Search

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 "French curves" (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. Index Terms--Curve fitting, image reconstruction, image segmentation.

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. Index Terms--Image line pattern analysis, archaeological image edge analysis, archaeological object reconstruction, curve fitting, statistical pattern matching.

An original general methodology is introduced to establish whether a handmade shape corresponds to a given geometrical prototype. This analysis is applied to the 1650 B.C. wall paintings from the prehistoric settlement on Thera, and interferences of great archaeological and historical importance are made.

A general methodology is described for computer-aided reconstruction of 1600 B.C. wall paintings from the Greek island Thera (Santorini).

Two kinds of numerical error occur during the execution of the Levinson-Durbin algorithm for solving a linear systems of equations. The first has an erratic nature and is generated by a particular iteration's erroneous value of input autocorrelation. Its effect is constrained to a specific recursion. The second is a systematic error that is enlarged with subsequent computations. Both, however, may be traced via a methodology that yields the exact number of erroneous digits during the computation.

The least squares (LS) FIR filtering and iota-step ahead linear prediction problems are evaluated. A symmetrical Toeplitz system with a positive definite system matrix is solved to obtain the filter coefficients for both problems. A recursive formula is then applied to determine the values of the lagged latticecoefficients. Results reveal that LS FIR filtering and the iota-step ahead prediction problem have different numerical behavior.

A new technique for automated recognition-identification of distorted musical recordings is presented.

A novel methodology is introduced here that exploits 2D images of arbitrary elastic body deformation instances so as to quantify mechanoelastic characteristics that are deformation invariant. Determination of such characteristics allows for developing methods offering an image of the undeformed body. General assumptions about the mechanoelastic properties of the bodies are stated which lead to two different approaches for obtaining bodies' deformation invariants. One was developed to spot a deformed body's neutral line and its cross sections, while the other solves deformation PDEs by performing a set of equivalent image operations on the deformed body images. Both of these processes may furnish a body-undeformed version from its deformed image. This was confirmed by obtaining the undeformed shape of deformed parasites, cells (protozoa), fibers, and human lips. In addition, the method has been applied to the important problem of parasite automatic classification from their microscopic images. To achieve this, we first apply the previous method to straighten the highly deformed parasites, and then, apply a dedicated curve classification method to the straightened parasite contours. It is demonstrated that essentially different deformations of the same parasite give rise to practically the same undeformed shape, thus confirming the consistency of the introduced methodology. Finally, the developed pattern recognition method classifies the unwrapped parasites into six families, with an accuracy rate of 97.6 percent. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, a general methodology is introduced for the determination of potential prototype curves used for the drawing of prehistoric wall paintings. The approach includes 1) preprocessing of the wall-paintings contours to properly partition them, according to their curvature, 2) choice of prototype curves families, 3) analysis and optimization in 4-manifold for a first estimation of the form of these prototypes, 4) clustering of the contour parts and the prototypes to determine a minimal number of potential guides, and 5) further optimization in 4-manifold, applied to each cluster separately, in order to determine the exact functional form of the potential guides, together with the corresponding drawn contour parts. The methodology introduced simultaneously deals with two problems: 1) the arbitrariness in data-points orientation and 2) the determination of one proper form for a prototype curve that optimally fits the corresponding contour data. Arbitrariness in orientation has been dealt with a novel curvature based error, while the proper forms of curve prototypes have been exhaustively determined by embedding curvature deformations of the prototypes into 4--manifolds. Application of this methodology to celebrated wall paintings excavated at Tyrins, Greece, and the Greek island of Thera manifests that it is highly probable that these wall paintings were drawn by means of geometric guides that correspond to linear spirals and hyperbolae. These geometric forms fit the drawings' lines with an exceptionally low average error, less than 0.39 mm. Hence, the approach suggests the existence of accurate realizations of complicated geometric entities more than 1,000 years before their axiomatic formulation in the Classical Ages. [ABSTRACT FROM AUTHOR]