Constantin Papaodysseus

Contour-shape based reconstruction of fragmented, 1600 BC wall paintings

A novel general methodology is introduced for the computer-aided reconstruction of the magnificent wall paintings of the Greek island Thera (Santorini), which were painted in the middle of the second millennium BC. These wall paintings have been excavated in fragments, and as a result, their reconstruction is a painstaking and a time-consuming process. Therefore, in order to facilitate and expedite this process, a proper system has been developed based on the introduced methodology. According to this methodology, each fragment is photographed, its picture is introduced to the computer, its contour is obtained, and, subsequently, all of the fragments contours are compared in a manner proposed herein. Both the system and the methodology presented here extract the maximum possible information from the contour shape of fragments of an arbitrary initially unbroken plane object to point out possible fragment matching. This methodology has been applied to two excavated fragmented wall paintings consisting of 262 fragments with full success, but most important, it has been used to reconstruct, for the first time, unpublished parts of wall paintings from a set of 936 fragments.

On the automated recognition of seriously distorted musical recordings

A new methodology is presented for the automated recognition-identification of musical recordings that have suffered from a high degree of playing speed and frequency band distortion. The procedure of recognition is essentially based on the comparison between an unknown musical recording and a set of model ones, according to some predefined specific characteristics of the signals. In order to extract these characteristics from a musical recording, novel feature extraction algorithms are employed. This procedure is applied to the whole set of model musical recordings, thus creating a model characteristic database. Each time we want an unknown musical recording to be identified, the same procedure is applied to it, and subsequently, the derived characteristics are compared with the database contents via an introduced set of criteria. The proposed methodology led to the development of a system whose performance was extensively tested with various types of broadcasted musical recordings. The system performed successful recognition for the 94% of the tested recordings. It should be noted that the presented system is parallelizable and can operate in real time.

Numerical error analysis in Zernike moments computation

Abstract An exact analysis of the numerical errors being generated during the computation of the Zernike moments, by using the well-known ‘q-recursive’ method, is attempted in this paper. Overflow is one kind of error, which may occur when one needs to calculate the Zernike moments up to a high order. Moreover, by applying a novel methodology it is shown that there are specific formulas, which generate and propagate ‘finite precision error’. This finite precision error is accumulated during execution of the algorithm, and it finally ‘destroys’ the algorithm, in the sense that eventually makes its results totally unreliable. The knowledge of the exact computation errors and the way that they are generated and propagated is a fundamental step for developing more robust error-free recursive algorithms, for the computation of Zernike moments.

Error sources and error propagation in the Levinson-Durbin algorithm

It is proved that there are two types of numerical error, due to finite precision, in the Levinson-Durbin algorithms; an erratic and a systematic one. The erratic one depends on the value the input autocorrelation accidentally takes at an iteration, and, essentially, it affects only the results obtained at this particular recursion. On the contrary, the systematic numerical error increases with the information the system carries and propagates essentially throughout the algorithm. It is shown that, for both types of error, as well as the overall one, there are specific intermediate quantities, calculated in the evolution of the algorithm, which may serve as precise indicators of the exact number of erroneous digits with which the various quantities are computed including the PARCOR coefficients and the filter coefficients. Therefore, the generated numerical error can be accurately traced. >

Numerical stability of fast computation algorithms of Zernike moments

Abstract A detailed, comparative study of the numerical stability of the recursive algorithms, widely used to calculate the Zernike moments of an image, is presented in this paper. While many papers, introducing fast algorithms for the computation of Zernike moments have been presented in the literature, there is not any work studying the numerical behaviour of these methods. These algorithms have been in the past compared to each other only according to their computational complexity, without been given the appropriate attention, as far as their numerical stability is concerned, being the most significant part of the algorithms’ reliability. The present contribution attempts to fill this gap in the literature, since it mainly demonstrates that the usefulness of a recursive algorithm is defined not only by its low computational complexity, but most of all by its numerical robustness. This paper exhaustively compares some well known recursive algorithms for the computation of Zernike moments and sets the appropriate conditions in which each algorithm may fall in an unstable state. The experiments show that any of these algorithms can be unstable under some conditions and thus the need to develop more stable algorithms is of major importance.

Automated classification of piano-guitar notes

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.

Identification of geometrical shapes in paintings and its application to demonstrate the foundations of geometry in 1650 B.C

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.

Comparing LS FIR filtering and l-step ahead linear prediction

This comparative study of the l-step-ahead linear prediction and least-squares finite impulse response (LS FIR) filtering problems emphasizes the numerical behavior of the resulting Toeplitz systems. It is shown that, although these systems are similar, the restraints on the autocorrelation coefficients fundamentally differentiate them. In the process of doing so, a new algorithmic scheme for the computation of the lagged lattice coefficients is developed, which exhibits fundamentally improved numerical behavior. Moreover, explicit formulas for the supremums of the absolute values of both the lagged lattice and filter coefficients are found theoretically and are experimentally confirmed by using the proposed algorithm. Finally, the bounds of the LS FIR filter coefficients are treated in comparison with the supremums of the lagged quantities. >

Error propagation and numerical recovery for a class of parametric DSP algorithms

The error propagation in various useful order- and time-recursive DSP algorithms is studied. It is demonstrated that in all these algorithms there are two kinds of error due to finite precision: an erratic and a systematic one. Examples of both kinds of error are provided, and special emphasis is given to the study of the systematic truncation or round-off error. It is shown that in the Levinson-type and Schur-type algorithms for the solution of the FLP (forward linear prediction) and the FIR (finite impulse response) problem, there is one dominant source of systematic error, while in the l-step ahead case there are two sources of such error. Moreover, it is pointed out that in the fast Kalman algorithms there are two kinds of systematic error. Precise indicators of the exact magnitude of the finite precision error are given, and possible recovery techniques are proposed.<<ETX>>

Identifying the writer of ancient inscriptions and Byzantine codices. A novel approach

In this paper, a novel methodology is presented aiming at the automatic identification of the writer of ancient inscriptions and Byzantine codices. This identification can offer unambiguous dating of these ancient manuscripts. The introduced methodology is also applicable to contours of complexes of letters or any class of similar curves. The method presented here initially estimates the normalized curvature at each pixel of a letter contour. Subsequently, it performs pair-wise comparisons of the curvatures sequences that correspond to two realizations of the same alphabet symbol. Then, it introduces a new Proposition that, on the basis of the previous results, offers a closed solution to the problem of matching two equinumerous digital contours in the Least Squares sense. Next, a criterion is employed quantifying the similarity of two realizations of the same alphabet symbol. Finally, a number of statistical criteria are introduced for the automatic identification of the writer of ancient manuscripts. The introduced method did not employ any reference manuscript neither the number of distinct hands who had written the considered set of manuscripts nor any related information whatsoever; it also performs quite efficiently even if a small number of realizations (less than 6) of certain alphabet symbols appear in a tested document. The only a priori knowledge is the alphabet of the language under consideration. We would like to stress that otherwise the method does not depend at all on the language itself. Namely it does not take into account if the alphabet is Latin, Greek, Etruscan, etc. The methodology and the related, developed information system has been applied to 46 ancient inscriptions of the Classical and Hellenistic era and 23 Byzantine codices, offering 100% accurate results, in the sense that the obtained results are in full agreement with prominent scholars in the field of Archaeology, History and Classical Studies.