The reconstruction of archaeological fragments in 3D geometry is an important problem in pattern recognition and computer vision. Therefore, we implement an algorithm with the help of a 3D model to perform reconstruction from the real datasets using the slope features. This approach avoids the problem of gaps created through the loss of parts of the artifacts. Therefore, the aim of this study is to assemble the object without previous knowledge about the form of the original object. We utilize the edges of the fragments as an important feature in reconstructing the objects and apply multiple procedures to extract the 3D edge points. In order to assign the positions of the unknown parts that are supposed to match, the contour must be divided into four parts. Furthermore, to classify the fragments under reconstruction, we apply a backpropagation neural network. We test the algorithm on several models of ceramic fragments. It achieves highly accurate results in reconstructing the objects into their original forms, in spite of absent pieces.