The reconstruction of archaeological objects is a very challenging problem and solving this problem is important. Occasionally, archaeological workers suffer when trying to match object fragments together, especially when there is a presence of significant gaps in the fragments, or even in the case of similarity, where fragments are mixed with fragments of other objects. The main theme of this study is a proposed method for the reconstruction of pottery from archaeological fragmented pots and vases, depending on the use of a polynomial function. In any case, there is an important fact that should be mentioned: The assembly of any object will rely on the edges of the fragment firstly, then the color and texture. Therefore, this study has adopted the edges of the fragments as a condition when reconstructing the objects, by exploiting the edges of the fragments as an important feature, mainly due to the fact that edges of the fragments are lines, corners and curves. A Canny filter was used to identify the edges of the fragments. In addition, for the purpose of obtaining the vector of coefficient for the set of edges, a polynomial function algorithm was applied. Lastly, the experiments shows that the algorithm is effective, especially when applying the correlation coefficient formula in the classification phase by using the data set which consists of 56 pieces and each one has edges at a rate of 3-5 cm. The experimental results achieved a high success rate that means the proposed system may produce high performance to recognize and match the edges by using a polynomial function to extract features and to classify them by using a correlation coefficient.

One of the major unresolved and difficult problems that occur through the field of computer vision is to reassemble broken or torn objects, such as archeological objects, documents, paleontology and art conservation, especially when exploring archaeological objects that are frequently in the case of being broken. Therefore, it is of great interest that the objects are assembled before they are lost or damaged (Casta?eda et al., 2011; Oxholm and Nishin, 2012). Another important issue is finding solutions that challenge the accurate restoration of the archaeological fragments to their original form because of their high value to scholars and their heritage, that represents the past civilizations and cultures and helps archaeologists make inferences about past civilizations (Funkhouser et al., 2011). As mentioned earlier, the artifacts are often found in a fractured state and the process of manually reconstructing them is time consuming and may take years of tedious work (Son et al., 2013). Therefore, their reconstruction is a challenging task, especially if they exceed thousands of fragments and the assembly process seems to be similar to assembling a jigsaw puzzle (Casta?eda et al., 2011; Funkhouser et al., 2011).

Recently, while the world has been witnessing a development, especially in the performance of computers as the use of image processing and pattern recognition techniques have emerged, many of the authors found algorithms to assist them in solving many problems. Thus, this study aims to find a solution for assembling archaeological fragments depending on the edges of the fragment to achieve high accuracy with the least time. To highlight the technique used in this study, the main feature to achieve accurate matching between a pair of fragments is to use the edge curve, because each edge is a curve that contains angles and curvatures. Therefore, it will be applied to the polynomial function to calculate the function for each edge and by comparing the coefficients of functions for both edges, the classification will be done based on the values of the coefficients and their signs. This study is structured as follows: The present background of study is drawn in section 2. An overview of the polynomial function is presented in section 3. Section 4 describes the system overview. Section 5 gives the details of experiments and results. Finally, a conclusion is given in section 6.

For the purpose of utilization of historical monuments and protecting them from damage, which they may be exposed to due to negligence or attempts to assemble them manually, it is necessary to find automatic solutions by using computer techniques. So much work has been done on the reassembling of fragments in both 2 and 3-dimensions. In order to highlight the most important studies that have addressed this problem based on 2-dimensional techniques, several important studies are taken into consideration. Leitao and Stolfi (2005) provided many of the studies in the field of assembling pottery fragments and the latest was in 2005.

This study determined pottery fragments that were matched by measuring the average amount of information contained in the form of a break line of a given length. Subsequently, most of the previous work focused on finding pairwise matches between adjacent fragments using surface color and texture, without reference to the use of the fragment edges and this is found in (Smith et al., 2010), where they suggested methods for ceramic fragments that were highly textured and classified them based on the color and texture characteristics. Generally, their algorithm resulted in better accuracy in the case of assembling the fragments and relying on their characteristics of color and texture. On the other hand, others relied on texture features only for classification of ancient-ceramic fragments, such as Ying and Gang (2010); their method can’t be applied when fragments do not have a texture. Toler-Franklin et al. (2010) disagreed with the authors who relied on the traditional features in the classification of archaeological fragments and they were relying on multiple-features that were extracted from fresco fragments based on color, shape and normal maps. Another work by (Kimia and Aras, 2010), includes a framework, or a practical system, that can be used by archaeologists in reassembling 2 dimensional archeological vessel fragments and that could be applied to 3dimensional fragments. Zhang et al. (2011) focused on the contour of the fragment in the matching process and their proposed method relies on a curve matching algorithm that is based on the multiscale space. On the other hand, a variety of algorithms have been proposed to reconstruct the fragments of wall panels excavating of the Greek island Thera (Santorini), which were painted in 1600 B.C. Skembris et al. (2012) proposed a methodology for the reconstruction of 2-dimensional fragmented wall paintings based on the maximum possible information extracted from the shape (contour) characteristics of the pieces, the chromatic and thematic content.

Another type of study on classification of fragments was proposed by (Makridis and Daras, 2012), they focused on the features that are extracted based on chromaticity and chrominance (color) and the low level features, such as standard deviation and the contrast. Also the medium level features such as the extraction of the edges of the fragment are carried out by using a kirsch edge map and extracting the texture depending on the LBP method. The results they obtained after testing the model on the pottery database with a total of 62 fragments achieved a success rate 70.97%, while the results after testing the model on the ceramic database of a total of 46 fragments, it achieved a success rate 78.26%. Also, to reconstruct fresco fragments, Funkhouser et al.(2011) investigated a machine learning method which computes the probability of the matching correctness, combining multiple effective features.