Abstract over a surface as they measure point

Abstract Displacement denotes the measure of the amount of movement of a point
from its reference position. The precise measurement of displacement is one of
the vital requirement in engineering which is the response given by the
structure or by the object to predict its behaviour under applied loads.
Advanced full field displacement measuring techniques are required to refine
the study of material behaviour. The existing contact based measuring systems
such as dial gauges and strain gauges are not capable of measuring full field
displacement over a surface as they measure point displacements eventually the
need of large number of probes which incur high cost. Also, the relative
stiffness of the probe and the object which is being measured for displacement
affects the accuracy. The non-contact based measuring systems readily available
in market consist of hardware and software components are expensive. Therefore, this research is focusing on developing a
cost-effective optic based full-field measuring system, i.e. developing an
algorithm using available software which is capable of measuring displacement
with locally available digital camera using DIC concept.

Keywords:  Digital Image
Correlation; Full-field displacement; Strain mapping; Speckle pattern; Low cost
measuring system

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1.   
Introduction

Displacement measurement plays a significant role in engineering which
is defined as the measure of change in position with respect to a reference
frame, involved in predicting material behaviour and parameters. As the researchers
are keen on refining the study of behaviour of materials and structures, modern
and complex displacement measuring techniques are required which should result full-field
displacement as contours over a surface rather than point measurements.

Conventional strain measuring means like dial gauges and strain gauges
fail to compute strain maps over an entire surface as they are expensive, and they
have some practical difficulties. Hence the requirement of developing a new
technique is enforced.

Digital Image Correlation belongs to the class of non-contact based
measuring technique which has the potential of being an ideal solution, consist
of capturing images of object under investigation, storing of images in digital
format, image analysis and computation of full-field displacement (Michael A. Sutton, Jean-José Orteu, Hubert
W. Schreier, 2009).

The DIC technique has been widely used for measuring deformation and
shape measurement, mechanical parameters characterization as well as numerical–
experimental and theoretical–experimental cross validations as it has distinct
advantages of simple experimental set-up, low-requirement on experimental
environment and wide range of applicability, (Bing Pan ,Kai Li , 2011).

Though the DIC technique has been experienced sufficient development,
it is not implemented in over-all practice as the systems including readily
available in the market are expensive. Hence, ultimate goal of this research is
to develop an algorithm using appropriate software that can measure full-field
displacement over a surface.

2.     
Digital Image Correlation

Computer vision is a science that
combines artificial intelligence and computer science which aims to give a
better visual understanding of world to machines through processing a set of digital
images. It is concerned with automatic acquisition of images followed by image
processing resulting analysis of useful information from digital images. Image matching which includes
Digital Image Correlation is a branch of computer vision that is fundamental to
a huge number of practical applications. The DIC technique comprise of a mathematical
correlation analysis to study a set of consecutive digital image data captured which
are under investigations.

The goal is to acquire
a one-to-one correspondence between material points in the reference image and
in the current displaced image. This is done by having subsections in the
reference image called subsets and finding their respective locations in the
current image. For each subset, we obtain displacement and strain information
through the transformation used to match the location of the subset in the
current configuration.

Many subsets are taken
in the reference image, with a spacing parameter to lessen the computational
cost. Typically, subsets overlap as well. The end result is a grid containing
displacement and strain information. The displacement/strain fields can then be
interpolated to form a “continuous” displacement/strain field.The subset’s
coordinates are shown as red crosses. It is not necessary to maintain the shape
of subset as square. It can be any shape that holds a centre point.

In order to capture the surface
characteristics using DIC technique, the specimen should be organized with
speckle pattern which is a random dot pattern. This technique begins with a
reference image and capturing images continuously while load is applied. The
deformed images will show a different speckle pattern form the reference image (Rommel Cintrón, Dr. Victor
Saouma, 2008).

1.1.   
Subpixel
DIC algorithms

Various techniques have been proposed
to improve DIC-based displacement measurements to the accuracy level of subpixel
resolution. But the most commonly used methods are the correlation coefficient
surface fitting method, Newton-Raphson iteration method, spatial gradient
method and iterative spatial gradient method that are relatively easy and give
accurate results (Chakinala, August, 2013).

Recently researchers have been
focused on deriving new algorithms as well as improving the existing algorithms
to enhance the accuracy that is of the subpixel resolution. One such research
done is improving the Newton-Raphson partial differential correction method.
Even though the method incurs higher computational cost, it is widely used in
most of the practical applications due to the appreciable performance. So, the
algorithm was improved by incorporating adaptive spatial regularization resulting
higher accuracy of strains.

1.2.   
Techniques
of image matching

Researches on comparing different
image matching technique also has been carried out. Three unique image matching
techniques named SURF, ORB and SIFT were tested for their performance which
indicates the accuracy of matching evaluation parameters against different
transformations and rotations. Based on the results it was concluded that ORB
is the fastest algorithm while SIFT could tackle most of the problems (Ebrahim Karami, Siva Prasad,
and Mohamed Shehata).

1.3.   
Template
Matching

Template Matching is a sophisticated computer vision technique that recognises
the parts of an image that match a predefined template. These techniques are
flexible and straightforward to use, which makes them one of the most popular
methods of object localization that is beneficial in displacement measurement. Applicability
of template matching is limited by the available computational power, as it
will be time-consuming when dealing with complex templates.

Feature based approach
can be effective when the reference image consists of solid feature while
template based approach could be adapted in absence of strong features in
reference image. Large number of sampling points is required template matching
method which extend the time of process. It can be omitted by reducing the
resolution of search image and performing the analysis in the aforementioned
down-sized image.

1.3.1.  Mathematical
Correlation for Template Matching

The following derivation of displacement estimation method is
based on minimizing the variance in grey value between a subset of reference
image and a displaced image. It assumed that same lighting has occurred for
both reference and displaced images. That is the variation between refence
image and displaced image is caused only by Gaussian random noise.

Symbols used for reference image and displaced
image are F and G respectively. Minimization of squared differences in grey
values which is named as sum of square deviation(SSD) is given as follows.1.      
Applications
of DIC

Various researches have been
carried out to measure displacement in several fields and to observe material
behaviour using DIC technique.  One such
attempt made is to develop a new and near-automatic landslide mapping method
termed as change detection-based Markov random field using DIC technique. The
methodology was generating difference image automatically from pre- and
post-event aerial orthophotos using change vector analysis (CVA). Then, the
training samples of landslide and non-landslides were generated from the
post-event aerial orthophoto using a multi-threshold method (Zhongbin Li, Wenzhong Shi,
Ping Lu, Lin Yan, Qunming Wang, Zelang Miao, 2016).

DIC technique has been applied in
experiments in laboratory as well as works in situ outside the laboratory. Some
of the researchers were interested on measuring crack opening in a concrete
beam which was subjected to three-point bending test. It was able to encounter
the cracks which are not visible for naked eye and could measure the crack
width through measuring the displacement across using DIC. Also, it was tried
to capture the deflection measurement of a bridge by analysing digital images
taken before and after load application (Nick McCormick, Jerry Lord,
2012).

Researches has been carried out in
accurate determination of surface reference data in digital photographs in
ice-free surfaces of Maritime Antarctica in 2016. The proposed method is based
on an object-based classification procedure built in two main steps: first, on
the automated delineation of homogeneous regions (the objects) of the images
through the watershed transform with adequate filtering to avoid an
over-segmentation, and second, on labelling each identified object with a
supervised decision classifier trained with samples of representative objects
of ice-free surface types (Pedro Pina, Gonçalo Vieira , Lourenço
Bandeira , Carla Mora, 2016)

Researches based on assessing the
applicability of DIC technique in measuring deformation in Nano-scale has been
carried out. It has proven that the measurement of C4 based components and
measurement of deformation in a stacked chip component can be done with
accuracy of 20 nm deformation resolution using DIC technique (Liam Kehoe, Pat Lynch, Vincent Guénebaut,
2006).

A research based on applicability
of DIC in a different concept like extracting vibration characteristics of a
guitar has carried out. A modal impact hammer test was performed on the
instrument in a free configuration. The response of the guitar to the
excitation was recorded using a pair of high-speed cameras. The recorded images
were processed to extract the natural frequencies and mode shape of the guitar (Kiran Patil and Javad
Baqersad, Daniel Ludwigsen, Yaomin Dong, 2017)

4.      
3D
reconstruction of 2D images using DIC

It is the reconstruction of
three-dimensional model using the parameters obtained from captured 2D
images.  It is exactly the reverse
process of capturing 2D images from 3D objects where the 3D point, the depth is
vanished. The 3D point for a single image is unknown as it lies along the line
of sight while the exact position is being unknown. In case of having two
images of an object captured from different positions, the 3D point can be
obtained using the concept of Triangulation. In detail, the 3D point can be
identified through observing the intersection of lines of sight. This is
fundamental of 3D reconstruction.

The aforementioned task consists of
two key stages, camera calibration and depth determination. Camera calibration
is the process obtaining intrinsic as well as extrinsic parameters which are
essential to transform the algorithm operational. Depth determination is the
most crucial phase as it computes the lost 3D component. It includes seeking
matches between images, so that, the matched images can be triangulated in 3D
space which result the depth. After obtaining several depth-maps they have to
be combined to form a final mesh through computing depth and projecting out of
the camera.

 

Contrarily an attempt has been made
to do 3D reconstruction from single 2D image. The problem addressed using an
example-based synthesis approach. The
proposed method utilises a database of objects stacked class wise comprising
example patches of feasible mappings from the appearance to the depth of each
object. For a given image the combination of known depths of patches from
similar objects is done to generate a reasonable depth estimation. This is
achieved by optimizing a global target function representing the likelihood of
the candidate depth (Tal
Hassner, Ronen Basri, 2006)

5.      
Conclusion
and future works

The previous research works stated above will
demonstrate the utility of Digital Image Correlation techniques in measuring
displacement in structures and in experimental setups. This technique combined
with simple, readily available, low-cost computational means will be the best
tool in acquiring full-field surface deformation. In order to enhance the
efficiency of DIC technique in measuring displacements, the future works should
be focused on