Dimitrios Fragoulis

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consisting of 262 fragments with full success, but most important, it has been used to reconstruct, for the first time, unpublished parts of wall paintings from a set of 936 fragments.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.

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.