Papers by Constantin Papaodysseus
Abstract—A novel methodology is introduced here that exploits 2D images of arbitrary elastic body... more 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 m...
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
The present thesis treats two main problems in the fields of Pattern Recognition, Digital Image P... more The present thesis treats two main problems in the fields of Pattern Recognition, Digital Image Processing and Archaeometry. The first part of the thesis deals with the problem of determining the method of drawing of a number of celebrated wall-paintings belonging to the Late Bronze Age (c. 1630 B.C.), excavated at Akrotiri, Thera, Greece. The solution of the first problem includes the following procedures. 1A)First stage possessing of the wall paintings digital images. Extraction of the contour of the main thematic entities. 1B) Fundamental definitions. The main hypothesis is stated: geometrical stencils were used for the drawing of the considered wall paintings. 1C)Selection of geometrical curves as potential prototypes of the employed stencils. 1D)First estimation of the probable one stoke parts of the contour. Curvature consideration and minimization of corresponding error functions. 1E)Introduction of a novel exhaustive curve fitting method. Optimal matching of two digital curv...
A Novel Approach and the Related Information System for the Identification of the Writer of Historical Documents
In this paper two complementary methodologies are introduced for classifying historical documents... more In this paper two complementary methodologies are introduced for classifying historical documents according to their writer. Historical documents’ writer identification is crucial for dating the written context, which in turn is of fundamental importance in the sciences of history and archaeology. To achieve this goal, first a kind of “platonic” or ideal prototype is computed for the letters of each document separately. On a complementary approach, exhaustive pairwise comparisons of the specific realizations of each alphabet symbol are employed so as to evaluate statistical hypotheses in connection with the writer of different documents. Finally, criteria of statistical nature are introduced to reject the hypothesis that two documents are made by the same writer. In this way, the number of distinct writers that created a given ensemble of documents is determined. Eventually, maximum likelihood considerations are employed to classify all documents of the ensemble to these writers. Th...
Advanced Geometric Guides Were Used for the Drawing of Celebrated Late Bronze Age Wall Paintings
The present paper analyzes the contours of the painted figures encountered in celebrated prehisto... more The present paper analyzes the contours of the painted figures encountered in celebrated prehistoric frescoes, and it establishes that advanced geometric guides were used in the drawing of these wall paintings. Namely, analysis of the frescoes that decorated the edifice “Xeste 3” in the prehistoric settlement of Akrotiri, Thera showed that the artist or group of artists had used five geometric archetypes and five corresponding well-constructed stencils (four hyperbolae and one Archimedes’ spiral). The same analysis indicated that the distinctive Mycenaean fresco “Lady of Mycenae” has been generated using four geometric prototypes (two linear spirals and two hyperbolae), of the same classes with the ones of Akrotiri, but with different parameters. The methodology considers the longer segments of the prototype geometric shapes, which can be optimally matched with a small fitting error, to the contour of an already drawn figure. Equivalently, the method introduced by the authors determ...
Heritage Science
The main goal of the present work is to determine the hand that has written two newly discovered ... more The main goal of the present work is to determine the hand that has written two newly discovered documents in Romania. For giving the proper answer, the authors introduced the notion of “Ideal Representative”, namely of an object that very well represents the corresponding ideal alphabet symbol that a writer had in his/her mind when writing a document by hand. Moreover, the authors have introduced a novel method, which leads to the optimal evaluation of the Ideal Representative of any alphabet symbol in association with any handwritten document. Furthermore, the authors have introduced methods for comparing these Ideal Representatives, so as a final decision about the hand that has written a document may be obtained with a highly considerable likelihood. The related analysis manifests that the two documents discovered in Romania in 1998, belong to the great personality of Rigas Feraios. The presented method of automatic handwriting Identification seems to be of general applicability.
Verfahren zur automatischen erkennung von musikstücken und klangsignalen
Pattern Recognition, 2013
In this paper, a novel approach is introduced for classifying curves into proper families, accord... more In this paper, a novel approach is introduced for classifying curves into proper families, according to their similarity. First, a mathematical quantity we call plane curvature is introduced and a number of propositions are stated and proved. Proper similarity measures of two curves are introduced and a subsequent statistical analysis is applied. First, the efficiency of the curve fitting process has been tested on 2 shapes datasets of reference. Next, the methodology has been applied to the very important problem of classifying 23 Byzantine codices and 46 Ancient inscriptions to their writers, thus achieving correct dating of their content. The inscriptions have been attributed to ten individual hands and the Byzantine codices to four writers.
IEEE Transactions on Signal Processing, 2001
In this paper, a new methodology is presented for the automated recognition-identification of mus... more In this paper, 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.
In the present paper, a novel approach is introduced for the study, estimation and exact tracking... more In the present paper, a novel approach is introduced for the study, estimation and exact tracking of the finite precision error generated and accumulated during any number of multiplications. It is shown that, as a rule, this operation is very “toxic”, in the sense that it may force the finite precision error accumulation to grow arbitrarily large, under specific conditions that are fully described here. First, an ensemble of definitions of general applicability is given for the rigorous determination of the number of erroneous digits accumulated in any quantity of an arbitrary algorithm. Next, the exact number of erroneous digits produced in a single multiplication is given as a function of the involved operands, together with formulae offering the corresponding probabilities. In case the statistical properties of these operands are known, exact evaluation of the aforementioned probabilities takes place. Subsequently, the statistical properties of the accumulated finite precision e...
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006
In this paper, a methodology of general applicability is presented for answering the question if ... more 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.
A Novel Information System for the Automatic Reconstruction of Highly Fragmented Objects with Application to the Reassembly of Prehistoric Wall Paintings and Vessels
10th International Symposium on the Conservation of Monuments in the Mediterranean Basin, 2018
This paper presents a set of novel methodologies and the corresponding information system, which ... more This paper presents a set of novel methodologies and the corresponding information system, which has been developed for processing 2D and 3D representations of fragmented archaeological finds, by means of which automated virtual and, eventually, actual reconstruction of the finds may be accomplished. The aforementioned system has been designed in order to provide ensembles of potentially matching fragments, together with a corresponding matching probability. One of the main novelties of the presented methodologies and the associated information systems is the use of many mathematical criteria, properly ordered, leading to fragmented pieces’ matching. These criteria employ notions and theorems of Differential Geometry, Calculus of Variations, and Algebra. The systems have been tested to the reassembly of parts of important archaeological finds, such as segments of wall paintings of the Minoan and the Mycenaean era. On the basis of these methodologies, parts of prehistoric wall paintings have been spotted for the first time, while the information systems’ matching proposals have been confirmed by scholars.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010
A novel methodology is introduced here that exploits 2D images of arbitrary elastic body deformat... more 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 %.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011
In this paper a general methodology is introduced for the determination of potential prototype cu... more 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. Index Terms-rotation and translation invariant curve fitting, pattern recognition in paintings, optimization in differentiable manifolds, geometric guides in prehistoric wall paintings, minimal parameters set for curve description, fitting prototype curves to drawn borders.
Abstract—In this paper a general methodology is introduced for the determination of potential pro... more 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 orientatio...
Classifying Event Related Potentials for Valid and Paradox Reasoning
International Joint Conference on Biomedical Engineering Systems and Technologies, 2012
Designing a Flexible, Highly Adaptable and Gracefully Expandable Information System for the Implementation of Complex Decision Support Systems
Abstract: In many cases, complex Decision Support Systems (DSS) used in business operations in bo... more Abstract: In many cases, complex Decision Support Systems (DSS) used in business operations in both the public and private domain may become very demanding, as far as the information system (IS) that implements them is concerned. Specifically, they may require very bulky databases, containing information that may be complex, diverse and even polymorph, a fact that makes the management, update and upgrade of the content of these databases and the corresponding IS very difficult or even practically unmanageable. Moreover, it has been observed that, due to the very rapid change in time of the main topics of interest of many modern businesses or public agencies, some complex DSS become obsolete even before they are fully developed and implemented. This paper introduces an innovative IS architecture, which significantly reduces the aforementioned risks. This architecture uses novel metadata architectures, in order to create DSS which are flexible, highly adaptable and can gracefully expa...
A New Approach to the Automatic Recognition of Musical Recordings
Journal of The Audio Engineering Society, 2001
A new methodology for the automatic recognition of musical recordings is presented. A system has ... more A new methodology for the automatic recognition of musical recordings is presented. A system has been developed that performs recognition among a set of specific musical recordings. The system claims a high rate of success (greater than 86%), even when the unknown compositions have suffered from up to a medium degree of distortion. It comprises a database of musical characteristics that correspond to a set of model musical recordings. These characteristics are derived by applying novel feature extraction algorithms to every model musical recording selected. In order to determine whether an unknown musical recording corresponds to a piece represented in the database, the same feature extraction algorithm is applied to it, and the characteristics thus derived are compared to the database contents by means of a set of criteria. The system can operate in parallel, essentially in real time, even for a considerable number of model musical recordings, as long as the hardware necessary is a...
International journal of imaging and robotics, 2011
In this paper two approaches of general applicability for placing fragments of important archeolo... more In this paper two approaches of general applicability for placing fragments of important archeological objects in their proper position are presented. Both methods are based on the thematic content of the drawings depicted on fragments of c.1650 B.C. wall-paintings, excavated at Akrotiri of the Greek island of Thera. The first method employs the statistical nature of the drawn figures’ dimensions and gives an estimate of the probability that two fragments belong to the same decorative element and are properly placed in it. During the second method, the authors exploit the fact that the contour lines of many drawn objects correspond to specific geometric archetypes. Subsequently, an exhaustive Least Squares novel approach is applied in order to correctly place fragments containing broken contour lines of the same decorative elements. Both methods have been successfully applied to the restoration of various fragmented wall-paintings. The methods are particularly useful in cases where ...
Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes
A first aim of the present work is the determination of the actual sources of the “finite precisi... more A first aim of the present work is the determination of the actual sources of the “finite precision error” generation and accumulation in two important algorithms: Bernoulli’s map and the folded Baker’s map. These two computational schemes attract the attention of a growing number of researchers, in connection with a wide range of applications. However, both Bernoulli’s and Baker’s maps, when implemented in a contemporary computing machine, suffer from a very serious numerical error due to the finite word length. This error, causally, causes a failure of these two algorithms after a relatively very small number of iterations. In the present manuscript, novel methods for eliminating this numerical error are presented. In fact, the introduced approach succeeds in executing the Bernoulli’s map and the folded Baker’s map in a computing machine for many hundreds of thousands of iterations, offering results practically free of finite precision error. These successful techniques are based ...
Identification of the Writer of Historical Documents via Geometric Modeling of the Handwriting
2021 IEEE International Conference on Signal and Image Processing Applications (ICSIPA)
In this work, a generic framework is developed that simultaneously embeds 2D shapes’ registration... more In this work, a generic framework is developed that simultaneously embeds 2D shapes’ registration, comparison and grouping, via the assumption that shapes of the same class are distorted level-sets of the same implicit function. The corresponding system is developed so as to deal with the automatic classification of documents according to their writers. The data that the system processes are the realizations of the individual characters, which are mutually aligned per document and per character, modulo affine transformations, and then reduced to a single representative shape. Stationarity conditions of these representatives are then used to statistically test the hypothesis that different documents bear a single representative. The considered documents are grouped according to their writer, by determining the maximal groups that also maximize the joint probability of the classification, computed over the characters, which occur in all documents. We have tested the system on 26 pages of Byzantine manuscripts that preserve Iliad. The computed classification of these pages in 4 writers has been independently verified by expert scientists.
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Papers by Constantin Papaodysseus