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This paper, introduces a new approach for the automated reconstructionreassembly 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 important, in the 2 virtual reassembling of parts of wall-paintings belonging to the Mycenaic civilization (c.1300 BC.), excavated highly fragmented in Tyrins, Greece.

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In this paper, a novel approach is introduced for classifying curves into proper families, according to their similarity. First, a mathematical quantity we call plane curvature is introduced and a number of propositions are stated and proved. Proper similarity measures of two curves are introduced and a subsequent statistical analysis is applied. First, the efficiency of the curve fitting process has been tested on 2 shapes datasets of reference. Next, the methodology has been applied to the very important problem of classifying 23 Byzantine codices and 46 Ancient inscriptions to their writers, thus achieving correct dating of their content. The inscriptions have been attributed to ten individual hands and the Byzantine codices to four writers.

In this article, an integrated conjecture about the method of drawing of monumental prehistoric wall-paintings is presented and supported. Specifically, the article deals with paintings that initially decorated the internal walls of the highest floor of a building, called "Xeste 3", at Akrotiri of the Greek island of Thera circa. 1650 B.C. It is argued that these wall-paintings could had been drawn while the brush was guided by an apparatus, which corresponds to advanced for the era of geometric prototypes with impressive precision. A set of assumptions concerning the actions the artists might have taken in order to create the spiral themes is stated and supported. These assumptions refer to the existence of a draft plan, the sequence of brush strokes, the placement of the brush on the wall, as well as the possible form of the apparatus. These conjectures are evaluated and tested by means of curve fitting and image analysis methods developed by the authors. The results indicate that all drawn contour parts optimally fit along a single prototype linear spiral with fitting error of less than 0.4mm, supporting existence of a very advanced culture for the era of geometric guide. It is statistically rejected that this guide could have the form of a stamp. Moreover, there is strong evidence that the painter might have used a draft plan of the spiral themes to prepare the final drawing and that the linear spiral guide has been used by alternating its placements in order to form the internal and external spiral contour.General Terms: Algorithms Additional Key Words and Phrases: Finding the method of drawing of paintings, prototypes determination in paintings, prehistoric paintings and geometry, curve fitting ACM Reference Format: Roussopoulos, P., Papaodysseus, C., Arabadjis, D., Exarhos, M., and Panagopoulos, M. 2010. Image and pattern analysis for the determination of the method of drawing celebrated Thera wall-paintings circa 1650 B.C. ACM J.