The optimisation of OCE through Digital Image Correlation on an OCT image stack

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The optimisation of OCE through Digital Image

Correlation on an OCT image stack

Vince Mens July 9, 2020

STUDENTNUMBER 12000809

RESEARCHINSTITUTE Biophotonics and Biomedical Imaging Group

FACULTY FNWI and FEW

UNIVERSITY University of Amsterdam and VU Amsterdam SUPERVISOR dr. Imran Avci

SECOND EXAMINER prof. dr. Ton van Leeuwen DAILY SUPERVISOR Luca Bartolini

EXERCISE Thesis Bachelor Project Physics and Astronomy

EC 15

VERSION Final version

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A change in the mechanical properties of skin can be caused by a skin or collagen dis-ease. A measurement of the change in mechanical properties of the skin can therefore be used in the diagnosis of some skin and collagen diseases. Optical Coherence Tomography Echography (OCE) is a method to track and spatially resolve deforming by comparing OCT tomograms at different times. The internal displacement caused by the deformation can be measured with Digital Image Correlation (DIC) to generate a displacement field that is the basis for the measurement of mechanical properties. That’s why this study presents an implementation of OCE through Digital Image Correlation of an OCT image stack in which the deformation of skin is captured. The python libraryµDIC has been used where the correlation is based on finite element discretization. We adaptedµDIC to our needs to optimize the correlation process by looking at the influence of a number of correlation parameters.

• Populair wetenschappelijke samenvatting:

De elasticiteit van de huid is een voorbeeld van een mechanische eigenschap die een verandering ondergaat bij enkele huid en collageen aandoeningen. Een meting van de verandering van de elasticiteit van de huid kan daarom worden gebruikt bij de diagnose van de desbetreffende aandoeningen. Om de elasticiteit van de huid te kunnen meten, is het allereerst van belang om de interne verplaatsing van de huid te meten wanneer deze wordt vervormd. Een vervorming van de huid kan makkelijk plaatsvinden door een opwaartse zuigkracht en deze vervorming wordt in ons geval vastgelegd met de beeld-vormingstechniek Optical Coherence Tomography (OCT). Het doel van dit onderzoek is om zo nauwkeurig mogelijk de interne verplaatsing te meten tussen de verschillende OCT afbeeldingen van de huid. Om de interne verplaatsing te meten is er in deze studie gebruik gemaakt van Digital Image Correlation. Bij deze mehtode wordt de huid in een onvervormde afbeelding opgedeeld in een bepaald aantal elementen die uit een stukje huid bestaan. In de vervormde afbeelding gaan de elementen op zoek naar het stukje huid waarover ze waren geplaatst in de onvervormde afbeelding. Aan de hand van de vervorming en verplaatsing van de elementen kan de interne verplaatsing van de hele huid worden bepaald.

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1 Introduction

In some tissues, changes in mechanical properties may play a role in human health. An exam-ple of such a tissue is the skin. The skin can be considered as a comexam-plex substrate possessing elastic, viscous and plastic properties (1). A change in one of the mechanical parameters such as elasticity, viscoelasticity or stiffness can be caused by a skin or collagen disease. A quanti-tative measurement of the change in these mechanical properties of the skin can therefore be used in the diagnosis of some skin and collagen diseases. The deformation of a tissue that has to take place in order to measure the mechanical properties can be visualized by an imaging technique. A measurement of the mechanical properties of the skin has the advantage of being accessible. There is no need to look deep inside the body and the deformation can easily take place due to an external factor.

Optical Coherence Tomography (OCT) is one of the imaging techniques that can be used for skin imaging. In a simple sense, OCT is based on the same principle as ultrasound imaging. The difference is that OCT uses light waves instead of sound waves. Due to the high resolution that can be obtained with OCT compared to other imaging techniques, it is also used in elas-tography down to the level of cell clumps. In elaselas-tography a tissue is loaded with a mechanical stimulus so that elastic properties can be mapped. The combination of OCT and elastography is called Optical Coherence Tomography Elastography (OCE). Although OCE was first used in 1998 the scientific restart didn’t seem to come until about 2005 (2). At this moment, it seems that OCE has a promising future in measuring mechanical tissue properties. However, there are also some factors that slow down progress. In this method, the resulting deformation of the tissue, caused by the mechanical stimulus, can be tracked and spatially resolved by comparing OCT tomograms at different times. The measurement of the degree of deformation, together with the choice of appropriate assumptions for the distribution of stress enables the mapping of the properties of tissue, such as strain or elasticity within the tissue.

With the use of OCE, a quantitative measurement of the elastic properties of skin can be made. Due to the relatively high resolution that can be achieved with OCE which is accompanied by a penetration depth of a few millimetres, OCE is a suitable technique to image movement at the skin-level. Moreover, OCE is also a non-invasive imaging technique so the deformation that is caused by a mechanical loading is not affected by the measurement.

Digital Image Correlation (DIC) can be used to conduct quantitative research to the internal displacements between consecutive OCT tomograms. DIC is a method that obtains the internal displacement field by looking for the one that provides maximum correlation between consecu-tive images. The determination of a correct displacement field is at the basis of a quantitaconsecu-tive measurement of the mechanical properties. That’s why this study presents an implementation

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Figure 1: A graphical representation of an OCT interferometer. Light from a broadband or swept source (1) is separated by a coupler (2). The two signals propagate through a reference arm (3) and a sample arm (4) where the signals eventually are reflected. In the reference arm, this reflection is caused by a reference mirror at a known distance. At the end of the sample arm, the light will be partially scattered back at different layers of the sample. The back-reflected signals are mixed in the same coupler and create an interference pattern at the output, which is measured with a photodetector (5). On the basis of this interference pattern, an axial scan (A-scan) can be established. By using the Galvanometric mirror (GM), an A-scan of the sample can be made from multiple positions, ultimately creating a 2D image, called B-scan.

of OCE through Digital Image Correlation of an OCT image stack acquired while a suction of 500 mbar was applied to skin. The sample was the thumb fingertip of a volunteer. The DIC algorithm was taken from an open-access Python library (4), which we adapted to our needs and for which we found optimal settings by a basic convergence analysis.

2 OCT

OCT is an non-invasive imaging technique that has been used in recent years and has much to offer (3). A schematic drawing of an OCT setup is shown in fig 1. The system explains the basic principle that applies to all methods of OCT. First of all, light from a broadband or swept source is separated by a 50 / 50 fiber optic coupler. The light is therefore split into two arms: reference arm and sample arm. The reference arm simply acts as delay line for the signal: a mirror reflects the signal back into the coupler. At the end of the sample arm, the light is focused perpendicularly onto a sample; the backscattered signal is collected and guided again through the coupler. The two reflected signals are mixed in the coupler and create an interference pattern, which is measured with a photodetector (5). The interference pattern is then deconvoluted to obtain the axial (A-scan), a line that reports the amount of light reflected from each depth into the sample. A Galvanometric mirror (GM in the figure) steers the beam on the sample, so that A-scans can be acquired at different locations. Eventually, those A-scans be juxtaposed to create a 2D image, called B-scan. By using light in the near-infrared, a resolution

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Figure 2: An example of a mesh over one of the OCT tomograms. This mesh is made up of 14 x-elements multiplied by 6 y-elements.

between 5 and 20_µm can be achieved with a penetration depth up to a few millimetres.

3 µ

DIC

To perform the Digital Image Correlation (DIC), we used the Python packageµDiC:https: //pypi.org/project/muDIC/. µDIC is a toolkit for the correlation of coordinates between a deformed image and a reference image. The correlation of coordinates enables the measure-ment of elastic properties of the imaged sample. A whole stack of images can then be analysed by pair-wise correlation. This section will describe how the DIC process works in_µDIC. Fur-thermore, a description will be given of the parameters that play a role in the optimization of the DIC.

3.1 Mesh generation

Initially, a mesh is placed over the first OCT tomogram (0-image) in the image set. This is the first reference image. In µDIC there’s a choice to set the vertices of the mesh or to drag the mesh itself as a rectangle. The mesh is divided into a number of elements. The number of x-and y-elements can be set in the code or interactively after dragging the mesh. An example of a mesh is shown in figure 2. The region of interest of the sample is thereby discretized into elements which are linked by (red) nodal points.

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As Olufsen,Andersen and Fagerholt suggested (4), the correlation is performed on the basis of conservation of optical flow. This means that the grayscale values in the reference images have been shifted but preserved. Since it is impossible to track each pixel individually, the finite elements are used. It is therefore the elements that will be tracked in the deformed image. Due to the element tracking, the finite elements deform so that the red nodal points move and have new coordinates. In OCE through DIC we assume has that the pixels will shift collectively due to the mechanical load. That’s why the position of pixels within an element in the deformed image will be determined by interpolation through B-spline basis functions (third polynomial order) and the positions of the nodal points which surrounds the element. As a result, inter-element coordinates x(u,v) can be described as follows:

x(u, v) = A(u, v)n, (1)

where n is a vector contains all the control point positions and A(u, v) is a matrix containing the values of the B-spline basis functions (4). In this method, called finite element discretization, all the elements will be involved at the same time for the correlation process. An advantage of this is that the continuity between the elements is maintained in a natural way (5).

3.2 Correlation criterion

Ideally, each element in the reference image would be perfectly tracked in the deformed image. In real situations we are dealing with imaging artefacts so this will hardly ever succeed. For this reason, the correlation criterion is based on the sum of squared differences (SSD) between the grayscale values of the control point positions in the reference and deformed image. This can be described with the following formula for the SSD which is denoted as R:

R = kIC(n) − IR(n0)k2 (2)

Where ICdenotes the grey-values in the deformed (current) image of the control point positions

n, IRthe grey-values in the reference image of the control point positions n0. Ideally, the value

of the SSD will be 0 for a set of control points in the deformed image. In real situations, the SSD should be minimized for a set of control points. The correct set of control points, which is found within a certain number of iterations with a certain increment size, will be obtained with a Newton Raphson scheme (6).

3.3 Displacement field and cumulative displacement

In the correlation process, by tracking the elements, the nodal points are assigned to new coordinates. The cumulative displacement of each nodal point can be calculated by subtracting

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the coordinates of the corresponding nodal point in the original mesh (initial coordinates). The displacement of each nodal point in each image is stored in a matrix for the x- and y-direction. On the basis of these displacements, a displacement field can be created over the deformed image. The field is a filled contour plot where the colour indicates the x- or y-displacement in pixels relative to the first image of the set. In the code you are able to select the direction, x or y, of the displacement field.

4 Parameters for DIC

4.1 Reference update

Standard OCT can resolve displacements of several microns. Therefore, the real displace-ment between two frames must be greater than that, but not too large as to lose the ability to correlate frames. This problem of a too large displacement may be avoided by performing a reference update after each image in the set. The reference image is reset during a refer-ence update. Each image is then correlated with the previous image. A referrefer-ence update after each image provides that the maximum detectable displacement is the displacement between a pair of images. Since a reference update does not make the correlation time much longer, the correlation of an entire image set is best performed with a reference update after each image. Therefore, this will also be maintained in this study. After how many images there should be a reference update can be set in the code.

4.1.1 Tolerance

The correlation criterion is based on the sum of squared differences (SSD) between the grayscale values in the deformed image and in the reference image. In_µDIC one can indicate for which value of the SSD, convergence is found. A lowering of this tolerance value will mostly be ac-companied with an increase in iterations to find convergence. This will require a longer and further searching for the elements tracking in the deformed image. It depends on the quality of the available images to which value this tolerance should be set. When the amount of itera-tions increase, noise will also be searched for at a further distance. This in turn leads to large, incorrect displacements in the displacement field that are caused by noise.

4.1.2 Mesh size

The third parameter which plays a role in the DIC of the OCT tomograms is the size of the mesh. A measurement of the whole thumb is required and that’s why the mesh at least should be placed over the whole area of the thumb in an OCT tomogram. In an ideal situation,

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el-Figure 3: OCT tomogram where the upper-noise is indicated in the green boxes. This type of noise can be seen in any OCT tomogram.

ements in the mesh that are placed above the thumb profile would not deform. There’s no movement of the thumb there. However, this is not the case in our image set. When looking at OCT tomograms in our dataset, it is noticeable that there is noise above the profile (figure 3). The profile is the outer layer of the thumb. This noise is due to back-reflections from the optics of the OCT probe, and is intrinsic to the measurements. Therefore, if elements in the mesh are found in this region, the algorithm will try and track the displacement of noise. Because the noise is irregular in the OCT tomograms, elements located above the thumb profile are expected to provide non-zero displacement. These elements will look for something that is no longer there in the deformed image. The extent of this displacement coming from noise above the thumb profile can be demonstrated with the displacement field.

This example looks at two consecutive images in our image set. The active suction power dur-ing the imagdur-ing of these OCT tomograms has caused the thumb to be deformed upwards. An upward displacement is therefore expected in the displacement field. As shown in figure 4, the field between two consecutive images (in the example, thumb_093 relative to thumb_092). The deformation is determined with 2 different meshes which will result in two displacement fields. The left mesh in figure 4 overlaps a large part outside the thumb area which means there are a number of elements above the thumb profile. The right mesh overlaps a smaller part outside the thumb area which means there are now fewer elements above the thumb profile. The sizes of the elements are approximately equal in both meshes.

The displacement fields for the different meshes are also shown in figure 4. The largest dis-placement in the thumb comes mainly from the area around the profile. This can be seen in

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Figure 4: In both the situations, left and right, thumb_092 is displayed at the top. In the left case, the mesh is defined at the following vertices: (30,50), (720,50), (30,400) and (720,400). This mesh consists of 20 x 10 elements, making one element 34.5 by 35 pixels. In the right case, the mesh is defined at the following vertices: (30,50), (720,50), (30,335) and (720,335). This mesh consists of 20 x 8 elements, making one element 34.5 by 35.25 pixels. At the bottom, the displacement fields of thumb_093 are shown for the 2 different meshes.

both displacement fields. However, there are also displacements coming from the elements that are above the thumb profile. In addition, the displacement of this upper-noise has the same order of magnitude as the displacement from the thumb profile, which should actually cause the largest displacement. In the displacement field of the right mesh we have to deal with this upper-noise displacement to a much lesser extent. We are experiencing a lot of this upper-noise in our OCT tomograms. To suppress this noise as much as possible, the top of the mesh is only set just above the thumb profile.

4.1.3 Number of elements in the mesh

Previously in this section it was discussed that the size of the mesh was important for the DIC. However, there’s another feature of the mesh which influences the DIC. This refers to the

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num-Figure 5: The expected relationship between the maximum nodal y-displacement and the number of y-elements.

ber of elements in the mesh or the element size. As mentioned before, in DIC an integer can be entered for the number of x- and y-elements. This leads to each element having a fixed length in the x- and y-direction. The smaller the element size, the closer you get to the situation where each pixel will be tracked individually. It has already been made clear that this is not the in-tention, otherwise the correlation process will become too complicated. A proper criterion for the ideal element size or the ideal number of elements can be related to the maximum nodal displacement and the displacement coming from noise. The maximum displacement should not really depend on the number of elements because it is a fixed value. However, a too low value for the number of elements results in a relatively large element size. Due to this large element size, it is unlike that the real maximum displacement will actually be found. The elements are then too generally distributed over the image, causing a too general and too small deformation. That is why a lower maximum is expected when the number of elements is too low. An increase in the number of elements ensures that the elements are less generally distributed across the mesh. An increase in the maximum displacement is therefore expected with an increase in the number of elements. This increase in maximum displacement will continue until a correct and fixed value. From this number of elements onwards, we expect that an increase will no longer cause an increase in the maximum displacement. Although a correct fixed value should be found from a certain number of elements, a too large number of elements leads to a too small

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element size. Due to this too small element size, some elements are mainly looking for noise. This results in incorrect nodal displacements that are likely to be larger than the real maxi-mum displacement. As a result, a certain finite range for the number of elements is expected to be suitable for the correlation process in order to achieve such an accurate and reliable result. When the maximum nodal displacement is plotted against the number of elements, the graph shown in figure 5 is expected. In this graph, the green line shows the relation between maxi-mum nodal displacement and the number of elements. As discussed, the maximaxi-mum displace-ment increases to a certain value creating a range, shown in blue, of the appropriate number of elements. As soon as the number of elements exceeds this range, the maximum displacement is likely to increase irregularly due to noise tracking. As soon as the displacement caused by noise is about the same size as the maximum displacement, the correlation process will become more inaccurate.

5 Method

5.1 Ideal number of elements

In our set of OCT tomograms, the deformation is caused by a suction force. As mentioned before, this suction ensures that the sample is sucked upwards. The part of the sample that will move up first because of this suction is the thumb profile. Based on this movement, the rest of the sample will move along. As a result, the displacement of the thumb profile should be the largest in an upward movement between two OCT tomograms. This should be reflected in the displacement field as the most intense part of displacement. To test the number of elements which is appropriate for the correlation, the maximum displacement is determined for image thumb_093 relative to thumb_092 for a different number of elements. These OCT tomograms are shown in figure 6. The top of the thumb profile is indicated in red. Between these images there has been an upward deformation that is barely visible to the naked eye. Because the correlation has to be performed between consecutive images, it is essential that such small movements are accurately tracked. When measuring the maximum displacement and the displacement field, the number of x- and y-elements are chosen in such a way that the elements have approximately the same length in both directions. So the elements are divided as squares over the mesh. To minimise upper-noise displacement, the mesh has the following limits:

x : 30 → 720 (3)

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Figure 6: Display of the OCT tomograms thumb_092 and thumb_093 where the thumb profile is in-cluded in red.

The number of elements in the y-direction varies from 2 to 14. To ensure that the elements have the same length in both directions, the number of x-elements increases in the following way: 5, 7, 10, 12, 14, 17, 19, 22, 24, 26, 29, 32 & 33. In the correlation between the two images, the tolerance is set to a value of 10. At this value, convergence will be found for each number of elements at the lowest value of the SSD within iteration 0. Because there are no iterations, noise displacements will be suppressed. When eventually the maximum displacement is plotted against the number of elements, a range of elements can be selected that is sufficient for the correlation process of the entire image set.

5.2 Image set

In our image set, the thumb starts in its original position with no suction. After a while the suction is turned on which will deform the thumb upwards to a certain maximum and stay there for a while. At the moment when the suction power is turned off, the thumb relaxes back downwards. Finally, the suction power is turned on again so that the thumb will deform up again to a certain maximum. This entire process is captured in an image set consisting of 900 images

In this OCT measurement two types of deformations are important. These are the upward and downward deformation. For this reason we want to apply the mesh, where the number of elements are within the appropriate range, to the image set to see how these upward and downward deformation can be visualized.

For the upward deformation, a pairwise correlation will be applied to finally determine the dis-placement field of image thumb_085 with respect to thumb_000. These tomograms are shown in figure 7. Between these two images an upward deformation is better visible. The other correlation parameters are set in the same way as when determining the ideal number of ele-ments.

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Figure 7: Representation of the OCT tomograms thumb_000 and thumb_085 between which is an up-ward deformation. At the bottom thumb_351 and thumb_395 are also shown between which is a down-ward deformation.

For the downward deformation, a pairwise correlation is performed that will start at image thumb_351. In this tomogram, the thumb is in its maximum position due to the suction force. Shortly after this, the suction force is turned off, causing the thumb to relax back. Therefore, the displacement field is determined for image thumb_395 with respect to thumb_351. The tomograms are also shown in figure 7.

6 Results

Figure 8 shows the graph where the maximum nodal y-displacement is plotted against the number of y-elements for thumb_093 and thumb_092. We expected an increase in the maxi-mum displacement with an increase in the number of elements until some certain value. This expectation does not entirely match the figure. The graph shows that there is an increase in maximum displacement from 2 to 3 y-elements. A further increase in elements leads to an approximately constant value of the maximum displacement until the number of y-elements exceeds 6. Where the number of elements equals 4 is an outlier. When the number of y-elements increases from 6 to 7, we see another increase in maximum displacement after which a further increase in elements, until the number of y-elements equals 9, leads to a new approxi-mate constant value of the maximum displacement. This situation of again constant maximum displacement is followed by an irregular progression of maximum displacement. The graph shows two ranges where a constant value is found for the maximum nodal y-displacement. A determination of the correct range can be done on the basis of visualization of the

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displace-Figure 8: In this graph, the maximum y-nodal displacement between thumb_093 and thumb_092 is plotted against the number of y-elements in the mesh.

ment fields at the different numbers of elements. Figure 9 shows the displacement field at 5 y-elements (range 1). The thumb profile is the most intense in this displacement field, allow-ing for the largest displacement. Furthermore, there are no intense point displacements here, which means that there is little noise tracking. In figure 10 we also see a displacement field but now at 9 y-elements (range 2). This displacement field shows that the largest displacement is still coming from the profile but there is also a high proportion of noise. This noise is mainly reflected under the thumb profile. Figure 9 shows that these noise displacements occur to a much lesser extent at the bottom of the thumb. Although the size of the noise displacements are smaller than the displacement of the thumb profile in figure 10, it already has a large influence on the displacement field. For this reason and not to make the correlation process too complicated, the number of y-elements can best be chosen to 3, 4, 5 or 6 (range 1). To obtain the displacement field at thumb_085 relative to thumb_000 and at thumb_395 relative to thumb_351, the number of y-elements are therefore set to 3, 4, 5 and 6. The corresponding number of x-elements are 7, 10, 12 and 14.

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Figure 9: A representation of the displacement field at thumb_093 with respect to thumb_092. The field is determined at 12 x 5 elements.

Figure 10: A representation of the displacement field at thumb_093 with respect to thumb_092. The field is determined at 22 x 9 elements.

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Figure 11: A representation of the displacement field at thumb_085 with respect to thumb_000. The displacement field is determined for 4 different numbers of elements.

6.1 Upward deformation

The displacement fields for thumb_085 with respect to thumb_000, where an upward deforma-tion occurred, are shown in figure 11. The figure shows that for each number of elements an upward deformation is found. A significant difference between the thumb profile and the rest of the thumb is noticeable when the number of y-elements equals 3, 5 and 6. When the num-ber of y-elements is 4, this difference is not visible in the displacement field. The value of the maximum nodal y-displacement with respect to thumb_000 is therefore also lower at 4, namely 13.66 pixels. For the number of y-elements equal to 3, 5 and 6 the maximum displacements are equal to 18.52, 18.22 and 20.30 pixels.

6.2 Downward deformation

Here the same has been done as above but now for image thumb_395 relative to humb_351. Between these images, the thumb start in its maximum deformation after which the suction force is turned off. So there is a downward deformation here. The displacement fields for the number of y-elements equal to 3, 4, 5 and 6 are shown in figure 12. For each number of elements a downward deformation is found in the displacement field. This is displayed as a negative displacement in the displacement field. However, a problem arises when the number of y-elements is equal to 3 and 4. Part of the thumb displacement is not visible in the displacement field. Because the mesh is placed completely over the thumb in the initial situation, there is

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Figure 12: A representation of the displacement field at thumb_395 with respect to thumb_351. The displacement field is determined for 4 different numbers of elements.

an accuracy error in the correlation. This may have been caused by the combination of the SSD tolerance being set to a too high value and the elements that are too generally distributed over the mesh. In the figure this problem is visible for each number of elements, where for the y-elements equal to 3 and 4 a large part of the profile does not be included in the displacement field. For the number of elements equal to 5 and 6, this is only the case for a small part of the profile. Since a large part of the thumb profile is not overlapped by the displacement field when the number of y-elements equals 3, a lower value for the minimum displacement, -14.96 is found here. For the number of y-elements equal to 4, 5 and 6 the minimum displacement is equal to -16.49, -17.34 and -17.28 pixels.

7 Discussion

The results demonstrate that at least the direction of the two types of deformation can be visualized with Digital Image Corrlation. For the upward deformation, the selected mesh is sufficient to measure the displacement of the whole thumb area. The mesh does not comply with this for the downward movement as shown in figure 12. This problem can be solved by in-creasing the number of elements so that the correlation become less general. Therefore, when the number of elements is equal to 3 or 4, the correlation cannot be performed sufficiently in the case of a downward deformation. For the upward deformation, however, the displacement

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of the entire thumb does return in the displacement field. But here the question can also be asked whether for each number of elements the correlation has been carried out sufficiently. The value of the maximum displacement seems to reasonably correspond when the number of y-elements equals 3, 5 and 6. Despite this, there is still a clear difference when the displace-ment fields for 5 and 6 eledisplace-ments are compared to the one for 3 eledisplace-ments. On the other hand, at 4 a lower value of the maximum displacement is found. That’s why it is hard to distinguish the profile from the rest of the thumb in this displacement field.

Although we are able to measure the different types of displacement in the displacement field, the whole set of 900 images cannot be pairwise correlated in one run. There will be a certain frame in the set where no reference update can be performed. As a result, the correlation will automatically stop at this frame. During a reference update, the new element coordinates are calculated by inverting the shape function of deformation. In this process an error occurs when the shape function is too complicated. In that scenario the program will take a root of a negative number which crashes the reference update and stops the correlation at that specific frame. An overly complicated shape function is caused by a combination of too many elements in the mesh and too much noise in the image. For our set of OCT tomograms, the correlation of 900 images in 1 run can only be done when the number of y-elements equals 2 and the number of x-elements 5. With the number of elements in the first range, between 85 and 200 images can be correlated in one run. The noise displacements could have a major influence on the complicated shape function. That’s the reason why our set of OCT tomograms contains too much noise. Cropping and filtering could include options to apply to the OCT images for noise reduction. This has not further been examined in this study.

8 Conclusion

The objective of this study was to implement OCE through Digital Image Correlation on an OCT image stack which was acquired while a suction of 500 mbar was applied to skin. In our image set mainly 2 types of deformations were important in the correlation process which were an upward and a downward deformation. Emphasis has therefore been placed on making the correlation of these two types of deformation in an appropriate way. In order to obtain such a result, the number of elements in the mesh is varied and the deformation is visualized by means of a displacement field. From the theory it should follow that there should be a certain range of elements that is sufficient for the correlation process when assessing the maximum displacement and the size of displacement coming from noise. The results show that there is indeed a range of number of elements that is suitable. This range consists of the following

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combination of x- and y-elements: 7 x 3, 10 x 4, 12 x 5, 14 x 6. However, in addition to maximum displacement and the size of noise, the deformation of the displacement field is also taken into account when assessing the number of elements, the results show that when the number of elements equals 7 x 3 and 10 x 4, the correlation is not performed well enough in the sense of an incorrect or too general deformation. From this it can be concluded that for a sufficient result the following combinations of elements are required: 12 x 5 and 14 x 6. At the moment it seems that OCE through Digital Image Correlation is a promising method in the correlation process of OCT tomograms. One point of improvement would be to reduce the noise in the OCT tomograms so that it would also be possible to analyse image sets of unprecedented size.

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The optimisation of OCE through Digital Image Correlation on an OCT image stack