17 results on '"Rousopoulos, Panayiotis"'
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2. Advanced Geometric Guides Were Used for the Drawing of Celebrated Late Bronze Age Wall Paintings
- Author
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Tsakalidou, Panagiota, Arabadjis, Dimitris, Papaodysseus, Constantin, Exarhos, Michalis, Rousopoulos, Panayiotis, Giannopoulos, Fotios, Fotopoulos, Evangelos, Panagopoulos, Michail, Koui, Maria, editor, Zezza, Fulvio, editor, and Kouis, Dimitrios, editor
- Published
- 2018
- Full Text
- View/download PDF
3. Efficient Solution to the 3D Problem of Automatic Wall Paintings Reassembly
- Author
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Papaodysseus, Constantin, Arabadjis, Dimitris, Exarhos, Michalis, Rousopoulos, Panayiotis, Zannos, Solomon, Panagopoulos, Michail, and Papazoglou-Manioudaki, Lena
- Subjects
Computer Science - Computer Vision and Pattern Recognition ,Mathematics - Differential Geometry ,49J40, 53A05, 68U99, 68T10 - Abstract
This paper introduces a new approach for the automated reconstruction - reassembly 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 importantly, in the virtual reassembling of parts of wall paintings belonging to the Mycenaic civilization (c. 1300 B.C.), excavated in a highly fragmented condition in Tyrins, Greece.
- Published
- 2012
- Full Text
- View/download PDF
4. A General Methodology for the Determination of 2D Bodies Elastic Deformation Invariants. Application to the Automatic Identification of Parasites
- Author
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Arabadjis, Dimitris, Rousopoulos, Panayiotis, Papaodysseus, Constantin, Panagopoulos, Michalis, Loumou, Panayiota, and Theodoropoulos, Georgios
- Subjects
Computer Science - Computer Vision and Pattern Recognition ,Computer Science - Artificial Intelligence - Abstract
A novel methodology is introduced here that exploits 2D images of arbitrary elastic body deformation instances, so as to quantify mechano-elastic characteristics that are deformation invariant. Determination of such characteristics allows for developing methods offering an image of the undeformed body. General assumptions about the mechano-elastic properties of the bodies are stated, which lead to two different approaches for obtaining bodies' deformation invariants. One was developed to spot 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 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 we 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 6 families, with an accuracy rate of 97.6 %.
- Published
- 2012
5. Optimization in Differentiable Manifolds in Order to Determine the Method of Construction of Prehistoric Wall-Paintings
- Author
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Arabadjis, Dimitris, Rousopoulos, Panayiotis, Papaodysseus, Constantin, Exarhos, Michalis, Panagopoulos, Michalis, and Papazoglou-Manioudaki, Lena
- Subjects
Computer Science - Computer Vision and Pattern Recognition ,Computer Science - Artificial Intelligence ,Computer Science - Computational Geometry - Abstract
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 a) preprocessing of the wall-paintings contours to properly partition them, according to their curvature, b) choice of prototype curves families, c) analysis and optimization in 4-manifold for a first estimation of the form of these prototypes, d) clustering of the contour parts and the prototypes, to determine a minimal number of potential guides, e) 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 introduced methodology simultaneously deals with two problems: a) the arbitrariness in data-points orientation and b) 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 it is highly probable that these wall-paintings had been 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 0.39mm. Hence, the approach suggests the existence of accurate realizations of complicated geometric entities, more than 1000 years before their axiomatic formulation in Classical Ages.
- Published
- 2012
- Full Text
- View/download PDF
6. On the mathematical formulation of the problem of reassembling fragmented objects: two new theorems
- Author
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Arabadjis, Dimitris, Papaodysseus, Constantin, Rousopoulos, Panayiotis, and Panagopoulos, Michalis
- Published
- 2010
- Full Text
- View/download PDF
7. Automatic writer identification of ancient Greek inscriptions
- Author
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Panagopoulos, Michail, Papaodysseus, Constantin, Rousopoulos, Panayiotis, Dafi, Dimitra, and Tracy, Stephen
- Subjects
Inscriptions, Greek -- Research ,Maximum likelihood estimates (Statistics) -- Usage ,Object recognition (Computers) -- Analysis ,Pattern recognition -- Analysis - Published
- 2009
8. Image and pattern analysis of 1650 B.C. wall paintings and reconstruction
- Author
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Papaodysseus, Constantin, Exarhos, Mihalis, Panagopoulos, Mihalis, Rousopoulos, Panayiotis, Triantafillou, Constantin, and Panagopoulos, Thanasis
- Subjects
Image processing -- Analysis - Abstract
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.
- Published
- 2008
9. Determination of the method of construction of 1650 B.C. wall paintings
- Author
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Papaodysseus, Constantin, Fragoulis, Dimitrios K., Panagopoulos, Mihalis, Panagopoulos, Thanasis, Rousopoulos, Panayiotis, Exarhos, Mihalis, and Skembris, Angelos
- Subjects
Object recognition (Computers) -- Research ,Pattern recognition -- Research ,Archaeology -- Analysis ,Archaeology -- Methods - Abstract
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.
- Published
- 2006
10. Development of novel pattern recognition methods and mathematical formulation for the determination of the method of construction of important archaeological finds and the identification of their creator
- Author
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Rousopoulos, Panayiotis Ch., Παπαοδυσσεύς, Κωνσταντίνος, Κουκούτσης, Ηλίας, Λούμος, Βασίλειος, Σταφυλοπάτης, Ανδρέας-Γεώργιος, Ρασσιάς, Θεμιστοκλής, Θεοδώρου, Νικόλαος, Ζερβάκης, Μ., and Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. Τομέας Επικοινωνιών, Ηλεκτρονικής και Συστημάτων Πληροφορικής
- Subjects
Prehistoric wall paintings ,Pattern Recognition ,Καμπυλογράφοι ,Archaeometry ,Χρονολόγηση αρχαίων επιγραφών ,Προϊστορικές τοιχογραφίες ,Dating Ancient inscriptions ,Αυτόματη αναγνώριση γραφέα ,Stencils ,Automatic writer identification ,Digital image processing ,Αναγνώριση Προτύπων ,Αρχαιομετρία ,Ψηφιακή επεξεργασία εικόνας - Abstract
296 σ., Η παρούσα διατριβή αφορά σε δύο θέματα: Το πρώτο περιλαμβάνει μία προσπάθεια εντοπισμού του τρόπου κατασκευής/σχεδίασης των φημισμένων τοιχογραφιών της Ύστερης Εποχής του Χαλκού (περί τα 1630 π.Χ. ), οι οποίες έχουν ανασκαφεί στο Ακρωτήρι Θήρας. Το δεύτερο θέμα αφορά στην αυτόματη ταυτοποίηση γραφέων αρχαίων επιγραφών με σκοπό την ορθή χρονολόγηση αυτών, η οποία είναι πολύ μεγάλης σημασίας για την Αρχαιολογία και την ορθή καταγραφή της Ιστορίας. Και τα δύο αυτά θέματα αντιμετωπίζονται για πρώτη φορά σε αυτήν την εργασία, αλλά και από την ερευνητική μας ομάδα. Το πρώτο θέμα αναπτύσσεται αναλυτικά στο πρώτο μέρος της παρούσης και περιλαμβάνει τα εξής επιμέρους στάδια: 1Α) Γίνεται μια πρώτη επεξεργασία των εικόνων των προς μελέτη τοιχογραφιών με σκοπό την εξαγωγή του περιγράμματος των απεικονιζομένων θεματικών ενοτήτων σε κατάλληλη μορφή. 1Β) Διατυπώνονται ορισμοί θεμελιωδών οντοτήτων καθώς και η βασική υπόθεση περί χρήσεως γεωμετρικών καμπυλογράφων στη σχεδίαση των τοιχογραφιών. 1Γ) Επιλέγονται πιθανά γεωμετρικά πρότυπα των καμπυλογράφων, με κριτήρια αρχαιολογικής και ιστορικής φύσεως. 1Δ) Γίνεται μία πρώτη εκτίμηση των πιθανών μονοκονδυλιών με χρήση της καμπυλότητας και ελαχιστοποίηση κατάλληλα επιλεγμένων συναρτήσεων λάθους. 1Ε) Παρουσιάζεται μια πρωτότυπη εξαντλητική μέθοδος προσαρμογής καμπυλών, η οποία προσφέρει την αδιαμφισβήτητα βέλτιστη σχετική θέση αυτών. 1ΣΤ) Επί τη βάσει των προηγουμένων, προσδιορίζονται οι ακριβείς παράμετροι των πιθανών καμπυλογράφων. 1Ζ) Υποστηρίζεται ουσιωδώς η υπόθεση περί χρήσεως καμπυλογράφων, με έμμεση αναπαραγωγή του τρόπου σχεδίασης των περιγραμμάτων. Παράλληλα προσδιορίζονται τα ακριβή όρια των πιθανών μονοκονδυλιών πάνω στις ζωγραφισμένες θεματικές ενότητες. Τα σχετικά αποτελέσματα μαζί με οπτική απόδοση τους επί των εικόνων των τοιχογραφιών παρουσιάζονται στο τέλος του πρώτου μέρους. Στο δεύτερο μέρος αυτής της εργασίας παρουσιάζεται για πρώτη φορά μια ολοκληρωμένη μέθοδος αυτόματης ταυτοποίησης γραφέα αρχαίων επιγραφών, η οποία περιλαμβάνει τα εξής επιμέρους στάδια: 2Α) Πραγματοποιείται μία πρώτη επεξεργασία των εικόνων των προς μελέτη επιγραφών με σκοπό την εξαγωγή του περιγράμματος, σε κατάλληλη μορφή, όλων των υλοποιήσεων των συμβόλων της αλφαβήτου (συμβολογραμμάτων) που εμφανίζονται σε αυτές. 2Β) Καθορίζονται κρίσιμα σημεία καμπής επί κάθε υλοποιήσεως ενός συμβολογράμματος, με ελαχιστοποίηση κατάλληλα επιλεγμένων συναρτήσεων λάθους και χρήση της καμπυλότητας. 2Γ) Πραγματοποιείται βέλτιστη προσαρμογή των υλοποιήσεων των περιγραμμάτων του ιδίου συμβολογράμματος με επέκταση και κατάλληλη τροποποίηση της μεθόδου προσαρμογής καμπυλών που παρουσιάζεται στο πρώτο μέρος. 2Δ) Επί της θέσης βέλτιστης προσαρμογής των περιγραμμάτων δύο γραμμάτων, ορίζονται ποσότητες που περιγράφουν την ποιότητα προσαρμογής. 2Ε) Διατυπώνονται πρωτότυπα στατιστικά κριτήρια για τον υπολογισμό της πιθανοφάνειας και τον έλεγχο της υπόθεσης εάν μία επιγραφή ανήκει σε ένα γραφέα ή όχι. 2ΣΤ) Παρουσιάζεται μία επιπλέον μέθοδος ταυτοποίησης γραφέα, η οποία χρησιμοποιεί γεωμετρικά χαρακτηριστικά που εξάγονται αυτόματα από τα περιγράμματα των γραμμάτων. Οι τιμές αυτών των χαρακτηριστικών ακολουθούν συγκεκριμένες στατιστικές κατανομές με χρήση των οποίων διατυπώνονται περαιτέρω κριτήρια για το εάν μια επιγραφή έχει χαραχθεί από ένα γραφέα ή όχι. 2Ζ) Και οι δύο ανωτέρω μέθοδοι συνολικά χρησιμοποιούνται για την ταυτοποίηση του γραφέα 32 αρχαιοελληνικών επιγραφών, τις οποίες επέλεξε ο παγκοσμίου φήμης επιγραφολόγος κύριος Steven Tracy τ. διευθυντής της Αμερικανικής Σχολής Κλασσικών Σπουδών στην Αθήνα και νυν καθηγητής της σχολής ιστορικών σπουδών του ινστιτούτου προηγμένων σπουδών του Princeton στο New Jersey των Ηνωμένων Πολιτειών. Ο ίδιος κατά βάσιν, καθώς και άλλοι διακεκριμένοι επιγραφολόγοι, αξιολόγησαν την επίδοση του συστήματος. Ο τρόπος εφαρμογής της μεθόδου ως και τα σχετικά αποτελέσματα παρουσιάζονται στο τέλος του δευτέρου μέρους. Τα αποτελέσματα και οι σχετικές μέθοδοι που αναφέρονται σε αυτή τη διατριβή παρουσιάζονται σε δέκα άρθρα δημοσιευμένα σε έγκριτα διεθνή επιστημονικά περιοδικά., The present thesis treats and tackles two main problems in the fields of Pattern Recognition, Digital Image Processing and Archaeometry. Consequently the thesis consists of two interconnected parts: The first part of the present work deals with the problem of determining the method of drawing of a number of celebrated and beautiful wall-paintings belonging to the Late Bronze Age (c. 1630 B.C.). These wall paintings have been excavated at Akrotiri, Thera, Greece. The second part deals with the automated identification of the writer of Ancient Greek inscriptions. The solution of this problem assists the archaeologists and historians in dating the content of the inscriptions. Actually, this seems to be the only objective method of dating this content in the case there is no explicit reference of a fact or an event in the inscription that can help the scholars in the process of dating. It should be emphasized that the unambiguous dating of the content of the inscriptions is the most powerful source in the study of History. More analytically the solution of the first problem presented in this thesis includes the following procedures. 1A) A first stage possessing of the wall paintings digital images takes place. The goal of this stage is to extract the contour of the main thematic entities of the wall paintings. This contour is determined in an appropriate form, necessary for the subsequent analysis. 1B) A number of fundamental definitions is given and the main hypothesis is stated, namely that geometrical stencils were used for the drawing of the considered wall paintings. 1C) Families of geometrical curves are selected as potential prototypes of the employed stencils. The selection is based on archaeological and historical criteria. 1D) A first estimation of the probable one stoke parts of the contour is undertaken. This estimation is based on curvature consideration and minimization of corresponding error functions. 1E) A novel exhaustive curve fitting method is introduced, which offers unambiguously optimal matching of two digital curves. 1F) Taking into consideration the previous stages, the exact values of the stencils parameters are determined. 1G) The hypothesis that stencils were used for the drawing of the considered wall paintings is supported substantially. At the same time, the most probable limits of the one stroke contour parts are determined. The related results are presented in the final section of this first part, together with a visual representation of the one stoke parts and the corresponding stencil segments on the wall paintings. In the second part of the thesis a method for the automated identification of the writers of Ancient Greek inscriptions is presented for the first time. This method consists of the following actions. 2A) A first stage possessing of the inscriptions digital images takes place. The goal of this stage is to extract a proper form of the contour of the letters on the inscriptions, necessary for the subsequent analysis. 2B) Critical turning points of the letter contours are spotted via minimization of properly defined curvature based error functions. 2C) Optimal matching of the contours of the realizations of the same alphabet symbols on the inscriptions is performed. This matching is achieved by means of a novel exhaustive curve fitting method, which is an extension of the method presented in 1E). 2D) Proper original quantities are defined, which describe the quality of matching of two letters contours. 2E) Novel statistical criteria are employed for stating and performing proper statistical tests of the hypothesis that two inscriptions have been cut by the same hand or not. The same criteria are employed for the computation of the likelihood that two inscriptions are curved by the same cutter. 2F) An additional method of writer identification is introduced, which employs properly defined geometric characteristics of a letter realizations contour. The values of these characteristics follow specific distribution functions, which are used for the development of additional statistical criteria for writer identification. 2G) Both methods have been used for the identification of the writers of 32 Ancient Greek inscriptions, which have been selected by the prominent epigraphist-archaeologist professor Steven Tracy. The methods and the developed criteria offered identification results, which have been fully accepted as correct by prof. Tracy and other prominent epigraphists for all 32 inscriptions. Ten (10) articles, associated with the results and methods presented in the thesis, appear in International Scientific Journals., Παναγιώτης Χ. Ρουσόπουλος
- Published
- 2010
- Full Text
- View/download PDF
11. An Overview of Methods for Automatic Reassembly of Fragmented Objects
- Author
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Arabadjis, Dimitris, primary, Exarhos, Michael, additional, Giannopoulos, Fotios, additional, Zannos, Solomon, additional, Rousopoulos, Panayiotis, additional, and Papaodysseus, Constantin, additional
- Full Text
- View/download PDF
12. Efficient solution to the 3D problem of automatic wall paintings reassembly
- Author
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Papaodysseus, Constantin, primary, Arabadjis, Dimitris, additional, Exarhos, Michalis, additional, Rousopoulos, Panayiotis, additional, Zannos, Solomon, additional, Panagopoulos, Michail, additional, and Papazoglou-Manioudaki, Lena, additional
- Published
- 2012
- Full Text
- View/download PDF
13. A new approach for ancient inscriptions' writer identification
- Author
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Rousopoulos, Panayiotis, primary, Panagopoulos, Michail, additional, Papaodysseus, Constantin, additional, Panopoulou, Fivi, additional, Arabadjis, Dimitris, additional, Tracy, Stephen, additional, Giannopoulos, Fotios, additional, and Zannos, Solomon, additional
- Published
- 2011
- Full Text
- View/download PDF
14. Handwriting automatic classification: Application to ancient Greek inscriptions
- Author
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Papaodysseus, Constantin, primary, Rousopoulos, Panayiotis, additional, Arabadjis, Dimitris, additional, Panopoulou, Fivi, additional, and Panagopoulos, Michalis, additional
- Published
- 2010
- Full Text
- View/download PDF
15. On the mathematical formulation of the problem of reassembling fragmented objects: two new theorems
- Author
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Arabadjis, Dimitris, primary, Papaodysseus, Constantin, additional, Rousopoulos, Panayiotis, additional, and Panagopoulos, Michalis, additional
- Published
- 2009
- Full Text
- View/download PDF
16. A General Methodology for the Determination of 2D Bodies Elastic Deformation Invariants: Application to the Automatic Identification of Parasites.
- Author
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Arabadjis, Dimitris, Rousopoulos, Panayiotis, Papaodysseus, Constantin, Panagopoulos, Michalis, Loumou, Panayiota, and Theodoropoulos, Georgios
- Subjects
- *
IMAGE processing , *ELASTICITY , *DEFORMATIONS (Mechanics) , *GEOMETRIC shapes , *PARASITES - Abstract
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]
- Published
- 2010
- Full Text
- View/download PDF
17. Optimization in Differentiable Manifolds in Order to Determine the Method of Construction of Prehistoric Wall Paintings.
- Author
-
Arabadjis, Dimitris, Rousopoulos, Panayiotis, Papaodysseus, Constantin, Exarhos, Michalis, Panagopoulos, Michail, and Papazoglou-Manioudaki, Lena
- Subjects
- *
PROTOTYPES , *MURAL art , *MANIFOLDS (Mathematics) , *MATHEMATICAL optimization , *FUNCTIONAL analysis , *DATA modeling , *PATTERN recognition systems , *CURVE fitting - Abstract
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]
- Published
- 2011
- Full Text
- View/download PDF
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