Restoration of Archaeological Artifacts by a Genetic Algorithm
with Image Features
Koji Kashihara
Institute of Techonology and Science, The University of Tokushima, 2-1 Minamijyousanjima, Tokushima, Japan
Keywords: Genetic Algorithm, Hill-climbing Algorithm, Three-Dimensional Rebuilding, Image Features.
Abstract: Archaeological artifacts have been discovered all over the world. The restoration work of archaeological
artifacts broken into pieces contains positioning problems. Therefore, an intelligent computer-assisted
system was proposed to rebuild archaeological discoveries from fragments. A real coded genetic algorithm
(GA) and a hill-climbing algorithm was evaluated to reconstruct a 3D object. The fitness function value for
the GA was computed from image features of the object. The ORB (Oriented FAST and Rotated BRIEF)
technique was used for solving the positional problem by the GA. The proposed method based on the GA
with the image features was able to efficiently regulate the 3D surfaces. In further researches, the proposed
method for 3D rebuilding could be applied to various practical applications.
1 INTRODUCTION
Archaeological artifacts have been discovered all
over the world. Because the discovered artifacts are
usually broken into some pieces, it takes a lot of
hours to rebuild them from fragments (Haliř, 1999).
Furthermore, the archaeological rebuilding is
interrupted when pieces are missing or damaged.
Archaeologists or experts must evaluate numerous
possible combinations under such situations, based
on their knowledge and experience.
Efficient methods for the virtual 3D visualization
(Scopigno, 2011) have been reported to make digital
archives, which could assist the restoration work.
Previous computer systems mainly focus on the
reconstruction of 3D objects with symmetric
patterns, comparing the broken surface boundary
curves (Sağiroğlu and Erçil, 2006). Such restoration
work needs computing complicated patterns and
geometric images by using well-defined
mathematical models. However, the 3D rebuilding
cannot be completed when the precise mathematical
models do not exist.
Intelligent computer systems may be able to
address this issue. An easier method for piecing
together archaeological objects without using a
mathematical model for surface curve fitting has not
been established. Here, genetic algorithms (GAs) are
one optimization method of positional regulation
including the evaluation of countless combinations
(Ray and Mahajan, 2002).
Instead of the complicated mathematical model,
the image features of 3D objects may be effective
for the GA process. SIFT - Scale Invariant Feature
Transform (Lowe, 1999) and SURF - Speeded-Up
Robust Features (Bay et al., 2008) are well known as
basic techniques for image feature detection. More
recently, the ORB - Oriented FAST and Rotated
BRIEF (Rublee et al., 2011) technique also shows
accurate performance, compared with the traditional
methods; it is based on the FAST keypoint detector
and the BRIEF descriptor. In addition, after a global
solution was computed from the GA, hill-climbing
methods to find a localized solution may be able to
fine-tune the 3D positions.
The purpose of this study was to investigate
effective methods for 3D reconstruction of artifacts
from fragments, so that the archaeologists can
shorten their working time. The proposed method
based on GA with a hill-climbing algorithm was
evaluated by using image features of a 3D object
without mathematical surface or border models. The
ORB technique was used for solving the positional
problem by the GA because it would be an efficient
method to search for similar image patterns.
691
Kashihara K..
Restoration of Archaeological Artifacts by a Genetic Algorithm with Image Features.
DOI: 10.5220/0004920106910695
In Proceedings of the 6th International Conference on Agents and Artificial Intelligence (ICAART-2014), pages 691-695
ISBN: 978-989-758-015-4
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
2 PROPOSED METHODS
The computer system was proposed to estimate the
correct positioning of archaeological fragments
(Open GL; Open CV ver. 2.4; Microsoft Visual C++
2012). For this system, GA computation can find a
global solution from numerous combinations of 3D
fragments. Fine-tuning is then performed by the hill-
climbing method. The 3D reconstruction is based on
the silhouettes of an object from some camera angles
in order to determine a correct match among
fragments. After the GA process, one of nine
operations in a target 3D fragment (rotations and
parallel movements in each axis) is selected during
the hill-climbing method.
2.1 Real Coded Genetic Algorithm
The real coded GA approach was applied to predict
the spatial positions of some pieces of a 3D object:
angles and coordinate x, y, and z axes. The 3D object
is formed by the polygonal meshes of fragments.
The GA process consists of the following operations.
(a) The initial population of individuals is randomly
generated within a set range. Each individual is
shown by real numbers; its score is calculated
from a fitness function. The fitness function
value is calculated by comparing the current
image results at some viewpoints with the correct
patterns. The best fitness value is maintained to
define the next generation.
(b) A selection operation chooses the individuals for
the generation of offspring, and tournament
selection is used for the choice of individuals.
(c) A crossover operation combines two individuals
to generate an offspring. A blend crossover
(BLX-α) operator (Eshelman and Schaffer, 1993)
was selected for this study.
(d) A mutation operator randomly changes some
individuals, altering the variables of a selected
individual to facilitate the diversity in the
population. The mutation can avoid falling into a
local solution.
The above GA operators are repeated to update
the population and create the next generations,
modifying the fitness of the population. The GA
process stopped after creating some generations.
2.2 Hill-climbing Method
The hill-climbing method was performed to fine
tune the positioning after the search spaces have
been reduced by the initial GA operation. This
method is a traditional optimization technique to
maximize a fitness function value. The proposed
system is composed of the following steps.
(a) Set the initial points of fragments in a search
space. These values are determined by the final
results of the GA process.
(b) Compute the fitness function values for all
neighbours based on the current state, changing
each parameter of the angles and positions of the
target fragment.
(c) Choose the neighbour with the best quality
indicating the largest fitness value and move to
the state.
(d) Repeat the steps (b) and (c) until all the
neighbours become no change or lower quality in
the fitness values. Change the target fragment to
the next one.
2.3 Fitness Function
The similarity of image features of a 3D object from
six viewpoints was evaluated to determine the
correct positions of fragments. This similarity was
the fitness function in the GA and hill-climbing
methods, meaning the accuracy of 3D rebuilding. A
normalized correlation coefficient (i.e., the similarity
between an original image A and an evaluated image
B) is denoted as:
N
i
i
N
i
i
N
i
i
N
i
i
i
N
i
i
B
N
BA
N
A
BBAA
BBAA
r
00
0
2
0
2
0
1
,
1
)()(
)()(
(1)
A
i
and B
i
are the brightness in each pixel and N is the
total number of pixels.
̅
and
show the mean value
of the brightness in each image. The correlation
coefficient of Eq. (1) approaches 1 when the
similarity increases.
The fitness function is the summation of
similarities computed from six camera angles.
Additionally, the image feature points were
calculated by the ORB technique. If image feature
points of two images are the same, the slope value
between the feature points will result in zero (Fig.
1A). Therefore, this slope value was added to the
fitness function for the GA.
ICAART2014-InternationalConferenceonAgentsandArtificialIntelligence
692
A. Matched case
B. Not matched case
Figure 1: Examples of image features acquired from the
ORB technique. The lines between the two objects
indicate the corresponding relationship between the
extracted feature points.
3 SIMULATION STUDY
The proposed method was assessed by using a 3D
model with asymmetric shapes digitized from an
actual object. The 3D reconstruction was performed
by the following steps: (1) Create correct patterns
using various camera angles; (2) Carry out GA
computation for a localized solution. The fitness
value of the GA was calculated from the image
features obtained from the ORB technique; (3)
Regulate 3D positions by the hill-climbing method.
3.1 Evaluation Method
3.1.1 3D Remodeling
To make a digitized 3D object with fragments,
photographs were taken from thirty camera locations
around the object with a calibration mat (Fig. 2A),
every 15 degrees at low angles (24 points) and every
60 degrees at high angles (6 points). After the
masking process was applied for the backgrounds of
acquired images, the 3D object with 6,000 triangle
polygons was created by fixing the position and
spatial relationship on the calibration mats of all the
images (STRATA FOTO 3D CX2). The 3D model
was output in the VRML 2.0 format to estimate the
optimal fitting and was divided into 7 fragments
(Metasequoia ver. 2.4).
A. Camera angles and fragments
B. Silhouettes of a 3D object
Figure 2: A. Thirty camera angles with a calibration mat to
construct a 3D object (left). Examples of 3D fragments
formed by polygonal meshes with triangles (right). B.
Correct images from various camera angles.
3.1.2 Parameter Setting
The real coded GA parameters were prepared as
follows. The initial population of 30 chromosomes
was randomly generated. The probabilities of
crossover and mutation were set at 0.50 (BLX-α =
0.40) and 0.01, respectively. The number of
iterations in the GA computation was 100
generations.
For the hill-climbing search, step sizes of a
fragment were three degrees in rotation angles and
0.002 in parallel movements to each axis of a 3D
coordinate. The initial values were based on the
result of the GA process. The searching space was
limited within the voxel size of an actual object in
parallel movement to each axis with free rotations.
The maximum number of iterations was set at 200.
As the first fitness function value, the correlation
coefficient between the correct and evaluated images
(24-bit grayscale; 400 × 400 pixels) was calculated
from Eq. (1). The correct images were acquired from
the six viewpoints for a 3D object (Fig. 2B). In
addition, the image features extracted from the ORB
RestorationofArchaeologicalArtifactsbyaGeneticAlgorithmwithImageFeatures
693
technique were output as bitmap images; the image
feature similarities were then computed as the fitness
value for the GA.
3.2 Results
Figure 3 shows the change of fitness values for the
GA process. The fitness function values gradually
increased and the maximum value (r = 3.15) of all
generations was obtained during the later iterations.
The ORB technique to extract the descriptor as an
image feature was also applied to the correct image
patterns to compute the fitness function value.
Figure 3: Simulation results of the GA process. A blue
line: average fitness values; dotted lines: standard
deviations in each generation; a red line: the maximum
fitness values.
Figure 4: Final simulation results of the GA and hill-
climbing methods (six camera angles).
The optimal regulation of fragments was roughly
completed by the GA. The fine-tuning was then
performed by using the hill-climbing method, which
allowed borders of curved surfaces to be smoothly
connected (Fig. 4). This result suggests the positive
effect of this method began with the initial values
determined by the GA process.
4 DISCUSSION
Previous researches for the rebuilding of
archaeological artifacts needed well-defined
mathematical or rule-based models for the surface
curve fitting of broken parts (Haliř, 1999). On the
other hand, the proposed method based on the
silhouettes of a 3D object can be used for nonlinear
and non-continuous surface curves without
mathematical models. In addition, the ORB
technique was able to fine-tune 3D positions because
it can be robust for searching similar images with
various rotations and scales.
Although an evaluation with texture mapping
was not applied to this research, the distribution of
curvatures and drawing patterns of surfaces with
colours may be efficient for 3D rebuilding
(Sağiroğlu and Erçil, 2006). It is also crucial to
prepare a 3D database for a supervised image with
correct or similar patterns because it determines the
accuracy of reconstruction.
As a user interface for the design drawing of a
3D object, the results of reconstruction could be
interactively modified to fine-tune the final
positioning of pieces. Actually, there exist optimal
visual angles with some perspectives to recognize
3D shapes as quickly as possible (Kashihara and
Nakahara, 2011; Kashihara, 2011). Therefore, this
result could be applicable to the user interface and
drawing design for the manual adjustment of a
reconstructed 3D object. The manually adjusted
values could be also used as the initial values for the
proposed algorithms to acquire the higher accuracy
of 3D rebuilding.
5 CONCLUSIONS
The intelligent computer system for reconstructing
archaeological artifacts with broken surfaces was
designed to assist archaeologists and to reduce
unnecessary manual operation. The GA with the
hill-climbing algorithm was optimal for determining
the best positions of fragments in a 3D object.
Furthermore, the ORB technique which can extract
the image features of an object was suitable for the
fitness function of the GA. In future studies, the
proposed method should be applied to practical
applications, improving the searching time and user
interface. In addition to the virtual repairing of
archaeological finds, the proposed system could be
available for restoration work on personal
possessions such as mementos.
1
1.5
2
2.5
3
3.5
0 20406080100
Fitness function values [-]
Generations [-]
average
maximum
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ACKNOWLEDGEMENTS
This study was funded by a Grant-in-Aid for the
Okawa Foundation for Information and
Telecommunications.
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