A new method to analyse mosaics based on Symmetry Group theory applied to Islamic Geometric Patterns

[EN] This article presents a new method for analysing mosaics based on the mathematical principles of Symmetry Groups. This method has been developed to get the understanding present in patterns by extracting the objects that form them, their lattice, and the Wallpaper Group. The main novelty of this method resides in the creation of a higher level of knowledge based on objects, which makes it possible to classify the objects, to extract their main features (Point Group, principal axes, etc.), and the relationships between them. In order to validate the method, several tests were carried out on a set of Islamic Geometric Patterns from different sources, for which the Wallpaper Group has been successfully obtained in 85% of the cases. This method can be applied to any kind of pattern that presents a Wallpaper Group. Possible applications of this computational method include pattern classification, cataloguing of ceramic coatings, creating databases of decorative patterns, creating pattern designs, pattern comparison between different cultures, tile cataloguing, and so on.The authors wish to thank the Patronato de la Alhambra y Generalife (Granada, Spain) and the Patronato del Real Alcázar de Sevilla (Seville, Spain) for their valuable collaboration in this research work.Albert Gil, FE.; Gomis Martí, JM.; Blasco, J.; Valiente González, JM.; Aleixos Borrás, MN. (2015). A new method to analyse mosaics based on Symmetry Group theory applied to Islamic Geometric Patterns. Computer Vision and Image Understanding. 130:54-70. doi:10.1016/j.cviu.2014.09.002S547013

Mo.Se.: Segmentación de mosaico de imágenes basado en aprendizaje profundo en cascada

[EN] Mosaic is an ancient type of art used to create decorative images or patterns combining small components. A digital version of a mosaic can be useful for archaeologists, scholars and restorers who are interested in studying, comparing and preserving mosaics. Nowadays, archaeologists base their studies mainly on manual operation and visual observation that, although still fundamental, should be supported by an automatized procedure of information extraction. In this context, this research explains improvements which can change the manual and time-consuming procedure of mosaic tesserae drawing. More specifically, this paper analyses the advantages of using Mo.Se. (Mosaic Segmentation), an algorithm that exploits deep learning and image segmentation techniques; the methodology combines U-Net 3 Network with the Watershed algorithm. The final purpose is to define a workflow which establishes the steps to perform a robust segmentation and obtain a digital (vector) representation of a mosaic. The detailed approach is presented, and theoretical justifications are provided, building various connections with other models, thus making the workflow both theoretically valuable and practically scalable for medium or large datasets. The automatic segmentation process was tested with the high-resolution orthoimage of an ancient mosaic by following a close-range photogrammetry procedure. Our approach has been tested in the pavement of St. Stephen's Church in Umm ar-Rasas, a Jordan archaeological site, located 30 km southeast of the city of Madaba (Jordan). Experimental results show that this generalized framework yields good performances, obtaining higher accuracy compared with other state-of-the-art approaches. Mo.Se. has been validated using publicly available datasets as a benchmark, demonstrating that the combination of learning-based methods with procedural ones enhances segmentation performance in terms of overall accuracy, which is almost 10% higher. This study’s ambitious aim is to provide archaeologists with a tool which accelerates their work of automatically extracting ancient geometric mosaics.Highlights:A Mo.Se. (Mosaic Segmentation) algorithm is described with the purpose to perform robust image segmentation to automatically detect tesserae in ancient mosaics.This research aims to overcome manual and time-consuming procedure of tesserae segmentation by proposing an approach that uses deep learning and image processing techniques, obtaining a digital replica of a mosaic.Extensive experiments show that the proposed framework outperforms state-of-the-art methods with higher accuracy, even compared with publicly available datasets.[ES] El mosaico es un tipo de arte antiguo utilizado para crear imágenes decorativas o patrones de pequeños componentes. Una versión digital de un mosaico puede ser útil a los arqueólogos, estudiosos y restauradores que están interesados en el estudio, la comparación y la preservación de los mosaicos. Hoy en día, los arqueólogos basan sus estudios principalmente en la operación manual y la observación visual que, aunque sigue siendo fundamental, debe ser apoyada con la ayuda de un procedimiento automatizado de extracción de la información. En este contexto, esta investigación tiene la intención de superar el procedimiento manual y lento del dibujo de teselas en mosaico proponiendo Mo.Se. (Mosaic Segmentation), un algoritmo que explota técnicas de aprendizaje profundo y segmentación de imagen; específicamente, la metodología combina la red U-Net 3 con el algoritmo Watershed. El propósito final es definir un flujo de trabajo que establezca los pasos para realizar una segmentación robusta y obtener una representación digital (vectorial) de un mosaico. Se presenta el procedimiento detallado y se proporcionan justificaciones teóricas, construyendo varias conexiones con otros modelos, haciendo que el flujo de trabajo sea teóricamente valioso y prácticamente escalable en conjuntos de datos medianos o grandes. El proceso de segmentación automática se probó con la ortoimagen de alta resolución de un mosaico antiguo, siguiendo un procedimiento de fotogrametría de objeto cercano. Nuestro enfoque se ha probado en el pavimento de la Iglesia de San Esteban en Umm ar-Rasas, un sitio arqueológico de Jordania, ubicado a 30 km al sureste de la ciudad de Madaba (Jordania). Los resultados experimentales muestran que este marco generalizado produce buenos rendimientos, obteniendo una mayor precisión en comparación con otros enfoques de vanguardia. Mo.Se. se ha validado utilizando conjuntos de datos disponibles públicamente como punto de referencia, lo que demuestra que la combinación de métodos basadosen el aprendizaje con métodos procedimentales mejora el rendimiento de la segmentación en casi un 10% en términos de exactitud en general. El ambicioso objetivo de este estudio es proporcionar a los arqueólogos una herramienta que acelere su trabajo de extracción automática de mosaicos geométricos antiguos.This work was partially found within the framework of the project Innovative technologies and training activities for the conservation and enhancement of the archaeological site of Umm er-Rasas (Jordan) funded by Ministero degli Affari Esteri e della Cooperazione Internazionale. The authors would like to express their gratitude to the ISPC CNR and in particular to Dott. Roberto Gabrielli (project leader) and Alessandra Albiero for providing the dataset.Felicetti, A.; Paolanti, M.; Zingaretti, P.; Pierdicca, R.; Malinverni, ES. 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Matching Islamic patterns in Kufic images

In this study, we address the problem of matching patterns in Kufic calligraphy images. Being used as a decorative element, Kufic images have been designed in a way that makes it difficult to be read by non-experts. Therefore, available methods for handwriting recognition are not easily applicable to the recognition of Kufic patterns. In this study, we propose two new methods for Kufic pattern matching. The first method approximates the contours of connected components into lines and then utilizes chain code representation. Sequence matching techniques with a penalty for gaps are exploited for handling the variations between different instances of sub-patterns. In the second method, skeletons of connected components are represented as a graph where junction and end points are considered as nodes. Graph isomorphism techniques are then relaxed for partial graph matching. Methods are evaluated over a collection of 270 square Kufic images with 8,941 sub-patterns. Experimental results indicate that, besides retrieval and indexing of known patterns, our method also allows the discovery of new patterns. © 2015, Springer-Verlag London

Computational Investigation of the Morphological Design Dimensions of Historic Hexagonal-Based Islamic Geometric Patterns

This dissertation examines the morphology of Islamic Geometric Patterns (IGP). Using mixed methods, including the simulation of historical designs and content analysis, this dissertation explores the question of how it is possible to mathematically describe the IGP. The study argues that the compositional analysis of geometry is not solely sufficient to investigate the design characteristics of the IGP, and the underlying mathematics and computational nature of the IGP should be considered when investigating historical IGP. The study presents a parametric description method that captures the reality of the IGP in numeric form and utilizes the form to derive representational codes that include the information necessary to construct a geometry. The representational codes are utilized to further investigate the actual and virtual design space of the IGP, aiming at identifying morphological similarities between historical designs. This research challenges the long-standing paradigm that considers compositional analysis to be the key to researching historical IGP. Adopting a mathematical description shows that the historical focus on existing forms has left the relevant structural similarities between historical IGPs understudied. The research focused on the historical, hexagonal-based IGP and found that hexagonal-based IGP designs correlate to each other beyond just the actualized dimension and that deep, morphological connections exist in the virtual dimension. Using historical evidence, this dissertation identifies these connections and presents a categorization system that groups designs together based on their ‘morphogenetic’ characteristics

Historical document analysis based on word matching

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 67-76.Historical documents constitute a heritage which should be preserved and providing automatic retrieval and indexing scheme for these archives would be beneficial for researchers from several disciplines and countries. Unfortunately, applying ordinary Optical Character Recognition (OCR) techniques on these documents is nearly impossible, since these documents are degraded and deformed. Recently, word matching methods are proposed to access these documents. In this thesis, two historical document analysis problems, word segmentation in historical documents and Islamic pattern matching in kufic images are tackled based on word matching. In the first task, a cross document word matching based approach is proposed to segment historical documents into words. A version of a document, in which word segmentation is easy, is used as a source data set and another version in a different writing style, which is more difficult to segment into words, is used as a target data set. The source data set is segmented into words by a simple method and extracted words are used as queries to be spotted in the target data set. Experiments on an Ottoman data set show that cross document word matching is a promising method to segment historical documents into words. In the second task, firstly lines are extracted and sub-patterns are automatically detected in the images. Then sub-patterns are matched based on a line representation in two ways: by their chain code representation and by their shape contexts. Promising results are obtained for finding the instances of a query pattern and for fully automatic detection of repeating patterns on a square kufic image collection.Arifoğlu, DamlaM.S

Segmentation based Ottoman text and matching based Kufic image analysis

Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013.Thesis (Master's) -- Bilkent University, 2013.Includes bibliographical references leaves 80-88.Large archives of historical documents attract many researchers from all around the world. The increasing demand to access those archives makes automatic retrieval and recognition of historical documents crucial. Ottoman archives are one of the largest collections of historical documents. Although Ottoman is not a currently spoken language, many researchers from all around the world are interested in accessing the archived material. This thesis proposes two Ottoman document analysis studies; first one is a crucial pre-processing task for retrieval and recognition which is segmentation of documents. Second one is a more specific retrieval and recognition problem which aims matching Islamic patterns is Kufic images. For the first segmentation task, layout, line and word segmentation is studied. Layout segmentation is obtained via Log-Gabor filtering. Four different algorithms are proposed for line segmentation and finally a simple morphological method is preferred for word segmentation. Datasets are constructed with documents from both Ottoman and other languages (English, Greek and Bangla) to test the script-independency of the methods. Experiments show that our segmentation steps give satisfactory results. The second task aims to detect Islamic patterns in Kufic images. The sub-patterns are considered as basic units and matching is used for the analysis. Graphs are preferred to represent subpatterns where graph and sub-graph isomorphism are used for matching them. Kufic images are analyzed in three different ways. Given a query pattern, all the instances of the query can be found through retrieval. Going further, through known patterns images can be automatically labeled in the entire dataset. Finally, patterns that repeat inside an image can be automatically discovered. As there is no existing Kufic dataset, a new one is constructed by collecting images from the Internet and promising results are obtained on this dataset.Adıgüzel, HandeM.S

Towards Generalized Noise-Level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e., in all real-world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review

Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Analysis, Modeling and Generation of Traditional Lao Woven Textile

Traditional Lao textiles are wealth in religious motifs, the motifs and patterns on the textiles reflect traditions, beliefs and livelihood of people. The creativity in playing with motifs and patterns represents valuable cultural heritage on clothes that seriously needs to be preserved and protected before it is depleted. The structure of Lao motifs and patterns are complicated, but weaving processes still use traditional techniques and simple floor-loom. Therefore, it takes a lot of time for making a weave-draft on the loom and percentage of losing weave-drafts is very high. In contrast, industrial textiles use electronic loom and digital weave-drafts to produce fabrics, which are suitable for fast production but lack complicated traditional patterns. As a result, in this research we investigated different scientific algorithms for digitizing motifs, patterns and weave-drafts of Lao textiles in order to fill the gap between traditional and modern weave techniques, and to improve processes of design and weaving. We developed three design Lao Textile (LT) modules for digitizing leading to international standard formats which are understandable and usable for both hand-weavers and weaving machines. The LT-Tieup module provides motifs and patterns construction. The LT-Weave is for motifs and patterns modification, and the LT-Design module is for textile design and visualization. All the digitized motifs and patterns are archived on our online repository for cultural preservation purpose, the online repository is a tool to store weave-drafts and for communication among researchers, weavers and cultural heritage experts. Experiment results of our research show that our approach closes the gap between traditional weaving and digital weave representations, fulfilling the aim of our project