A Search Method for Reassembling the Elements of a Broken 2D Object

Abstract

Searching for and reassembling the elements that used to form one whole is a very common issue faced by archaeologists. This is because preparing an interesting museum exhibition consists in the presentation of the objects that have been put together, not a pile of messily disassembled puzzle pieces. The article presents the concept of using the linguistic methods in the process of joining the elements of a 2D jigsaw puzzle. The method developed in the first stage creates the edge description of an object by defined unit vectors of the same length but different directions, and assigns them a designation in the form of letters, which leads to the creation of abstract words in the form of a sequence of signs. In the second stage, the words with a defined length of strings belonging to two different objects are compared. The authors have created a program that performs an exhaustive search until the pool of available elements is fully exhausted. The conducted numerical experiments indicate the correctness of the method and effectiveness in determining the places of joining elements. The developed method will be useful to automate the reassembly of 2D elements from archaeological excavations.

The Use of Fuzzy Evaluation and Radical Cut-Off Strategy to Improve Apictorial Puzzle Assembly with Exhaustive Search Algorithm Performance

“…1). The process of creating the contour, its features, as well as the principle of operation of the method have already been discussed in the article [10]. The description of the contour used diff ers from those that can be found in the literature, e.g.…”

“…However, this is burdened with a large number of calculations (including comparing sub-strings, of a certain length, from every two elements contours, shifted by one character) and a long execution time [14]. The complexity of calculations, as the number of computations and the time it takes to complete them, grows exponentially with each successive element added to the initial pool (Table 1) [10].The obvious solution would be to implement vertical scaling (increasing the computing power of the calculating machine, concurrent processing), horizontal scaling (spreading calculations over many machines) or both. This action would lead to a general reduction in the duration of searching for all possible solutions, however it would not help to improve the quality, which can be interpreted, inter alia, as performing mainly processes that can bring the actual results.…”

“…In this way, it would be possible to achieve both an increase in quality and a reduction in the time needed to perform the calculations. The results of the previous numerical experiments [10,14] showed that in the constructed algorithm too many comparisons are made, even in situations that do not lead to obtaining solutions forming a compact system. The attempts to limit the number of potential connections, by implementing fail-fast components, so far have proved that it is possible to rapidly reduce the final number of comparisons made (Table 2).…”