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ISSN 2320-5407 International Journal of Advanced Research (2015), Volume 3, Issue 3, 712-714
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Journal homepage: http://www.journalijar.com INTERNATIONAL JOURNAL
OF ADVANCED RESEARCH
RESEARCH ARTICLE
A Survey of Computer Methods in Reconstruction of 3D Archaeological Pottery Objects
Nada A. Rasheed and Md Jan Nordin
Dept. of Computer Science, University Kebangsaan Malaysia, Kuala Lumpur, Malaysia
Manuscript Info Abstract
Manuscript History:
Received: 15 January 2015
Final Accepted: 22 February 2015
Published Online: March 2015
Key words:
Survey, Reconstruction Fragment,
Archaeological Objects, Three
Dimensional.
*Corresponding Author
Nada A. Rasheed
An automatic reconstruction of ancient artifact fragments is of great interest
in archaeology, and is considered important because it helps archaeologists
make inferences about past cultures and civilizations. Therefore, numerous
researches proposed various methods to put together and restore the
fragments of a piece of pottery to its original form. The aim of this paper is
to present an in-depth review of the most important available publications in
computer applications related to the area of the classifying and reconstruction
of three-dimensional model for archaeological pottery objects over the epoch
in the early eighties until the end of 2013. This task classified according to
the feature extraction, the classification process and the matching techniques
implemented for the purpose of restoration of the fragments of pottery object
to its original form. Moreover, this paper focused on review and analyze the
results that they have achieved.
Copy Right, IJAR, 2015,. All rights reserved
INTRODUCTION
Archaeology is the scientific study of the last remnants of humanitarian civilization, which means exploring the lives
of ancient peoples by examining their waste, and discovering human activity in the past through the recovery and
analysis of the material culture and environmental data that they have left behind, which includes artifacts,
architecture and cultural landscapes. Incidentally, it should be mentioned that the area of ceramics is one of the most
common in archaeology in terms of ancient fragments (Kampel & Sablatnig 2004). Hence, the reconstruction of
unknown objects from a large number of smaller pieces may involve thousands of irregular fragments, and is a
tedious task, especially in case of the loss some pieces. It sometimes requires laborious effort, and may take years of
tedious work and may involve a great number of laborers and experienced archaeologists. The laborers and
archaeologists involved must deal with the artifacts cautiously to avoid further damage, especially with the edges of
fragments, when they attempt to assemble the fragments manually, because assemble the fragments are similar to
assemble the pieces of a jigsaw puzzle (Castañeda et al. 2011; Funkhouser et al. 2011). Numerous archaeologists
challenged the task of achieving the accurate reassembly of the archaeological fragments and returning them to their
original form because of the high value in information that represents past civilizations and cultures. This paper will
carry out a review to the studies that were performed using computers to retrieval archaeological excavation
fragments into their original form. The main objective of the review of previous studies is to facilitate the task of
subsequent studies by proposing new algorithms in order to achieve better results than the previous algorithms.
This paper is structured into several sections. An overview of the reconstruction of fragmented objects is presented
in Section 2, the structure search is drawn in Section 3, and Section 4 provides studies performed during the period
eighties until the end of 2013. An important analysis is presented in Section 5. Finally, Section 6 summarizes and
highlights the most important conclusions.
2- Reconstruction of Fragmented Objects
The world has witnessed great development in the performance of computers as the use of image processing and
pattern recognition techniques, which encouraged researchers to attempt to solve the problem of reconstruction of
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fractured objects from a large collection of randomly mixed fragments via proposed systems instead of manually
assembling them, which is a tedious and time consuming task. To overcome this problem, several authors have
worked on the automated reconstruction of fragmented objects, and the core concept of this problem is finding a
solution for many applications. One application is reconstructing torn documents (Richter et al. 2011; Lin & Chiang
2012) that are assembled for the purpose of extracting the text in the torn documents, which it is an important
process in the field of forensics.
Another application is the restoration of the fragments of archaeological objects, specifically ceramic and pottery
fragments, which has been presented by several researchers (Leitao & Stolfi 2005; Smith et al. 2010; Oxholm &
Nishino 2012) who were interested to find the solutions to broken fragmented pottery. Furthermore, numerous
researchers (Toler-Franklin et al. 2010; Shin et al. 2010; 2012) have worked on the reconstruction historical wall
paintings, which are usually scattered into many hundreds or even thousands of fragments, located in many sites,
such as the seventeenth century BC fragmented wall paintings, excavated in Akrotiri, Santorini, Greece. In terms of
the restoration of broken glass plates, the study carried out by Stanco et al. (2011) about the virtual restoration of the
fragments of glass plate photographs of archaeological repertoires. This study focused on the methods that aimed to
reconstruct the fragments of ancient pottery artifacts.
3- The Structure Search
In order to review previous studies, this paper concentrates on matching and reconstructing three-dimensional of
historical pottery fragments. It divides the previous studies into four groups according to the period that the study
has been prepared. For each group, all studies are classified based on the extracted features, the classification
technique that was used, and the results achieved, as shown in Figure 1.
Fig. 1. The structure of the research.
4. Studies Performed: Since 1980 - 2013
This review summarizes all works implemented since 1980 up to 2013, and discusses the implications for
classifying and reassembling artifact fragments. We would like to point out that this study focuses on pottery
fragments only. The discussion of the involved studies is divided into four periods, according to the year the study
was published:
4.1 Studies during the period in the 80’s
In the mid-eighties, researchers were interested in systems that draw, archive, store, and retrieve the fragments that
were excavated. In the field of reassembling objects, many methods have been presented to assemble jigsaw puzzles,
and also to generate models of solid objects through using three-dimensional surfaces. Hall and Laflin (1984)
describe the use of B-splines for shape representation. They exploited the idea that allows three-dimensional curved
solids of revolution to generate curves based on B-spline curves, which fit the technique to generate object outlines
and draw a profile of the pottery vessels. The advantage of this method is that it allows drawings of the 3D modeling
of pottery profiles and compression prior to storage via computers for subsequent display and facilitates statistical
analysis.
3D Archaeological Pottery
Fragments
1990-1999
1980-1989
2000-2009
2010-2013
Features
Classification
Results
Features
Classification
Results
Features
Classification
Results
Features
Classification
Results
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4.2 Studies during the period in the 90’s
Attention of researchers began in the mid-nineties focus on the necessary solutions in the reconstruction of antiques.
There are a number of research works that pertain to the field of automated restoration of antiques and bring them
back to their original form. The most important studies are summarized and classified according to the type of image
that has been obtained:
Through assuming that the pottery object is rotationally symmetric, Halíř and Flusser (1997) proposed a model to
estimate the profile based on the archaeological fragment with high accuracy. The researchers proved that can
estimate the parameters including the diameter and the perimeters of the object by identifying the radius of one
fragment. Also, they proved that the intersections of the surface fragment with several parallel planes produce
parallel arcs with different diameters and one axis. In order to form a circular arc, the fragment is placed in the
correct orientation, which is estimated by expert archaeologists, so the intersection between the surface of the
fragment and the projected laser plane generates the circular arc. The algorithm has been evaluated on both synthetic
data and real pottery data; it achieved an error rate equivalent to 2-3 mm.
By adopting several shapes and partial information such as the rim and base of the fragment, Sablatnig & Menard
(1997) proposed an automatic classification system for the reconstruction of full vessels based on the attributes of
the profile’s curvature, the subdivision of the profile between the rim, body, and the base (ring and flat). The
researchers relied on the bottom-up design for reconstructing the fragments. The descriptive profile is formed when
the profile is divided into the primitive elements and stored. They used a descriptive language to classify the
unknown fragments by comparing its descriptive language with other fragments through calculating the graph
similarity. Finally, the reconstruction of the object was achieved according to the highest similarities between the
graph and subgraph.
Several researchers addressed the problem of reconstructing the fragments as matching the boundary curve instead
of matching entire surface (Üçoluk & Toroslu 1999) introduced the automatic reconstruction of broken 3D surface
objects by exploiting the outlines of the shapes to achieve the matching of adjacent contour pixels of two ceramic
fragments, despite the loss of some of the fragments. Their algorithm includes a 3D object with closed curves and
thin-walled fragments. The feature vector was extracted at each discrete boundary curve point of the fragment, in
other words calculating the curvature and torsion scalars. In order to obtain the best matching, a Noise Tolerant
algorithm was applied by using simulated broken objects. They match and align the vase fragments through a
comparison of the broken surface boundary curves.
Halíř (1999) proposed an automatic estimation of the axis of rotation of archaeological pottery fragments based on
geometrical properties. They exploited the fact that any ceramics are made on the wheel, and the horizontal section
of broken fragments is in the form of a circular arc. Their approach consists of several steps to estimate the axis of
rotation, which can detect the accurate estimation from the first step. It can be improved by applying the direct least
squares optimization and by using the M-estimators method to obtain a more robust estimation. Sometimes there are
influencing factors to estimate the axis of rotation, such as noise outliers and systematic errors. They address this
problem by applying an iterative refinement of the estimated rotation axis by a robust circle and line fitting. Their
approach was evaluated through using synthetic objects and real pottery fragments.
4.3 Studies during the period in the 2000s
This section gives a brief description of the most common research works that pertain to the field of automated and
semi-automated reconstruction of archaeological pottery objects. In this phase, the work during about ten years was
primarily centered on the estimation of shape models from 3D surface data. The research works are divided into two
types, as follows:
An approach depends on surface morphology is presented by Papaioannou et al. (2000), which was aimed at the
semi- automatic reconstruction of archaeological finds by exploiting their geometrical information. Their approach
includes estimating the fracture side of the fragment depending on surface bumpiness by the depth buffer approach,
and for the purpose of achieving matching, the system candidates the sides that were relatively bumpy. The error
matching is computed for all candidate facets for every pairwise of fragments via optimizing the surface similarity
error between two fragments with reference to their relative orientation. Finally, the reconstruction activity begins
through governed basic rules, and was applied on the pairs of candidate fragments that have small matching errors.
In order to improve the clustering process, other characteristics such as the material or prior structural knowledge is
used. Their algorithm has been applied to synthetic and real data, and the result achieved 50% without material and
structural constraints or user enforced selectively, and achieved 90% with constraints and user intervention.
Assuming that all the pots have an axial symmetry property, through the estimation of break-curves and profile-
curves, Willis et al. (2001) created a framework for the automatic assembling of 3D pots by obtaining a 3D
measurement of data of fragments. Therefore, the researchers depend on extracting the geometric shape information
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and its covariance, rather than using raw measurement-data of fragments to estimate the geometric parameters of the
fragments, such as the vessel axis in standard position, profile-curve and z- axis, a portion of the outer surface,
break-curves to whole pots, and 3D Euclidean transformations. In order to combine and formulate the geometric
parameters, the authors applied a Bayesian method, where the search strategy reduces the comparisons of
configurations that are not possible, and at the same time, it provides a strong computational method for aligning
breaks curves and outer surfaces.
Schindler et al. (2001) have developed an automated classifying archaeological ceramic fragment system by
depending on the profile. Therefore, researchers assumed that the object has an axial symmetry property and the
profile can represent a closed curve in the plane. Hence, the researchers merged several methods of approximation
and interpolation of the closed curve by using B-splines, because this function has the property of exhaustive
approximation. After testing the method by using real and synthetic data, it achieved results through the graphical
output and provided the best representation for the reconstruction of the fragments.
The framework for automatic assembly of broken pottery vessels was developed by Andrews & Laidlaw (2002). In
this framework the match is achieved through a multi-feature, which includes comparing the features automatically
to reconstruct vessels from a pairwise of pottery fragments. The researchers relied on the geometric relationships for
matching pairwise fragments, and the evaluation of the probability of the matching according to the fragment
position by using a χ2 -statistic. The result was obtained through the testing of eight groups that consisted of 16
fragments; their method achieved the correct reconstruction for only 13 valid pairwise matches.
Based on a Hough-inspired method that can estimate the rotation to orientate the three dimensional model, an
automated system for classification of fragments by Mara et al. (2002) was developed. The classification of the
fragments depends on the profile of the fragment, which represents the longest elongation on the surface of the
fragment that is a parallel to the rotational axis through two points, and also depended on multiple measurements of
the fragment, such as the diameter rim, diameter of the wall, height, and the characteristic ratio. Therefore, the
authors estimated the profile of the fragment and the curvature points. This helps for segmenting the curvature into
its primitives. The researchers tested their system to classify a total of 70 real fragments. Through the estimation of
the rotational axis, they were able to classify 62 fragments successfully.
Through small fragments, it is possible to estimate the geometric structure for pots that have a symmetrical axis.
This a robust approach proposed by Cao and Mumford (2002). The authors exploited the information of the surface
of the revolution, where the maximal spheres that are tangent to the surface will be centered on the axis of
symmetry. To estimate the centers, the authors calculated the line that minimizes the weighted least squares
distance, and then estimated both symmetry axis and the profile curve. For the purpose of assembly of the pot from
several fragments, the authors used estimations that depended on computing the confidence bounds for the axis and
the profile curve by using bootstrap methods.
Papaioannou et al. (2002) proposed an automatic 3D reconstruction based on the matching and alignment of parts.
The authors focus on the surface geometry, so the matching was performed directly through the plane between two
arbitrary fragments, where the distance was calculated between the mutually-visible faces of the fragments by
utilizing the 3D points of the whole surfaces for pair fragments. Afterwards, they computed an error measure
between the distances for both of the two faces of the fragments, and minimized the distance between the 3D surface
points of the two fragments by using the standard global optimization scheme. During the z-buffer method, the
matching error was computed, and minimized this matching error for the purpose of obtaining the best fit between
the objects. They tested their method on the digitized models of real fragments and the results achieved matching the
fragments with constraints or without constraints.
Willis et al. (2003) presented a method for automatically estimating the axially symmetric surface geometry of pot
fragments and reconstructing the three dimensional fragments by depending on the estimation of both the axis and
the profile curve for every small fragment of the archaeological object, through computing the axially symmetric
algebraic surface. Also, the authors relied on axially symmetric implicit polynomial surface models to extract a
geometric model, and the error was analyzed statistically. The authors applied their method by testing five fragments
selected from Petra, Jordan. In order to enhance the robustness of their method and remove the noise that was caused
by the measurement errors, they used a bootstrap algorithm that included a set of information for each fragment,
such as a covariance matrix for axis parameters.
A fully automated system for the reconstruction of pottery fragments depended on the profile of the fragment was an
approach proposed by Kampel and Sablatnig (2003a). The core idea of this approach is to find the original form of
the pot through one fragment and assemble the fragments without manual intervention. In order to classify the
fragments, the authors focused on the estimation of the correct orientation and the profile of the fragment. To
achieve the reconstruction stage, the authors depended on the partial similarities of the profiles, and the pots were
assembled on the basis of the description of the data stored. Their method has been tested on 40 pottery fragments,
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and the result it achieved was 50% successful. Note that it has discarded 18 fragments due to the wrong estimation
for the axis of rotation. In the same year, Kampel and Sablatnig (2003b) presented an automated archival,
classification, and reconstruction of archaeological ceramic system. By depending on both the front and back
surfaces of the ceramic fragments, the features are extracted automatically by computing the profile, and the
measurements such as the ratio of the fragment area of an object and both the dimensions and diameter of the object.
Their approach requires prior knowledge to the type and class of the object, and also an estimation of the correct
orientation of the fragment for the purpose of determining the exact position of a fragment according to the original
object. By using the mathematical curves, the fragments are classified depending on cubic B-splines, and their
methods achieved a success value of 50%.
A semi-automatic system developed by Melero et al. (2003) for the 3D reconstruction of Iberian vessels by
estimating the orientation of the fragment, computing the symmetry axis, and detecting the profile. In order to
estimate the correct axial angle of an orientation fragment with the aim of extracting a vessel profile, the authors
selected the genetic algorithms because it is a flexible approach and make the method more robust. Through
simulating the method of archaeologists and relying on some measurements, such as the estimation of the diameter
at different heights, rim angle, orientation of shape, extracting the profile and drawing of the fragment, it can
classify the vessel fragments according to rim-fragments. Therefore, by using the 2D drawings of synthetics and the
real fragments to reconstruct Iberian pottery, the system could reduce the error margin to 60%.
A complete framework was proposed by Willis & Cooper (2004) to automatically assemble pots from three-
dimensional fragments, taken into consideration that the pots are axially symmetric. The geometric information was
extracted, which included the symmetric surface axially, the axis of the vessel, the fracture curve and 3D Euclidean
transformation. The authors assumed three assumptions, the surface measurement points which distributed Gaussian
normal distribution, surface measurement normal distributed circularly symmetric Gaussian perturbations on the unit
sphere, and the break-curve measurement points that are distributed spherically symmetric Gaussian. Through
applying the Maximum Likelihood Estimation, the system obtained the ability to assemble the fragments.
Afterwards, the authors applied a Bayesian approach to formulate and merge the four parameters previously
mentioned, and the result that was obtained was the assembling 10 of the 13 fragments belonging to one pot.
Reassembling rotationally symmetric archaeological fragments is a model proposed by Kampel and Sablatnig
(2004). This approach was carried out by determining the correct alignment of the fragment that represents the right
position for the original vessel. In order to classify the fragments, the features were extracted based on the profile
section and the absolute measurement such as color, surfaces and type of material. The matching process has been
done by primitives and relations between the fragments. The authors proposed an approach for a matching algorithm
relying on the point-by-point distance between facing outlines. Their algorithm was applied by the utilization of a
synthetic pot that consisted of five parts, and one rim and two wall fragments. Matching results have been achieved
in some fragments and failed in others.
A fully automated approach has been proposed for the reconstruction of archaeological thin pottery based on
concentric circular rills. It was proposed by Kampel et al. (2005). Their algorithm begins through defining the inner
side of the fragment, and sometimes the other side which contains rills, then the surface of the fragment is
segmented into upper, medium and lower curvatures. The orientation of the fragment is estimated and the
classification process is based on external points and estimate the oriented profile. They tested their method by using
35 fragments of a small size and the lower curvature.
Based on the technique of implicit surfaces and Genetic algorithms for automated pottery classification approaches,
a method was presented by Maiza & Gaildrat (2005). The main idea is the classification of three dimension
archaeological fragments pots, by computing the distance between the tested model and the position of the specified
fragment. Therefore, the features that are used in this work depended on the profile of the object, which includes the
position and the orientation for each fragment. In order to reduce the distance between two pottery fragments and to
find the perfect location based on profile computation, a genetic algorithm was applied and obtains the best match.
Their approach was applied to 100 individuals, including three types of fragments (high, central and low).
A more sophisticated method than the previous in the adoption of the axis of rotation to determine the direction of
the fragment was adopted by Mara & Sablatnig (2006), where they noted that previous methods require the object be
symmetric and complete as well as including manual interaction. Therefore, they presented an automated system to
discard the manual interaction when the profile lines are extracted through dependence on circle templates. In order
to estimate the rotation axis, the authors implemented their method by using synthetic fragments in different shapes
and small sizes and applied the method on real well-known vessels. Hence, the results that were achieved in relation
to the fragments of the object were that the method was able to orientate 24 fragments out of the 25, while applying
the method on a set of 24 synthetic fragments such as a cylinder, cone, sphere and s-shaped object. The method
achieved a small amount of errors. A method based on region features instead of points to automatically reassemble
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3D solid objects was introduced by Huang et al. (2006). This technology includes the application of the
segmentation algorithm based on the graphcuts method for the purpose of spotting the potential surfaces for the
fragment; in this case, the authors computed the boundary of the fragment edges on each face to identify fractured
regions. For the purpose to classify the faces of the fragment, the authors checked the roughness of the fragment
faces, and then generated clusters of feature patches for alignment based matching. The features in this work are
characterized by clusters and overlapping. The matching process between the fragments of an object generates a set
of possible matches. In order to successfully carry out the reconstruction the object, global multi-piece matching was
computed, and a local multi-piece registration was performed at the same time.
Depending on some numeric measures, Igwe & Knopf (2006) used a multi-variable technique for clustering the
fragments automatically, and using unsupervised learning self-organizing feature map (SOFM) algorithm, the
fragments are aligned to achieve matching. They exploited the topological structure and established the lattice
spherical mesh with triangular elements based on a three dimensional SOFM. To deform the node locations and
spherical mesh, each node is given by the weight vectors of elements. The reconstruction process selects the largest
fragment to be the target and are assembled with the rest of the parts that have a similar geometry; the objects that
are assembled using this model do not possess specific geometric features, but depended on data points from each
piece. A study that was focused on assembling thin artifact fragments by obtaining 3D geometric data was presented
by Zhou et al. (2007). The authors relied on external and internal contour features, which are extracted from the
boundary edges of the fragment by using a multiplicity of edge method. After that, polygonal arcs of a triangular
shape are analyzed and a matching algorithm was implemented based on junction vertices. In order to make the
matching algorithm quick and easy, the authors reduced the problem of matching from three dimension polygonal
arcs to one dimensional numerical string, and the reconstruction process was represented as a root of a binary tree,
and the fragments were represented as nodes. Also, they treat the problem of holes and seams through removing the
redundancy triangles, and by generating suture lines, linking all vertices.
Other approaches for automatic assembling of fractured objects that are based on the interaction of archaeologists
for reassembling artifacts was proposed by Lu et al. (2007). Their approach consisted of the transfer of the boundary
of the fragment into curvature and torsion that represents features, and then applying the cyclic edit distance
algorithm, to achieve the matching process between the two fragments. The boundary of fragments was displayed to
the archaeologists, and through their experience, they selected the fragment which is the most probable to be
reconstructed with the other.
One of the works that exploited the edge of a geometric object to match three dimensional fresco fragments was
proposed by Brown et al. (2008), who offered an automatic system for computer-aided documentation and
reassembly of Theran Wall Paintings. Their method includes capturing a virtual 3D model of each fragment along
with high-resolution color and texture information of the front surface. By depending on the shape information on
the side of the fragments and color, plaster surface texture, and surface roughness information, the method attempts
to fit pairs of fragments. The results indicated that the proposed algorithm to match the fragments has achieved high
results when using a ribbon matcher, which depends primarily on the edge of the geometry and the decorations
continuity of the fragments.
4.4 Studies from 2010 till to 2013
In order to highlight the most important studies that have addressed the problem of reconstruction of pottery
fragments within the phase between 2010 and up to 2013:
Through two theorems of mathematical formulation, Arabadjis et al. (2010) presented a methodology to reconstruct
three- dimensional solid objects. Their method relies on selecting one fragment randomly that was considered a
fixed fragment, and as the axis of its center was located on the z -axis. The selection of another one was considered
to be the rotator fragment, which is a random orientation around its central axis, as well its position is random as
well. By exploiting the boundary of the fragments and the application of the mathematical criteria, the researchers
were able to achieve the matching between wall-painting fragments, even when there were gaps between the
fragments, which matched at a rate 50 times of complete matching. For the restoration of Yao Zhou’s famous
porcelain, Zhou et al. (2010) presented a method for estimating the profile and symmetry axis. To briefly review the
method, the rotation axis of the symmetric surface were estimated by relying on the Pottmann and optimization
method, and then calculating the full profile of the pottery fragment by assembling neighboring fragments through
matching features of the various fragments. Also the researchers used texture mapping for the purpose to obtain the
pottery model more realistically.
One approach that merged multiple match properties into a scoring function by using machine learning was
presented by Toler-Franklin et al. (2010). In order to extract features from the database, the authors used three forms
of the database, which were color maps, normal maps and 3D meshes. Based on the differences between the
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calculated properties of patches, the classifier was trained to score patch pairs. Depending on the normal maps, the
authors focused on evaluating the discriminability of their new patch properties. It was noted that the authors were
provided with three new features for special cases. The normal-based features that depended on the fragment when
the color varies from one location to another, sometimes the fragment was exposed to erosion, and sometimes the
fragments contain different types of brush strokes. Therefore, the researchers have relied on extracting features
through calculating the min values, mean values, max values, and the standard deviation values for each feature. The
authors conducted classification experiments on three datasets of fresco fragments. Their method achieved a correct
percentage of the features selected by 90%, and non-match 78%.
As a result of the combined experience and feedback of archaeologists and the use of 3D convex hull technology
with vessel surface markings, Cohen et al. (2010) formulated a generic vessel model. Their work consists of
extracting 3D convex hulls for each fragment from surface markings, which was extracted by using color
information. Through all points on the marking, the matching procedure was done depending on absolute affine
invariant moments, where matching was achieved through a predefined threshold value. The first tests for this
method of the dataset consist of three ceramic vessels that having surface markings. The amount of the residual
alignment errors was in the range between 1.34 x 10-5 and 4.56 x 10-1 when using a nonlinear quadratic map for
each fragment and generic vessels. In the case of the use of a global affine map, the amount of residual alignment
errors was in the range between 0.8 to 15.6 for fragments and generic vessels.
Karasik & Smilansky (2011) proposed a technique based on profile morphological analysis for the classification of
ceramic. Their method depended on the mathematical representation of the profile for ceramic fragments on the
basis of three functions (radius, tangent, and curvature). The authors employ the Cluster Analysis (CA) method to
cluster and classify the fragments by using Discriminate Analysis (DA). The proposed algorithm has been applied
on 358 fragments to reconstruct five types of vessels, and the results showed that the fragments were classified
correctly 94.8%.
In order to determine the pair of candidate fragments for matching fragments depending on the threshold, an
automatic method was presented by Funkhouser et al. (2011). It combines two previous ideas from Shin et al. (2010)
and Toler-Franklin et al. (2010). Their method includes creating the classifier based on many properties extracted
from the fragments match such as contour and ribbon, junction angle and others, for the purpose to achieve accurate
expectations for reconstruction of fresco fragments. They selected the training set, and chose a classification model
that was built from the training set, which depended on M5P regression trees. It then estimated the accurate
probability for new candidate matching between a pair of the fragments, and the classifier become a trainer. By
training a machine on the three datasets taken from different regions, the results indicate that it is possible to train
the classifier for matching a dataset depending on its properties, and then used it for the purpose of prediction
matching from another set.
Belenguer & Vidal (2012) suggested an automatic technique for the reconstruction of 3D archaeological flat
fragments based on the Graphics Processing Unit (GPU) Depth Maps technique. The proposed technique determines
the fragment characterization based on a projection that was calculated through the graphics processing unit, and
that reduces the complexity of the comparison between fragments. The distances on the surface of the fragments can
be measured via the orthographic projection matrix, and this can be determined through the angle of the plane. A
search algorithm is then applied to obtain the alignments between fragments. By employing the hierarchical search
technique, it obtains the optimal solution for the problem of storage in memory. In order to reduce the pre-
processing time and improve the efficiency of calculating the best displacement, the technique of hierarchical
displacement is applied.
Contrary to previous methods, some works did not rely on the border models or mathematical surfaces, but rather
relied on the silhouettes method, such as Kashihara (2012), who suggested an algorithm for the automatic
reconstruction of three-dimensional artifacts from fragments quickly and with high accuracy. The study focused on
the development a Hybrid Genetic algorithm because it is important for defining the approximately spatial position
of 3D fragments and reduced search spaces. To regulate the positioning of 3D fragments, a hill-climbing method
was applied and the features were extracted by using the speeded up robust features (SURF) technique. Therefore, in
this case, the fitness function is evaluated to determine the correct positions of fragments. The author executed the
experiment on a vase that consisted of five fragments. Through the design of a user interface, this enables the
archaeologists to reconstruct the archaeological fragments.
An efficient solution for the automatic reconstruction of three-dimensional Wall-Paintings introduced by
Papaodysseus et al. (2012), where they define the dataset through the surfaces of the upper, lower, sides, and the
central axis of each fragment. In order to get an accurate match, the authors performed a procedure to rotate the
fragment on its central axis at a very small angle around the fixed fragment, which was selected randomly. At the
same time, the probability of contact between their surfaces was determined. There are four criteria are applied in
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each placement to test the matching. The first criterion involves examining the relative lengths of the curves of the
upper surfaces to the joint between two fragments that were potential matching for the purpose of reaching a
suitability match. In the second criterion, the connection between the fixed fragment and the fragment that revolved
around it might obtain some local overlap, so this criterion prevents overlap through the use of a threshold. The third
criterion deals with contact surfaces, and used a theory that had been proved by the authors. The last criterion was
checking the length of the contact curve between the two fragments that had a potential matching, and the matching
was achieved when the volumes of the fragments are less than the threshold that has been estimated previously. The
proposed method was applied to the 41 fragments that were taken from different islands and has achieved a success
rate in some cases by 100%, and did not achieve matching in other instances. Son et al. (2013) proposed to solve the
problem of the automatic restoration of three thin clay pots, mixed with each other, or in case of presence of gaps.
The authors relied on the geometric structure of the object and the way the fragment was broken. They considered
that the object was axially symmetric. They solved the problem by exploiting the two approaches that took
advantage of the local and global geometric structure, and their methods include estimating the accurate Axis of
symmetry Profile Curve (APC) for each fragment by using circle templates. The classification of fragments was
separated into four types depending on the criteria sufficiency and distinctiveness that was done, and the matching
of the fragments that have characteristics of symmetry were also implemented. Other algorithms were applied in the
absence of the symmetry properties of the fragments because they were small, flat or spherical. These algorithms
were based on extracting the feature points from fractures curves. The system was able to reassemble three pots
consisting of 48 fragments during 10.56 hours by using the Intel Core i7 processor.
5- Analysis the Results
A variety of algorithms have proposed methods to reconstruct the archaeological pottery fragments. This paper is
interested to analyze the most successful research works that were implemented in the period between 1980 and
2013. In particular, those who have worked in the field of reconstruction of three-dimensional pottery fragments,
and several works focused on the field of solid objects, such as Hall and Laflin (1984), Huang et al. (2006), and
Arabadjis et al. (2010).
Table 1. Demonstrates Studies Performed during 1970 -2013
Study period
No. of Study
1980-1984
1
1995-1999
4
2000-2004
13
2005-2009
8
2010-2013
9
Total
35
Fig. 2. Demonstrates the Studies Performed Since 1980 - 2013
As shown in Table 1 and Fig 2, there are a few studies that are interested in reconstructing the fragments in the
eighties. The researchers focused on the archiving, documentation, drawing, and storage of thousands of broken
fragments that have been excavated in a numerous locations. So, they exploited the computer for creating a large
database to facilitate viewing and accessing information quickly. We would like to point out that the authors began
0
5
10
15
1980-1984
1995-1999
2000-2004
2005-2009
2010-2013
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720
their interest to find solutions for reassembling fragments of objects during the last three decades; especially in the
2000’s and onward.
It turns out that most of the studies suggested an automated system, except the few studies that required intervention
by the archaeologists to take a decision for the reconstruction of fragments, i.e., semi-automatic systems such as
(Melero et al. 2003). Therefore, automatic methods were used to increase accuracy.
Additionally, this study focused on most of the features that were extracted for the purpose of reconstruction of
archaeological pottery fragments in the previous research works. Most of these research works followed to estimate
the profile that includes the details in Table 3; in particular, during the 2000s, the authors focused on the geometric
surface in order to obtain the clustering and matching of the fragments, and sometimes also the edges, such as
contours, outlines and boundaries. Table 2 and Figure 2 show that the authors reduced their dependence on profiles
during the period from 2010 to 2013, and focused more on color and texture to extract features.
Table 2. Shows most of the Features used in articles during the period 1980–2013.
The study period
Features extracted
Number of articles
Studies in the 80’s
-B-Spline curves
1
Studies in the 90’s
- Geometric.
- Outlines of the shapes.
2
1
Studies in the 2000s
- B-Spline.
- Boundary of the fragment
- Profile.
1
2
18
Studies from 2010-2013
- Color.
- Edges.
- Profile.
2
2
4
Fig. 2. demonstrates most of Features used in articles during the period 1980–2013
Table 3. Shows the details of the Profile that estimated.
The study period
Profile
Studies in the 80’s
- Outlines.
Studies in the 90’s
- Estimate the parameters such as diameter and the perimeters of the object
- Axis of rotation .
Studies in the 2000s
- Estimating the fracture side or break-curves
- Estimated the curvature points and the rotational axis
- Symmetry axis
- Axial angle of an orientation of the fragment
- The measurements such as the ratio of the fragment area of an object and both
the dimensions and diameter of the object
Studies from 2010-
2013
- Rotation axis of the symmetric surface were estimated
- Radius, tangent, and curvature
- Estimating the accurate Axis of symmetry Profile Curve (APC)
0
2
4
6
8
10
B-spline
curves
Geometric.
Outlines
B-spline
Boundary
Profile
Geometric
Color
Edges
Profile
Geometric
80’s
Studies in the
90’s
Studies in the 2000s
Studies from 2010-2013
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721
In order to highlight the most important techniques that the authors adopted over the past decades about the
classification of archaeological fragments in the light of extracted features, and reconstruction into their original
form. Table 4 shows most of the techniques that have been used it to implement the classification and matching
process.
Table 4. Shows most of the Classification and matching technique used since 1980 until 2013
The study period
Classification
Matching
Studies in 90’s
- Descriptive language
- Highest similarities between the graph and sub-
graph.
- Noise Tolerant algorithm.
Studies in 2000s
- Genetic algorithms.
- Self-organizing feature map
(SOFM) algorithm.
- Governed basic rules.
- Bayesian method.
- Evaluation of the probability a χ2 -statistic.
- Computing the confidence bounds for the axis and
bootstrap methods.
- Minimized the distance by the standard global
optimization scheme.
- Partial similarities of the profiles.
- Maximum Likelihood Estimation and Bayesian
approach.
- Point-by-point distance.
- Global Multi-Piece.
- Rest of the parts that have a similar geometry.
- Matching algorithm was implemented based on
junction vertices.
- The cyclic edit distance algorithm.
Studies from 2010-
2013
- Based on the differences between the
calculated properties of patches.
- Discriminate Analysis (DA).
- M5P regression trees.
- Distances.
- Hybrid Genetic algorithm.
- Fixed fragment, and rotator another fragment
random orientation around its central axis.
- Assembling neighboring fragments through
matching features.
- Absolute affine invariant moments.
- Graphics Processing Unit.
- Four criteria are applied in each placement to test
the matching.
- Criteria sufficiency.
Through the review of the mentioned studies, it was found that most authors relied on synthetics and the real
fragments to apply their proposed algorithms. Some authors relied on the Genetic algorithms classifier such as
(Melero et al. 2003; Maiza & Gaildrat 2005), the result that (Melero et al. 2003) have achieved reduced the error
margin to 60%. (Karasik & Smilansky 2011) have applied Discriminate Analysis, and achieved a success rate of
94.8% by using a database of a total of 358 fragments to test their model. It turns out that the proposed solutions to
the classification technique is still not meet the ambitious.
As for the match and reconstruction methods many researchers proposed different methods, for example Sablatnig
& Menard (1997) relied on highest similarities between the graph and subgraph; Whereas Üçoluk & Toroslu (1999)
depended on Noise Tolerant algorithm. The previous studies through period 2000 to 2009 relied on statistical
methods to reconstruct the fragments to the original form such as Willis et al. (2001); Andrews & Laidlaw (2002);
depended on Bayesian methods, evaluation of the probability a χ2 - statistic respectively. Also the previous studies
depended on mathematical methods such as Papaioannou et al. (2002); Kampel and Sablatnig (2004); relied on
minimized the distance by using the standard global optimization scheme, and point-by-point distance.
Whereas Zhou et al. (2007) reconstruct the object by employing fragments matching algorithm, that was
implemented based on junction vertices. Finally, (Papaodysseus et al. 2012; Son et al. 2013) the highest approximate
results achieved in some cases by 100% when applied spatial criteria in each placement to test the matching.
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722
CONCLUSION AND RECOMMENDATIONS
One of the main challenges is the reconstruction of fractured archaeological artifacts through a large number of
fragments that are excavated, and finding the correct matching between them. In this paper, we attempt to
summarize most of the previous research work for the purpose of facilitating new proposed methods, and to find the
necessary solutions for the classify and reconstruction of archaeological fragments. We conclude that the previous
computer methods for this task relied on the geometric features in the case of three-dimensional models, and the
authors relied on the estimation of the profile, which includes the symmetry axis and orientation of the fragment.
Nevertheless, use of the profile decreased during the period of 2010 to 2013, where researchers instead focused on
other features such as the color and edges.
On the whole, the computer assists in reconstructing the archaeological fragments accurately and reassembling them
to the original form in a two-stage process involving classification the fragments into groups and reconstruct. We
conclude that the researchers focused on reconstructing the object without classification the fragments into groups,
note that the artifacts normally are found in a fractured state and mixed randomly, and the process of manual
classification may require a great deal of time and tedious work. Hence, it is important to come up with a solution
for the classification of the archaeological fragments accurately into groups and reassembling each group to the
original form by using computer techniques.
Additionally, we concluded that numerous studies depended on the principle component analysis method (PCA) to
speed up the computation process and maintain most of the information, and also to select the best features. The
other observation in most of the studies is that the reassembly of fragments adopted statistical methods, geometrical
properties across fracture surfaces, the mathematical criteria and surface morphology. Also, some systems relied on
archaeologists experience, and most previous works have focused on pairwise matching between two adjacent
fragments by aligning fragments in fractured edges. Also, they usually exploited one feature without using the
combination of many features, i.e., combining between the fragment structure that is divided into two main parts,
shape features, and properties of the fragment, for the purpose to obtain the best classifiers.
In the future, more details about the contents of the studies must be mentioned in order to formulate a large database
that may be a reference for researchers working in this field.
ACKNOWLEDGMENTS
The researchers wish to thank Universiti Kebangasaan Malaysia (UKM) and Ministry of Higher Education
Malaysia for supporting this work by research grant ERGS/1/2012/STG07/UKM/02/9.
REFERENCE
A. Castañeda, B. Brown, S. Rusinkiewicz, T. Funkhouser and T. Weyrich, “Global consistency in the automatic
assembly of fragmented artefacts,” Proceeding of the 12th International Symposium on Virtual Reality,
Archaeology and Cultural Heritage VAST, 2011, pp.73–80.
A. Karasik and U. Smilansky, “Computerized morphological classification of ceramics,” Journal of Archaeological
Science 38, 2011, pp.2644-2657.
A. Willis, S. Andrews, J. Baker, Y. Cao, D. Han, K. Kang, W. Kong, F. F. Leymarie, X. Orriols, S. Velipasalar, E.
L. Vote, D. B. Cooper, M. S. Joukowsky, B. B. Kimia, D. H. Laidlaw and D. Mumford, “Assembling virtual
pots from 3D measurements of their fragments,” ACM. Proceeding of conference on Virtual reality archeology
and cultural heritage, 2001, pp.241–254.
A. Willis, X. Orriols and D. Cooper, “ Accurately estimating sherd 3D surface geometry with application to pot
reconstruction,” IEEE, Proceedings of the Conference on Computer Vision and Pattern Recognition
Workshop, In CVPR Workshop ACVA, vol.1, June, 2003, pp.1–7.
A. R. Willis and D. B. Cooper, “Bayesian assembly of 3d axially symmetric shapes from fragments,” IEEE
Computer Society Conference on CVPR, vol.1, 27 June-2 July, 2004, pp.82-89.
B. Brown, C. Toler-Franklin, D. Nehab, M. Burns, D. Dobkin, A. Vlachopoulos, C. Doumas, S. Rusinkiewicz and
T. Andweyrich, “A System For High-Volume Acquisition And Matching of Fresco Fragments: Reassembling
Theran Wall Paintings,” ACM Transactions on Graphics (Proc. SIGGRAPH), vol. 27, no. 3, August, 2008,
pp.1-9.
C. Maiza and V. Gaildrat, “Automatic Classification of Archaeological Potsherds,” ACM Journal on Computing and
Cultural Heritage, vol. 5, no. 4, Article 15, 2005, pp.135-147.
ISSN 2320-5407 International Journal of Advanced Research (2015), Volume 3, Issue 3, 712-714
723
C. Papaodysseus, D. Arabadjis, M. Exarhos, P. Rousopoulos, S. Zannos and L. Papazoglou-Manioudaki, “Efficient
Solution to the 3D Problem of Automatic Wall Paintings Reassembly,” Computers and Mathematics with
Applications, vol.64, no.8, 2012. pp.2712–2734.
C. S. Belenguer and E.V. Vidal, “Archaeological Fragment Characterization and 3D Reconstruction based on
Projective GPU Depth Maps,” IEEE 18
th
International Conference on VSMM, September, 2012, pp. 275-282.
C. Toler-Franklin, B. Brown, T. Weyrich, T. Funkhouser, S. Rusinkiewicz, “Multi-feature matching of fresco
fragments,” ACM Transactions on Graphics (Proc. SIGGRAPH Asia), vol. 29, Issue 6, Article No., 2010,
185 :185.
D. Arabadjis, C. Papaodysseus, Ρ. Rousopoulos and M. Panagopoulos, “On the Mathematical Formulation of the
Problem of Reassembling Fragmented Objects: Two New Theorems,” Journal of Applied Mathematics and
Computing. Springer, vol. 34, 2010, pp.81-100.
F. Cohen, Z. Zhang and P. Jeppson, “Virtual reconstruction of archaeological vessels using convex hulls of surface
markings,” In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops
(CVPRW), ISSN (2160-7508), 2010, pp.55–61.
F. J. Melero, J. C. Torres and A. León, “On the interactive 3D reconstruction of iberian vessels,” Proceeding of the
4
th
International conference on Virtual Reality, Archaeology and Intelligent Cultural Heritage, 2003, pp.71-78.
F. Richter, X. C. Ries and R. Lienhart, “A graph algorithmic framework for the assembly of shredded documents,”
IEEE International Conference on Multimedia and Expo ICME, July, 2011, pp.1–6.
F. Stanco, D. Tanasi and G. Gallo, “Virtual restoration of fragmented glass plate photographs of archaeological
repertoires,” Virtual Archaeology Review VAR, vol. 2, no. 3, 2011, pp.141–144.
G. Oxholm and K. Nishino, “A flexible approach to reassembling thin artifacts of unknown geometry,” The
ScienceDirect interface, Journal of cultural heritage, val. 14, no. 1, 2012, pp.51–61.
G. Papaioannou, E. A. Karabassi and T. Theoharis, “Automatic Reconstruction of Archaeological Finds- A Graphics
Approach,” Proceeding of the 4
th
Intern. Conf. Computer Graphics and Artificial Intelligence, 2000, pp.117–
125.
G. Papaioannou, E. A. Karabassi and T. Theoharis, “Reconstruction of three-dimensional objects through matching
of their parts,” IEEE Transactions on Pattern Anal. vol.24, no.1, 2002, pp.114-124.
G. Üçoluk and I. H. Toroslu, “Automatic reconstruction of broken 3-D surfaces objects,” The ScienceDirect
interface, Computer and Graphics, vol. 23, no. 4, 1999, pp. 573–582.
H. Mara, M. Kampel and R. Sablatnig, “Preprocessing of 3D-Data for Classification of Archaeological Fragments in
an Automated System,” Proceeding of the 26
th
Workshop of the Austrian Association for Pattern Recognition,
Vision with Non-Traditional Sensors (ÖAGM), 2002, pp. 257–264.
H. Mara and R. Sablatnig, “Orientation of Fragments of Rotationally Symmetrical 3D-Shapes for Archaeological
Documentation,” IEEE Third International Symposium on 3D Data Processing, Chapel Hill, NC. USA, June,
2006, pp.1064-1071.
H. Leitao and J. Stolfi, “Measuring the information content of fracture lines,” Springer Science, International
Journal of Computer Vision, vol. 65, no. 3, 2005, pp. 163–174.H. Shin, C. Doumas, T. Funkhouser, S.
Rusinkiewicz, K. Steiglitz, A. Vlachopoulos and T. Weyrich, “Analyzing fracture patterns in Theran wall
paintings,” ACM, JOCCH Homepage archive, vol. 5, no. 3, Article No. 10, 2010, pp. 1–8.
H. Shin, C. Doumas, T. Funkhouser, S. Rusinkiewicz, K. Steiglitz, A. Vlachopoulos and T. Weyrich, “Analyzing
and simulating fracture patterns of Theran wall paintings,” ACM Journal On Computing And Cultural
Heritage, vol. 5, no. 3, Article 10, 2012, pp.1–14.
K. H. Schindler, M. Kampel and R. Sablatnig, “Fitting of a closed planar curve representing a profile of an
archaeological fragment,” ACM Proceeding of the Conference on Virtual reality, archeology and cultural
heritage, 2001, pp.263–269.
K. Kashihara, “Three-dimensional Reconstruction of Artifacts Based on a Hybrid Genetic Algorithm,” IEEE
International Conference on Systems, Man and Cybernetics, October, 2012, pp.900-905.
K. Son, E. B. Almeida and D. B. Cooper, “Axially Symmetric 3D Pots Configuration System Using Axis of
Symmetry and Break Curve,” IEEE Conference on Computer Vision and Pattern Recognition, June, 2013,
pp.257-264.
M. Kampel and S. Sablatnig, “3d Puzzling of Archaeological Fragments,” Proceedings of the 9
th
Computer Vision
Winter Workshop. January 2004, pp.31–40.
M. Kampel and R. Sablatnig, “Profile-based Pottery Reconstruction,” IEEE, Proceedings of Conference on
Computer Vision and Pattern Recognition Workshop, Wisconsin, June, 2003a, pp.1–6.
M. Kampel and R. Sablatnig, “ An Automated Pottery Archival and Reconstruction System. Journal of Visualization
and Computer Animation,” vol. 14, 2003b, pp. 111–120.
ISSN 2320-5407 International Journal of Advanced Research (2015), Volume 3, Issue 3, 712-714
724
M. Kampel, R. Sablatnig and H. Mara, “Robust 3d Reconstruction of Archaeological Pottery Based on Concentric
Circular Rills,” Proceeding of 6
th
International Workshop on Image Analysis for Multimedia Interactive
Services, Monterux, Switzerland, 2005, pp.14-20.
M. Zhou, G. Geng, Z. Wu, X. Zheng, W. Shui, K. Lu and Y. Gao, “A System for Re-Assembly of Fragment Objects
and Computer Aided Restoration of Cultural Relics,” Tiré-à-part des Actes du colloque, Virtual Retrospect
2007 Pessac (France), 2007, pp. 21-27.
M. Zhou, G. Geng, Z. Wu and W. Shui, “A Virtual Restoration System for Broken Pottery,” CAA Conference 37
th
Computer applications and quantitative methods in archaeology, 2010, pp. 391-396.
N.S. Hall and S. Laflin, “Computer Aided Design Technique for Pottery Profiles,” Proceeding of Conference
Centre for Computing and Computer Science, Birmingham, 1984, pp.178–188.
P. C. Igwe and G. K. Knopf, “3D Object Reconstruction Using Geometric Computing,” IEEE In Geometric
Modeling and Imaging, New Trends, August, 2006, pp. 9-14.
P. Smith, D. Bespalov, A. Shokoufandeh and P. Jeppson, “Classification of archaeological ceramic fragments using
texture and color descriptors,” IEEE , Society Conference on Computer Vision and Pattern Recognition
Workshops (CVPRW), June, 2010, pp. 49–54.
Q-X. Huang, S. Flory, N. Gelfand, M. Hofer and H. Pottmann, “Reassembling fractured objects by geometric
matching,” ACM Transactions on Graphics, vol. 25, no.3, 2006, pp.569-578.
R. Halíř and J. Flusser, “Estimation of Profiles of Sherds of Archaeological Pottery,” Proceeding of the Czech
Pattern Recognition Workshop, February, 1997, pp.126–130.
R. Halíř, “An Automatic Estimation of the Axis of Rotation of Fragments of Archaeological Pottery: A Multi-Step
Model-Based Approach,” Proceeding of 17
th
International Conference in Central Europe on Computer
Graphics, Visualization and Interactive Digital Media, 1999, pp:1–7.
R. Sablatnig and C. Menard, “3D Reconstruction of archaeological pottery using profile primitives,” Proceeding of
the International Workshop on Synthetic-Natural Hybrid Coding and Three-Dimensional Imaging, Rhodes,
Greece, September, 1997, pp:93–96.
S. Andrews and D.H. Laidlaw, “Toward a Framework for Assembling Broken Pottery Vessels,” Proceeding of 18
th
International Conference on Artificial Intelligence, 2002, pp. 945–946.
T. Funkhouser, H. Shin, C. Toler-Franklin, A. G. Castañeda, B. Brown, D. Dobkin, S. Rusinkiewicz and T.
Weyrich, “Learning how to match fresco fragments,” Journal on Computing and Cultural Heritage (JOCCH),
vol. 4, no.7, April, 2011, pp. 1–7.
Y. Cao and D. Mumford, “Geometric structure estimation of axially symmetric pots from small fragments,”
Proceeding of the International Conference on Signal Processing, Pattern Recognition and Applications, June,
2002, pp.92–97.
Y. Lin and W. Chiang, “Reconstruction of a shredded document based on image feature matching,” The Science
Direct interface Expert, Systems with Applications, vol. 39, no. 3, 2012, pp.3324–3332.
Y. Lu, H. Gardner, H. Jin, N. Liu, R. Hawkins and I. Farrington, “Interactive Reconstruction of Archaeological
Fragments in a Collaborative Environment,” IEEE 9
th
Biennial Conference of the Australian Pattern
Recognition Society on Digital Image Computing Techniques and Applications 3, 2007, pp.23-29.
