Efficient Solution to the 3D Problem of Automatic Wall Paintings Reassembly

TL;DR

This paper presents a novel automated method for reassembling 3D fragments of wall paintings using new criteria based on volume, overlap, and calculus of variations, successfully applied to ancient artifacts.

Contribution

It introduces four innovative criteria for matching fragments, combining volume, overlap, and calculus of variations principles, to improve automated reassembly accuracy.

Findings

Successful reconstruction of artificially broken objects.

Effective virtual reassembly of ancient wall paintings.

High accuracy in fragment matching using new criteria.

Abstract

This paper introduces a new approach for the automated reconstruction - reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D scanning of the available fragments. The obtained representations are properly processed so that they can be tested for possible matches. Next, four novel criteria are introduced, that lead to the determination of pairs of matching fragments. These criteria have been chosen so as the whole process imitates the instinctive reassembling method dedicated scholars apply. The first criterion exploits the volume of the gap between two properly placed fragments. The second one considers the fragments' overlapping in each possible matching position. Criteria 3,4 employ principles from calculus of variations to obtain bounds for the area and the mean curvature of the contact surfaces and the length of contact curves, which must hold if the two fragments match. The method has been applied, with great success, both in the reconstruction of objects artificially broken by the authors and, most importantly, in the virtual reassembling of parts of wall paintings belonging to the Mycenaic civilization (c. 1300 B.C.), excavated in a highly fragmented condition in Tyrins, Greece.