In this paper, a color image segmentation method and a pattern analysis are presented, in connection with the extraordinary 1650 B.C. wall paintings found in the Greek island of Thera. These wall paintings are usually reconstructed from thousands of fragments widely scattered in the excavated site. The fragments' depiction manifests inhomogeneous color decay, cracks, added extraneous material, etc. The proposed color image segmentation method takes into account the decay problems and offers a very good approximation of the initial fragment depiction as the artist drew it in the late Bronze Age. The algorithm performs essentially better than other standard segmentation schemes as extensive qualitative tests indicate. Moreover, it offers clear-cut color regions and region borders for each fragment depiction. The whole approach is based on classifying the pixels into a number of regions where each region is described by a normal distribution, followed by fragment-decay reduction and edge refining. Extensive pattern analysis to the obtained region borders leads to the conclusion that 3650 years ago, the artist most probably used advanced geometrical methods in order to construct handcrafted ldquoFrench curvesrdquo (stencils or templates) and use them to draw certain figures. On the basis of the aforementioned results, specific pattern matching techniques are employed for the reconstruction of wall paintings, depicting spirals, from their constituent fragments.

In this paper, a methodology of general applicability is presented for answering the question if an artist used a number of archetypes to draw a painting or if he drew it freehand. In fact, the contour line parts of the drawn objects that potentially correspond to archetypes are initially spotted. Subsequently, the exact form of these archetypes and their appearance throughout the painting is determined. The method has been applied to celebrated Thera Late Bronze Age wall paintings with full success. It has been demonstrated that the artist or group of artists has used seven geometrical archetypes and seven corresponding well-constructed stencils (four hyperbolae, two ellipses, and one Archimedes' spiral) to draw the wall painting "Gathering of Crocus" in 1650 B.C. This method of drawing seems to be unique in the history of arts and of great importance for archaeology, and the history of mathematics and sciences, as well.

In this paper, a new decisively important factor in both the perceptual and the automated piano-guitar identification process is introduced. This factor is determined by the nontonal spectral content of a note, while it is, in practice, totally independent of the note spectrum tonal part. This conclusion and all related results are based on a number of extended acoustical experiments, performed over the full pitch range of each instrument. The notes have been recorded from six different performers each of whom played a different instrument. Next, a number of powerful criteria for the classification between guitar and piano is proposed. Using these criteria, automated classification between 754 piano and guitar test notes has been achieved with a 100% success rate.

In this paper, an original general methodology is introduced to establish whether a handmade shape corresponds to a given geometrical prototype. Using this methodology, one can decide if an artist had the intention of drawing a specific mathematical prototype or not. This analysis is applied to the 1650 B.C. wall paintings from the prehistoric settlement on Thera, and inferences of great archaeological and historical importance are made. In particular, strong evidence is obtained suggesting that the spirals depicted on the wall paintings correspond to linear (Archimedes) spirals, certain shapes correspond to canonical 48-gon and 32-gon, while other shapes correspond to parts of ellipses. It seems that the presented wall paintings constitute the earliest archaeological findings on which these geometrical patterns appear with such remarkable accuracy.