of Toulouse researchers and makes it freely available over the web where ossible. This is an author-deosited version ublished in: Erints ID: 5597 To link to this article:doi: /j.otlaseng htt://dx.doi.org/doi: /j.otlaseng To cite this version: Fazzini, Marina and Mistou, Sébastien and Dalverny, Olivier and Robert, Laurent Study of image characteristics on digital image correlation error assessment. (2009) Otics and Lasers in Engineering, vol ISSN Any corresondence concerning this service should be sent to the reository administrator:

2 Study of image characteristics on digital image correlation error assessment M. Fazzini a,n, S. Mistou a, O. Dalverny a, L. Robert b a Ecole Nationale d Ingenieurs de Tarbes, LGP, 47 avenue d Azereix, Tarbes, France b Ecole Mines Albi, CROMeP, Camus Jarlard, Albi, France a b s t r a c t Keywords: Digital image correlation Error assessment Saturation Encoding In this aer, errors related to digital image correlation (DIC) technique alied to measurements of dislacements are estimated. This work is based on the generation of synthetic images reresentative of real seckle atterns. With these images, various arameters are treated in order to determine their imact on the measurement error. These arameters are related to the tye of deformation imosed on the seckle, the seckle itself (encoding of the image and image saturation) or the software (subset size). 1. Introduction Digital image correlation (DIC) is an otical full-field measurement technique that was aeared twenty years ago [1 3]. It consists in recording with a camera some digital images of a secimen undergoing an in-lane dislacement field and comuting the image correlation by aroriate software. It is among the most oular otical methods, but it still suffers from a lack of characterization. In this way, very few studies have been conducted. The arameters tested in this investigations are, for examle, the seckle attern [4 7], the subset size [4,6,8,9] or the subset shae function [9,10]. Recently, systematic studies have been roosed by the French CNRS research network 2519 based on synthetic images undergoing a sinusoidal dislacement field [11 14]. These results focus on the effect of arameters that have to be set in a DIC measurement relative to the software, namely subset size, shae function order and image interolation. In this aer, we are going to study the arameters in relation with the encoding of the image: differences between series of 4-bit, 6-bit or 8-bit images (simulate images with high gradients of grey levels) and image saturation (simulate overexosed images), based on images similar to those used by the CNRS research network Digital image correlation shae function in Aramis 2D [15] Digital image correlation allows the measurement of dislacement fields of a lanar surface; a single camera acquires a n Corresonding author. Tel.: ; fax: address: marina.fazzini@enit.fr (M. Fazzini). sequence of images of a lanar object under lane strain. Dislacements of oints distributed over the surface of the object are calculated from the grey-level analysis of the images [2]. Given two images corresonding to two deformation states of an object, to determine the corresondent of a oint and its signature of the first image in the second, a similarity function is used. In ractice, a single grey-level value is not the unique signature of a oint, hence neighbouring ixels are used. From its rincile, the image correlation technique can work correctly only with objects having a surface with a sufficiently random texture. Let f ðx Þ and gðx Þ be the grey levels in the reference and deformed images, resectively of a same material oint, and let x ¼ ðx; yþ and X ¼ ðx; YÞ be the corresonding coordinate vectors. The unknown aarent 2D mechanical transformation F M is such thatu M ðx Þ ¼ X. Perfect advection of the texture would ensure the conservation relation: gðu M ðx ÞÞ ¼ f ðx Þ This mechanical transformation F M can be locally aroximate by a shae function F because the correlation domains (D) are small. Let x 0 ¼ ðu0 ;v 0 Þ be a oint in the centre of the subset D in the reference image, and let x=(u, v) an another oint in this subset. In this oint x, the mechanical transformation is defined by: X ¼U M ðx Þ Uðx Þ ¼ x þwðx Þ where C(x) is the dislacement in the oint x. With a Taylor exansion of this dislacement C(x) about the centre x 0 of the subset D, we can write: Uðx Þ ¼ x þwðx ðx 0Þðx x 0 Þþ 1 2 ðx x 0Þ 2 2 ðx 0Þðx x 0 Þþ... ð1þ ð2þ ð3þ doi: /j.otlaseng

Fig. 1. Examle of simulated synthetic images: reference (a) and deformed images (=260 ixels, (b) a=0.02, (c) a=0.1). Fig. 2.

Truncation at various orders leads to different shae functions for the dislacement field comonents along horizontal and vertical axes, resectively in the subset.

3 Fig. 1. Examle of simulated synthetic images: reference (a) and deformed images (=260 ixels, (b) a=0.02, (c) a=0.1). Fig bit (a), 6-bit (b) and 8-bit (bit) reference images and grey-level histogram. Truncation at various orders leads to different shae functions for the dislacement field comonents along horizontal and vertical axes, resectively in the subset. Zero-, first- and secondorder shae functions have already been tested in the work of the French CNRS research network 2519 [14]. In this study, the DIC software used (Aramis 2D s [15]) rovides a first-order shae function that corresonds to the following bilinear transformation: Uðx Þ ¼ a! 1 þa 2 ðx x 0 Þþa 3 ðy y 0 Þþa 4 ðx x 0 Þðy y 0 Þ a 5 þa 6 ðx x 0 Þþa 7 ðy y 0 Þþa 8 ðx x 0 Þðy y 0 Þ The values a 1 and a 5 describe the translation of the facet s centre; the others describe the rotation and the deformation of the facet. Then, the general algorithm consists in determining these arameters (a i ) by minimizing a correlation coefficient C(F), which measures the disarity between the grey-level distribution over the domain D in the reference image and the distribution over the deformed image back converted to the reference image according to F, as U D ArgminCðUÞ U A D ð4þ ð5þ The correlation coefficient used by Aramis 2D s reads: R D CðUÞ ¼ 1 ðf ðx iþ f ÞðgðUðx i ÞÞ gþdx qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D ðf ðx iþ f Þ 2 R dx D ðgðuðx iþþ gþ 2 dx with f ¼ R Df ðx Þdx 3. Results analyses rocedure As for the work of the French CNRS research network 2519 reviously discussed, the sets of synthetic seckle-attern images are obtained using the TexGen software [16]. These images are generated with a continuous noise function created from a Perlin s coherent noise. This function allows you to simulate a seckle attern as realistic as ossible sread over 256 grey levels with control of the seckle size, which roduces synthetic 8-bit seckle-attern images as realistic as ossible to DIC seckle atterns. The set of deformed images is obtained assuming only an unidirectional sinusoidal dislacement, which is given by U ðx Þ ¼ asin 2x e x ð7þ ð6þ

Subset size s is equal to (a) 15, (b) 21 and (c) 31 ixels resectively (4-bit, 6-bit and 8-bit).

4 Fig. 3. Reference images for the 3 sets and grey-level histogram. (a) high saturated set, (b) saturated set and (c) standard set). Fig. 4. Standard deviation of the dislacement errors normalized by 4 2 as 2 / as a function of eriod for various strain amlitudes a. Subset size s is equal to (a) 15, (b) 21 and (c) 31 ixels resectively (4-bit, 6-bit and 8-bit). U ;x ðx Þ ¼ 2acos 2x e x ¼ U max ;x cos 2x U ;xx ðx Þ ¼ 42 a sin 2x e x ¼ U max ;xx cos 2x where is the eriod in ixel and a the amlitude. Chosen values for the amlitude a and for the eriod are aa{0.02, 0.01, 0.005, 0.001} and A{10, 20, 30, 60, 130, 260, 510} ixels, resectively for ixel images. Note that corresonding values of the maximum strain are 12.6%, 6.3%, 3.1% and 0.6%. Fig. 1 shows some examles of both reference and deformed images. They are e x e x ð8þ ð9þ obtained for =260 ixels and a=0.1 (U, x max =62.8%) and 0.02 (U, x max =12.6%). A reference set is created with a grey-level histogram adjusted to obtain a broad distribution covering all 256 grey levels (Fig. 2(c) and Fig. 3(c)) and an autocorrelation radius of 2.2 ixels, radius at half height of the normalized autocorrelation function of the reference image, generally admitted as a value of the mean seckle grain size. As a first ste, 4- and 6-bit like images are created. Aramis 2D s software uses only 8-bit images; that is why 16 grey levels of the 4-bit images and 64 grey levels of the 6-bit images vary between 0 and 255 (Fig. 2(a) and (b). This set simulates images more or less contrasted.

In a second stage, images simulating some more or less imortant light saturation generated by multilying each ixel of each image of the reference set (reference and deformed images) by a factor of 2

5 In a second stage, images simulating some more or less imortant light saturation generated by multilying each ixel of each image of the reference set (reference and deformed images) by a factor of 2 (Figs. 3(b)) or 4 (Fig. 3(a)), values uer than 255 are set to the 255 level. 4. Results Dislacements are calculated at all locations of a regular square grid defined in the initial image, with itches (sx; sy) such that subsets at adjacent ositions do not overla, thus ensuring the statistical indeendence of the corresonding errors. In ractice sx=sy=s+1, where s is the subset size. Square subsets of different sizes s are used, namely, 15, 21 and 31 ixels. Measured dislacements U mes are comared to imosed dislacements U th located at the centre of the subsets. The standard deviation s U of dislacement errors (U mes U th ) at the Fig. 5. Comarison of the asymtotic standard deviation of the dislacement errors normalized by 4 2 as 2 / as a function of the tye of image. centre of a subset is calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P ðu s mes U U ¼ th Þ 2 ð P ðu mes U th ÞÞ 2 nðn 1Þ ð10þ Fig. 4 shows the standard deviation normalized by a factor roortional to the square of the subset size and to the maximum second gradient of the dislacement as a function of eriod for 4-, 6- and 8-bit images. It has been shown in [11 14] that these curves can be analysed considering three zones. In the first one for small eriods (tyically for rs), the software evaluate nothing else than the standard deviation of the dislacement itself. When the eriod is greater than about 5 s, an asymtotic value k a can be reached. This asymtotic value is indeendent of a and s and is around The second zone is the transition zone between the other two. However, it has been shown that for small subset and small strains, asymtotic value is not reached and is indeendent on and a. It is clearly seen that a decrease in the encoding deteriorates the measurement. Fig. 5 shows that the asymtotic value k a of 6-bit like image results are uer but close to 8-bit image results, and 4-bit like image results are bad (excet for the largest subset). For subset sizes of 15 or 21 ixels, the error value for large eriod (smallest strain gradient) is clearly deendant on the dynamic of images. Indeed, k a values for 8-bit images are lower than k a values for 4-bit images. When a larger subset size is considered, k a values are much closer and the coding influence becomes negligible. As there is less information in 4-bit like images than in 8-bit images, for a giving error it needs a larger subset size that decreases the satial resolution. Fig. 6 shows the standard deviation normalized by a factor roortional to the square of the subset size and to the maximum second gradient of the dislacement as a function of eriod for the reference image set and for image set where each ixel of each image of the reference set is multilied by a factor of 2 or 4 and limited to 255 grey level (saturated images). In this case, an asymtotic value k a is never reached with the smallest subset size (Fig. 7). In fact, when the image is very exosed to light, size of the Fig. 6. Standard deviation normalized by 4 2 a/ as a function of eriod for various strain amlitudes a. Subset size s is equal to (a) 15, (b) 21 and (c) 31 ixels (saturation).

decrease in encoding deteriorates the measurement by 2. The results of the second set show that an overexose of the seckle deteriorates the measurement by 10.

6 decrease in encoding deteriorates the measurement by 2. The results of the second set show that an overexose of the seckle deteriorates the measurement by 10. Acknowledgements This work was erformed within the French CNRS research network 2519 Full field measurement and identification in solid mechanics. References Fig. 7. Comarison of the asymtotic standard deviation of the dislacement errors normalized by 4 2 as 2 / as a function of saturation. white seckle grains increases (level 255) as size of the seckle grains of other grey level decreases. This results to images comosed of small black atterns and large white atterns. Image correlation cannot work in this case if small subset size is used. The small subset/small amlitude effect reviously seen in the Fig. 4 becomes more imortant with saturated images and can be found also with the larger subset. It is necessary, in this case too, to use subset sizes much more imortant to get an asymtotic value, but which worked in a more imortant error due to the subset size itself. 5. Conclusion The aim of this work is to characterize the software in order to facilitate its use. Thus, different controllable arameters in a conventional use of the system (i.e. on real images catured with CCD) have been tested here. By creating well-controlled synthetic images, we are able to vary some arameters such as the tye of encoding (4-, 6- or 8-bits) and the saturation indeendently. The DIC software treatment has been realised with different subset sizes, in order to highlight the relationshi between image arameters and the DIC software arameters. With deformed images obtained assuming a unidirectional sinusoidal dislacement with different values for the amlitude and the eriod, we created a set of images with a strong gradient of grey level (for 4- and 6-bit like images) and a set of images that simulates overexosed seckle. The results of the first set show that a [1] Peters W, Ranson W. Digital imaging techniques in exerimental stress analysis. Ot. Eng. 1982;21(3): [2] Sutton M, Wolters W, Peters W, McNeill S. Determination of dislacements using an imroved digital correlation method. Image Vision Comut. 1983;1: [3] Sutton M, McNeill S, Helm JD, Chao YJ. Advances in two-dimensional and three-dimensional comuter vision. In: Rastogi PK, editor. Photomechanics. Berlin, Germany: Sringer; [4] Lecomte D, Smits A, Bossuyt S, Sol H, Vantomme J, Hemelrijck DV, Habraken A. Quality assessment of seckle atterns for digital image correlation. Ot. Lasers Eng. 2006;44: [5] Triconnet K, Derrien K, Hild F, Batiste D. Parameter choice for otimized digital image correlation. Ot. Lasers Eng. 2009;47: [6] Haddadi H, Belhabib S. Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique. Ot. Lasers Eng. 2008;46: [7] Pan B, Lu X, Xie H. Mean intensity gradient: an effective global arameter for quality assessment of the seckle atterns used in digital image correlation. Ot. Lasers Eng., in ress, 2009, doi: /j.otlaseng [8] Yaofeng S, Pang JH. Study of otimal subset size in digital image correlation of seckle attern images. Ot. Lasers Eng. 2007;45: [9] Lava P, Cooreman S, Coieters S, De Strycker M, Debruyne D. Assessment of measuring errors in DIC using deformation fields generated by lastic FEA. Ot. Lasers Eng. 2009;47(7 8): [10] Schreier H, Sutton M. Systematic errors in digital image correlation due to undermatched subset shae functions. Ex. Mech. 2002;42: [11] Bornert M. Resolution and satial resolution of digital image correlation techniques. Photomechanics. France: Clermont-Ferrand; [12] Orteu J.-J. and Robert L., Estimation of digital image correlation (DIC) erformances, International Conference on Exerimental Mechanics (ICEM 13), Alexandrouolis (Greece), 1 6 July [13] Orteu J.-J., Digital Image Correlation (DIC) Error Assessment, SEM Conference on Exerimental and Alied Mechanics, Sringfield, Massachusetts, USA, 4 6 June [14] Bornert M, Brémand F, Doumalin P, Duré JC, Fazzini M, Grédiac M, et al. Assessment of digital image correlation software ackages. Ex. Mech. 2009;49(3): [15] Aramis 2Ds software. GOM-Gesellschaft für Otische Messtechnik mbh, Otical Measuring Techniques, htt:// [16] Orteu J.-J., Garcia D., Robert L., and Bugarin F. (2006) A seckle-texture image generator. Proceedings of the Seckle 06 international conference, Nîmes, France.

Error assessment in Image Stereo-correlation

EPJ Web of Conferences 6, 6 31009 (2010) DOI:10.1051/epjconf/20100631009 Owned by the authors, published by EDP Sciences, 2010 Error assessment in Image Stereo-correlation M. Fazzini 1,a, S. Mistou 1 and