Software Data
Resume:
Experimental Mechanics (****) **:*** ***
Experimental and Numerical Methods for Exact
Subpixel Shifting
P.L. Reu
Received: 21 April 2010 / Accepted: 27 September 2010 / Published online: 13 November 2010
# Society for Experimental Mechanics 2010
Abstract An approach to quantifying the errors in digital shifted images to calculate the errors [4]. It should be noted
image correlation (DIC) is presented using experimentally that the calculated errors are only as accurate as the
produced images. The challenge arises in creating exact numerical shifting scheme used. Therefore understanding
subpixel shifted images in an experiment. This was the numerical shifting method used is critical to the
accomplished via numerical binning of an ultra-high accuracy of the uncertainty bounds derived.
resolution image. The shifted images are then used for a The importance of having a method of creating images
preliminary analysis of 2D correlation software uncertainty with known displacements and strains has not gone
and investigation of speckle pattern quality. Because it is unnoticed [4]. A number of numerical techniques have
often necessary to use numerically shifted images, for been created to deal with the problem. Pan [5] has created a
uncertainty quantification for instance, the optimum method function where the speckle size and distribution can be
of Fourier shifting is also presented. controlled, this function can then be sampled to create a
speckle image with any translation or strain. Orteu [6] has
Keywords Digital image correlation . Uncertainty created a simulation scheme which seeks to capture the
quantification . DIC . Subpixel experimental aspects of the detector, including noise and
photo-diode fill factor. These numerically generated images
can then be used for testing 2D correlation schemes. Lava
[7] has created a method of overlaying a speckle pattern
Introduction
onto deformations calculated via FE software, again, for the
Digital image correlation (DIC) has become one of the evaluation of 2D correlation methods. These image simu-
standard tools in the solid mechanicist s toolbox. The great lation codes are useful for testing how well the correlation
flexibility of the technique enables DIC to exploit the many codes will work with a given set of image parameters.
advances in imaging technology to make quantitative However, as with any numerical technique, we are still left
measurements; including stereo-microscopes, atomic force with the lingering question of how well it represents an
microscopes, scanning electron microscopes, ultra-high- experiment.
speed cameras, etc. Many of these new imaging technolo- Another challenge is when a particular experimentally
gies produce less than ideal images. Understanding the obtained image needs to be evaluated for its correlation
resultant errors introduced by these images is important. accuracy. This is when numerical interpolation or shifting
schemes, such as the fast Fourier transform (FFT) must be
Numerically shifted images are most often used to do this
[1 3]. For example, DIC uncertainty quantification and the used. The use of a Fourier filter for shifting images to
evaluation of interpolation functions all use numerically evaluate 2D DIC is presented by Schreier in his discussion
of errors in DIC caused by the interpolation function [1].
The method is also used by Cheng in his evaluation of the
P.L. Reu (*, SEM member) b-spline interpolation method [3]. In more recent work it is
Sandia National Laboratory,
also fundamental to the calculation of the 2D uncertainty
Albuquerque, NM 87185, USA
quantification presented in papers by Wang [8, 9], because
e-mail: *****@******.***
Exp Mech (2011) 51:443 452
444
Fig. 1 Prosilica experimental
setup
implicit in the calculation of the DIC errors, are the use of to ensure nothing moved between images. Because the
numerically shifted images. The accuracy of the error plate is never moved, stage errors, non-planarity and lens
estimate, therefore, is only as good as the numerical shift. distortions are not an issue. The speckle patterns were
If a purely experimental technique of obtaining subpixel printed on label paper using a standard laser printer. This
shifted images were available, it would provide a set of data allowed the speckle size and the contrast to be easily
by which to evaluate both the shifting methods and any 2D- controlled. The speckle field was illuminated using a
DIC algorithm implementations. There is of course the variable intensity fiber light source. The experimental setup
difficulty of coming up with a traditional translation is shown in Fig. 1.
experiment that allows subpixel shifting, without introduc- With this simple single camera experimental setup the
ing other experimental uncertainties, such as stage or imaging parameters can easily be changed to create high-
encoder error, motion error, and drift, which can overwhelm resolution images of different contrast and noise levels to
the DIC errors. To avoid this problem, a method of creating later be processed to create images of varying quality. Both
experimentally subpixel shifted images using a high- the noise and the contrast have been shown to be the
resolution camera was created [10]. defining parameters in the final 2D uncertainty [8, 12]. The
This article will outline the experimental setup and contrast was varied by printing out the same speckle pattern
methods used to acquire the super-resolution images and but with different printed contrast. The effective contrast is
how the data was processed to create the exact experimental also controlled via the lighting. The speckle gradients were
subpixel shifted images. This includes information on the controlled by the sharpness of the focus. Changing the
decimation schemes used that best mimic the functioning of focus sharpness effectively introduces a low pass optical
a digital camera. A discussion of numerical shifting filter which removes high-frequency image content such as
hard speckle edges. The noise level of each image was
methods will then be presented ending with an explanation
of the best method for shifting images using the Fourier controlled by adjusting the camera gain and the lighting
filter. A comparison of interpolation filters is discussed together. The real-time image histogram was used to control
using both experimentally and numerically shifted images. the illumination level to keep the contrast as consistent as
Using the experimentally shifted images, a preliminary possible between various images. This is shown in Fig. 2.
analysis of three different 2D DIC codes is conducted. And
finally, optimum speckle patterns are illustrated using
experimentally shifted images.
Experimental Setup
A 16-Megapixel Prosilica GE4900 camera was used for
imaging the speckle pattern. This camera uses a Kodak
KAI-16000 sensor. This high-resolution sensor uses micro-
lenses to maintain a fill factor of 100% [11]. The 12-bit
sensors were used in both 8-bit and 12-bit mode with tiff
format images being saved by the camera control software
with no image compression. A Sigma zoom lens was used
to image various speckle patterns attached to a flat glass Fig. 2 Histogram comparison for the high contrast images with two
plate. All components were rigidly fixed to an optical table different gains (noise levels)
Exp Mech (2011) 51:443 452 445
resolution of the final binned image. In Fig. 3 a 4 4 array
of super-pixels are shown along with three binned images
each with a different shift. Each super-pixel is now a single
averaged pixel value in the binned image. As the index is
changed, it has the effect of causing one row/column to
enter the super-pixel area while one leaves it. This is
mathematically identical to the binning done on the
hardware of some cameras, whereby neighboring pixels
are electronically summed. Numerical binning removes the
problem of the low virtual fill factor and alleviates any
aliasing issues, as long as the original speckles were large
enough in the full-resolution image. The binning alleviates
the aliasing but does not remove it. Aliasing is implicit in
all digital imaging because of the box-car sampling of the
Fig. 3 Illustration of a 4 4 super-pixel array, each 10 10 pixels. The
pixel. Noise in the image is convolved with the box-car
inset figures show the binning decimated and shifted images with the
filter response and will alias components of the broad band
corresponding labeled pixels
noise into the image. This numerical binning, being
The contrast between the black and white speckles was 170 identical to binning in the camera is an ideal representation
of an experimental subpixel shift, analogous to moving
counts for the high contrast image and 30 counts for the
low contrast image (for an 8-bit 255 count image). This the speckle pattern exactly 0.1 pixels between images.
parameter could of course be increased by changing the Furthermore, as the box-car sampling is maintained in the
lighting and the bit depth of the sensor. experimental process, any deleterious aliasing effects which
will be produced in all imaged patterns are accurately
replicated in the binned images. All results presented in this
paper were created using the virtual binning method.
Numerical Binning
To use the decimated images for DIC work, it is
Numerical binning is used rather than a pure decimation important to choose the speckle size appropriately. For this
scheme to avoid some of the problems of aliasing and to case a speckle size of approximately 50 pixels was chosen
more accurately replicate the way a digital camera works. for the full-resolution images, with a 10 reduction in
Decimation does have a use for simulating low fill-factor resolution via the binning, this yields final speckles of
cameras, such as the Shimadzu HPV-2. If decimation is approximately 5 pixels. The full resolution images are
chosen, the deleterious effects of aliasing can be minimized 4,872 3,248 pixels and yield a final resolution of 487 324
by first low-pass filtering the image to remove frequency pixels after processing (see Fig. 4). This gives, in the final
image, a good resolution, if slightly low by today s
content that could be aliased. However, for this paper,
numerical binning, or more simply binning, was used to standards.
more accurately reflect how a digital camera acquires an Using 10 images created from only one high-resolution
image. Numerical binning is done by averaging together the image introduces a complication when using the images to
values of a super-pixel consisting of 10 10 physical pixels. evaluate 2D DIC functionality. Because the first and last
Of course, any number of pixels can be contained in a image are calculated exactly the same way and have exactly
super-pixel, as long as the binning parameters are set the same noise contained in them, they do not accurately
appropriately. Ten was chosen because it gives a good represent an experimental one-pixel shift. This is because
compromise between subpixel shifting and maintaining the two independent images would have independent and
Fig. 4 Numerical binning con-
cept showing the full-resolution
image and the sub-pixel shifted
images
Exp Mech (2011) 51:443 452
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Table 1 Image naming
Full res. image Decimated image Subpixel shift DIC image
Image 2 Image 2 Shift 0 0 Reference Image
Image 1 Image 1 Shift 0 0 Shifted Image
Image 1 Image 1 Shift 1 0.1 Shifted Image
Image 1 Image 1 Shift 2 0.2 Shifted Image
Image 1 Image 1 Shift 3 0.3 Shifted Image
Image 1 Image 1 Shift 4 0.4 Shifted Image
Image 1 Image 1 Shift 5 0.5 Shifted Image
Image 1 Image 1 Shift 6 0.6 Shifted Image
Image 1 Image 1 Shift 7 0.7 Shifted Image
Image 1 Image 1 Shift 8 0.8 Shifted Image
Image 1 Image 1 Shift 9 0.9 Shifted Image
Image 1 Image 1 Shift 10 1 Shifted Image
uncorrelated noise. The DIC software is able to match this are better at fitting the data, or may preferentially filter the
1-pixel shift exactly in the absence of noise. Because of data to cause them to work better or worse with the 2D
this, when using the virtual images for testing DIC, two correlation. It is important to remember that any numeri-
cally shifted image is assuming a grey level function for the
independently acquired high-resolution images are binned.
The images are taken immediately one after the other with pixels; cubic, spline or sinusoidal, are popular examples. It
the camera and pattern rigidly fixed to the optical table to is not clear to this researcher how one would best determine
ensure there is no relative motion. Ten decimated images what function should be used. The fact that the correlation
are then created from a single high-resolution image, each software does a better job of predicting the numerically
with a 0.1-pixel shift. Another high-resolution image is then applied shifts is begging the question. By numerically
used, with a zero shift to create the reference image. This shifting, you are in fact modifying the image and this
process is outlined in Table 1. The only difference between modification may either improve or corrupt the image in
the images is then the noise of the detector and any sub- terms of fitting with the chosen interpolation function in the
pixel shift. This methodology was used for all analysis in correlation algorithm. Another way of thinking of this is
the paper. A confirmation of the validity of this method was that the interpolation or shifting function will be filtering
accomplished by using 11 independent high-resolution the image. This filtering will be changing the image and
images, and creating 11 binned images such that all binned may not accurately reflect the experimentally shifted result.
images were independent. The correlation results were the This is why the need for creating experimentally shifted
same. images is so important. As can be seen Fig. 5, choosing the
correct shifting method can have a large effect on the
apparent errors in the DIC results. The subpixel error is
defined in Fig. 5 as the difference between the calculated
Numerical Shifting Methods
DIC results using a cubic polynomial interpolation and the
While it would be nice to always use experimentally
created images for testing of DIC software it is neither
practical nor possible, as very few perfect images are
available. Comparisons against known translations and
strains are useful, but do not completely quantify the
uncertainty of the correlation measurements. Because
image shifting will be required for calculating the uncer-
tainties in DIC, it is important to find the optimum method
of image shifting. Interestingly, image shifting and interpo-
lation are in essence the same; they both provide intensity
information between the pixels.
Various methods of shifting, shown in Fig. 5, were tested
to see which leads to the best results. Best is used in
quotes here because all interpolation schemes are modify-
ing the image to create the subpixel shift. Some methods Fig. 5 Comparison of interpolation schemes
Exp Mech (2011) 51:443 452 447
calculated image shift using the noted shift method. By far Where:
the lowest error method is the FFT and has been shown by
Xm is the FFT of the signal
this research and that of others to most accurately represent
xi original spatial domain signal
an experimentally shifted image. The quality of the FFT
m is the FFT index from 0, 1,, N-1
shift results themselves depend on how the shift is done.
L is the number of data points in the FFT
Results for two different shift methods are shown in Fig. 6.
Ym is the shifted signal in the frequency domain
Also shown here is a numerically created image proposed
k is the shift amount in pixels
by Bing Pan [5] which presents a numerically created and
ym is the shifted signal in the spatial domain.
sampled image. Most interesting about these results is the
disappearance of the sinusoidal bias error seen with all of When implementing this equation in code, there are a
the other shift methods. It is not known at this time why few important points to remember. First, the FFT is a
this is the case, but the disappearance of the sinusoidal symmetric result, with half of the data repeated. The
amplitude data is symmetric about N/2, and the phase is
interpolant error is most likely an artifact of the numerical
anti-symmetric about N/2. The results are also different if
speckle pattern generation.
the signal length, m, is odd or even, and care must be taken
when adding the phase shift in the frequency domain to
take this into account. The transforms are done via 1D
Optimized Numerical Shifting
FFT s one row or column at a time. For a 1D shift, only the
The Fourier shifting method has many positive attributes, rows or columns need to be processed. For a 2D case, the
not the least of which is creating the smallest error in the rows are shifted and then the columns are shifted via the
shifted image (See Fig. 5). The mathematics for doing the same technique. While the methodology of doing the shift
FFT are also straightforward. The image is first shifted into is simple, there are a number of decisions on pre-processing
the frequency domain via the FFT. A linear phase shift is the data that can influence the quality of the outcome. If
applied in the complex plane with the amount of phase done properly the results for either an image or a subset will
added determining the amount of shift. The image is then have almost no numerical error in the final shifted image.
transformed back to the spatial domain via an inverse FFT. This can be tested by shifting an image a subpixel amount,
The equations describing this as a discrete Fourier and then shifting that image back by the same amount and
transform (DFT) are [13]: checking the amplitudes between the images. While shifts
other than pure translation are possible with the FFT, by
X
L 1
applying a non-linear phase shift, that is not the focus of
xi e j2pmi=L
Xm 1:1
this paper. A fundamental shortcoming of the FFT can be
i 0
easily overcome in image shifting by windowing. Window-
ing has been discussed by Hild [14] where it was
Ym Xm e j2pmk =L 1:2 implemented to improve the accuracy of their multi-scale
displacement measurement technique using a modified
Hanning window. Windowing is important because the
ym FFT 1 fYm g 1:3 assumptions of the FFT dictate that the sample be infinite in
length. The image subset by definition violates this. The
subset selection itself is, in fact, a square window by
definition. That is at the edges, the samples are truncated.
Each type of window has different properties that are useful
to deal with different types of problems in signal process-
ing. For the current application, the most important criterion
to keep in mind is maintaining the correct intensity
amplitude in the subset region, while minimizing the
negative effects of signal truncation. These negative effects
include ringing due to the fact that impulse-like steps are
created at the boundaries. There are many popular windows
that are used for digital signal processing; however, the
requirements for image shifting are unique. The need to
keep the intensity the same in the subset, led to the
selection of the Tukey window. Equation (1.4) shows the
equation used to calculate the window. It is a modified
Fig. 6 Comparison of FFT shifting and Bing method
Exp Mech (2011) 51:443 452
448
Fig. 7 1D Cut through an image showing the window
Cosine window convolved with a rectangular window. As Fig. 8 2D Padded subset from a speckle image
the width of the rectangle window in the center varies to
zero, it becomes a Hanning window, at a width of one it Fig. 7 showing a subset sized 1D cut from a speckle image.
becomes a rectangular window. The flat top is important so The window can be seen to be one within the subset data
as not to modify the amplitude of the result which would area, and slopes to zero in the data pad region. This is also
affect the matching. An example of the window is shown in shown for a 2D subset in Fig. 8.
8
2p i
> 1
> xi 1 cos where i 0; 1; 2; . . . ; m 1
>
>
> 2m
2
>
yi 1 xi 1 cos 2p n i 1 1:4
where i n m; . . . ; n 1
>2 2m
>
>
>
> xi elsewhere
>
:
therefore obvious that the method of interpolation will be
Where:
critical to minimizing the errors in the matching. Typically, the
i is the sample index
cubic polynomial, one of the earlier interpolation functions
n is the number of elements in the sample, and
h nr i used for DIC, introduces a larger phase error than other
m methods and therefore has a larger matching error. This is
2
anecdotally seen in Fig. 5, as well as in Fig. 9 where the 4-tap
b-splines outperform the cubic polynomial. The b-spline has
r is the ratio of the total length of the tapered section to
lower bias error because of the lower phase error for a given
the whole signal length.
number of fitting coefficients as compared to the cubic
polynomial. With the x-tap filters, there is an added
If r 0 the window is a rectangular window and for r 1
computational expense of using a recursive pre-filter applied
it is a Hanning window [15].
to the image. However, because of the improvement in phase
error it is worth the added computational cost. For filters of
4-, 6- and 8-taps (pixels), the recursive pre-filter has been
Interpolation Filter Analysis
integrated into the B-spline transform. For details see Sutton
[16]. Finding the optimum interpolation function is important
Errors in DIC can be attributed to a number of parameters,
to minimizing errors, however this raises a question: Does
including the minimization function, the subset shape function
the numerical shifting change the effectiveness of the
and the interpolation function used. This section looks at the
interpolation filter matching? It does. This is demonstrated
errors caused by the interpolation, which is based on the phase
using 2D DIC (Vic2D) and some sample images that are
error introduced by the interpolant. The interpolation function
either experimentally shifted as described above, or numer-
is important because the subpixel matching that makes DIC
useful is obtained by fitting the data between pixels. It is ically shifted using an optimized FFT shift. To demonstrate
Exp Mech (2011) 51:443 452 449
Fig. 11 Comparison of ARAMIS, MatchID and Vic2D correlation
Fig. 9 High contrast image comparison for experimentally and results for a high-contrast image. The inset shows the speckle pattern,
numerically shifted images area-of-interest, and relative subset size
the effect of the numerical shifting, the reference image from the experimental results, the 4-tap is still the best, but the
the experimentally produced images was numerically shifted, cubic polynomial is next, being better than both the 6 and 8-
and both sets of images were evaluated using the SSD tap interpolation method. The difference in results is because
correlation and the noted interpolation functions. The results the Fourier shift method pre-conditions the image for better
for a high-contrast image are shown in Fig. 9. For the FFT fitting by the interpolation filters, particularly the 8-tap filter.
shifted images, the 8-tap filter was the best and the cubic Most likely the preconditioning is a filtering of the high-
polynomial interpolation was the worst method when frequency content. Another way of expressing this is that the
compared to the known shift amount. Correlation error is frequency content of the interpolation filter should match the
defined here as the difference between the calculated average unaliased frequency content of the speckle pattern. This is
displacements of the area-of-interest subtracted from the important because the choice of interpolation method affects
known shift. Interestingly, the results of the experimentally the quality of the result, and the numerically determined
created images show that the 4-tap interpolation scheme is optimum is not the true optimum. In these cases, one could
the best, while the cubic polynomial is still the worst. The both improve the matching and the solution time by selecting
same analysis was done with the low contrast image, with the 4-tap interpolation method over the better 8-tap.
somewhat different results as seen in Fig. 10. In this case for
Fig. 12 Comparison of ARAMIS, MatchID and Vic2D correlation
results for a low-contrast image. The inset shows the speckle pattern,
Fig. 10 Low contrast comparison between numerically and experi-
area-of-interest, and relative subset size
mentally shifted images
Exp Mech (2011) 51:443 452
450
Fig. 13 Illustration of hard and
soft speckle edges showing both
the full-resolution images and
the binned images. The green
square is the subset size
For these results, a subset size of 29 was used with a step
Correlation Software Comparison
size of 10. The area of interest was the entire image less a
Now that we have perfectly shifted experimental images small border on the outside. Figure 11 illustrates the results
using the binning technique, we can more easily evaluate of the three software packages for a high-contrast low-noise
results between various software packages. These results image. Figure 12 shows the same information but for a low-
are a preliminary evaluation of three software packages. As contrast image. Please note that particularly for the standard
there are many different options that can be chosen during deviation, data smoothing and post-processing may be
the correlation, including interpolation method, image different for the various software packages.
filtering, minimization method, data post processing, and
data filtering, these results are not to be taken as the final
answer. Rather they are presented here to show that with the Speckle Quality Analysis
Prosilica experimental images, we now have a data set on
which the various correlation schemes can be tested. Also, A determining factor in the quality of the DIC results is the
because some codes are black-boxes it is not possible to speckle pattern. In general, high-contrast and low-noise
determine what interpolation function was used. The images will yield better results. Speckle quality was investi-
software parameters were chosen that gave the lowest error.
Fig. 15 Bias error results for cubic polynomial interpolation for the 8-
Fig. 14 1D Cut from the soft edge and hard edge images bit images
Exp Mech (2011) 51:443 452 451
gated using the Prosilica experimental setup. A speckle
pattern was generated that would yield very high gradients
(see Fig. 13) by printing ovals of varying size on the paper.
To create speckles with hard edges, the camera was set at
best focus, for soft edges, the camera was defocused. The
defocus of the camera acts as a low pass filter in the optical
domain which removes the hard edges in the pattern. On the
bottom of Fig. 13 the binned images and the representative
subset size are shown. It is often easier to visualize the
gradients in 1D so this has been illustrated in Fig. 14. The
soft gradients show more data points in the speckle edge, and
nearly the same number of counts between black and white.
The images were analyzed in the 2D DIC software using
both a cubic polynomial and 4-tap interpolation function.
The 8-bit images were shifted using the binning scheme
Fig. 17 Comparison between high and low contrast image results
outlined earlier. Figures 15 and 16 show the resulting bias
errors. Some important things to note are that the
correlation errors are significantly reduced between the
the bias error and increases the measurement variance by an
hard edged speckles and the soft edge speckles. Nearly the
order of magnitude. The relatively small impact of the bit
same result can be obtained by digitally low-pass filtering
count in the contrast is summarized in Fig. 18, where it can
the image during the analysis. The filtering effect is much
be seen that the improvement in results between 8-bit and
smaller for the soft edge speckles because there is little high-
12-bit is small or non-existent. This is true even though the
frequency content to remove from the images. As a general
image gradients are orders of magnitude larger. The high-
rule for cubic polynomial interpolation, every image tested
has shown an improvement in the results when filtered. Not and low-contrast results are from the patterns shown in
Fig. 17. Apparently, after a certain threshold of information
only are the hardness of the edges important on the speckle,
is achieved within a subset, there is adequate information to
but the contrast between the black and white speckles is
important. Figure 17 shows a comparison between a low calculate a match smaller than the other contributing error
sources, such as the interpolation function.
contrast image with 30 counts between black and white and
a high contrast image with 170 counts between black and
white. The bias errors and variance of the measured
displacement are shown along with an inset showing a Conclusions
sample of the pattern and subset size. Probably more
important than the absolute counts between the two for this A method of producing experimental images with exact
subpixel shifting has been presented. While it is not
case, is the relative noise level which adds both a linear tilt to
possible to use this for uncertainty quantification, it is an
ideal method of testing 2D DIC because it more accurately
represents the sampling effects of a digital camera. Future
work will compare this technique with numerically gener-
ated images created using the TexGen software [6]. An
overview of the optimum numerical shift using a windowed
FFT is presented for cases where experimental images are
unavailable. The experimental images were used to test
interpolation methods with the result that the optimum
method was different depending on whether the image was
numerically or experimentally produced. Ideal speckle
patterns were examined to gain insight into what reduces
the correlation error. In general, soft edges with at least 4-
bits of contrast between the black and the white are best. As
noise increases, the ratio of noise to contrast needs to be
maintained, or both the bias errors and the variance of the
measurement will negatively impact the results. Of the
interpolation methods tested, the optimum is the 4-tap b-
Fig. 16 Bias error results for 4-tap interpolation for the 8-bit images
Exp Mech (2011) 51:443 452
452
Fig. 18 Error summary for
8 and 12-bit images with hard
and soft speckle edges
4. Reu PL et al (2009) Uncertainty quantification for digital image
spline. This interpolant seems to mix the best qualities of
correlation. In Society for Experimental Mechanics. SEM,
filtering the image, while maintaining enough frequency
Albuquerque
content to have very low matching errors. With the 5. Pan B et al (2006) Performance of sub-pixel registration algorithms
in digital image correlation. Meas Sci Technol 17(6):1615 1621
Prosilica exact shifted images there now exists a true
6. Orteu J-J et al. (2006) A speckle texture image generator. SPIE
experimental data set that can be used for 2D correlation
7. Lava P et al (2009) Assessment of measuring errors in DIC using
code development and testing.
deformation fields generated by plastic FEA. Opt Lasers Eng 47
(7 8):747 753
8. Wang YQ et al (2009) quantitative error assessment in pattern
Acknowledgements I would like to thank Prof. Mike Sutton and Dr. matching: effects of intensity pattern noise, interpolation, strain and
image contrast on motion measurements. Strain 45(2):160 178
Hubert Schreier for many fruitful discussions on these results and their
interpretation. I would also like to thank my reviewers David Epp and 9. Wang ZY et al (2007) Statistical analysis of the effect of intensity
Timothy Miller for the valuable comments. This acknowledgement pattern noise on the displacement measurement precision of
does not however, imply their complete agreement or endorsement of digital image correlation using self-correlated images. Exp Mech
47(5):701 707
the interpretation of the results.
Sandia is a multiprogram laboratory operated by Sandia Corpora- 10. Reu PL (2010) Experimental validation of 2D uncertainty quantifi-
tion, a Lockheed Martin Company, for the United States Department cation for digital image correlation, in International Conference on
of Energy under contract DE-AC04-94AL85000. Experimental Mechanics 14, F. Bremand, Editor. Poitiers, France
11. Kodak (2007) Kodak KAI-16000 image sensor Device perfor-
mance specifications. Kodak. p 10
12. Pan B et al (2008) Study on subset size selection in digital image
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