Optical recognition of modern and Roman coins

The recently granted EU project COINS aims to contribute substantially to the fight against illegal trade and theft of coins that appears to be a major part of the illegal antiques market. A central component of the permanent identification and traceability of coins is the underlying image recognition technology. However, currently available algorithms focus basically on the recognition of modern coins. To date, no optical recognition system for ancient coins has been successfully researched. It is a challenging task to work with medieval coins since they are – unlike modern coins – not mass manufactured. In this project, the recognition of coins will be based on new algorithms of pattern recognition and image processing, in a field – classification and identification of medieval coins – as yet unexplored. Since the project recently started, preliminary results and work already performed in this field are presented and discussed

Quantum walks: Schur functions meet symmetry protected topological phases

This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting of quantum walks, i.e. quantum analogs of classical random walks. We prove that topological indices classifying symmetry protected topological phases of quantum walks are encoded by matrix Schur functions built out of the walk. This main result of the paper reduces the calculation of these topological indices to a linear algebra problem: calculating symmetry indices of finite-dimensional unitaries obtained by evaluating such matrix Schur functions at the symmetry protected points $\pm1$. The Schur representation fully covers the complete set of symmetry indices for 1D quantum walks with a group of symmetries realizing any of the symmetry types of the tenfold way. The main advantage of the Schur approach is its validity in the absence of translation invariance, which allows us to go beyond standard Fourier methods, leading to the complete classification of non-translation invariant phases for typical examples.Comment: 33 pages, 1 figur

The topological classification of one-dimensional symmetric quantum walks

We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalues at symmetry protected points, and satisfy a mild locality condition. No translation invariance is assumed. The classification is parameterized by three indices, taking values in a group, which is either trivial, the group of integers, or the group of integers modulo 2, depending on the type of symmetry. The classification is complete in the sense that two walks have the same indices if and only if they can be connected by a norm continuous path along which all the mentioned properties remain valid. Of the three indices, two are related to the asymptotic behaviour far to the right and far to the left, respectively. These are also stable under compact perturbations. The third index is sensitive to those compact perturbations which cannot be contracted to a trivial one. The results apply to the Hamiltonian case as well. In this case all compact perturbations can be contracted, so the third index is not defined. Our classification extends the one known in the translation invariant case, where the asymptotic right and left indices add up to zero, and the third one vanishes, leaving effectively only one independent index. When two translationally invariant bulks with distinct indices are joined, the left and right asymptotic indices of the joined walk are thereby fixed, and there must be eigenvalues at $1$ or $-1$ (bulk-boundary correspondence). Their location is governed by the third index. We also discuss how the theory applies to finite lattices, with suitable homogeneity assumptions.Comment: 36 pages, 7 figure

Reconhecimento automático de moedas medievais usando visão por computador

Dissertação de mestrado em Engenharia InformáticaThe use of computer vision for identification and recognition of coins is well studied and of renowned interest. However the focus of research has consistently been on modern coins and the used algorithms present quite disappointing results when applied to ancient coins. This discrepancy is explained by the nature of ancient coins that are manually minted, having plenty variances, failures, ripples and centuries of degradation which further deform the characteristic patterns, making their identification a hard task even for humans. Another noteworthy factor in almost all similar studies is the controlled environments and uniform illumination of all images of the datasets. Though it makes sense to focus on the more problematic variables, this is an impossible premise to find outside the researchers’ laboratory, therefore a problematic that must be approached. This dissertation focuses on medieval and ancient coin recognition in uncontrolled “real world” images, thus trying to pave way to the use of vast repositories of coin images all over the internet that could be used to make our algorithms more robust. The first part of the dissertation proposes a fast and automatic method to segment ancient coins over complex backgrounds using a Histogram Backprojection approach combined with edge detection methods. Results are compared against an automation of GrabCut algorithm. The proposed method achieves a Good or Acceptable rate on 76% of the images, taking an average of 0.29s per image, against 49% in 19.58s for GrabCut. Although this work is oriented to ancient coin segmentation, the method can also be used in other contexts presenting thin objects with uniform colors. In the second part, several state of the art machine learning algorithms are compared in the search for the most promising approach to classify these challenging coins. The best results are achieved using dense SIFT descriptors organized into Bags of Visual Words, and using Support Vector Machine or Naïve Bayes as machine learning strategies.O uso de visão por computador para identificação e reconhecimento de moedas é bastante estudado e de reconhecido interesse. No entanto o foco da investigação tem sido sistematicamente sobre as moedas modernas e os algoritmos usados apresentam resultados bastante desapontantes quando aplicados a moedas antigas. Esta discrepância é justificada pela natureza das moedas antigas que, sendo cunhadas à mão, apresentam bastantes variações, falhas e séculos de degradação que deformam os padrões característicos, tornando a sua identificação dificil mesmo para o ser humano. Adicionalmente, a quase totalidade dos estudos usa ambientes controlados e iluminação uniformizada entre todas as imagens dos datasets. Embora faça sentido focar-se nas variáveis mais problemáticas, esta é uma premissa impossível de encontrar fora do laboratório do investigador e portanto uma problemática que tem que ser estudada. Esta dissertação foca-se no reconhecimento de moedas medievais e clássicas em imagens não controladas, tentando assim abrir caminho ao uso de vastos repositórios de imagens de moedas disponíveis na internet, que poderiam ser usados para tornar os nossos algoritmos mais robustos. Na primeira parte é proposto um método rápido e automático para segmentar moedas antigas sobre fundos complexos, numa abordagem que envolve Histogram Backprojection combinado com deteção de arestas. Os resultados são comparados com uma automação do algoritmo GrabCut. O método proposto obtém uma classificação de Bom ou Aceitável em 76% das imagens, demorando uma média de 0.29s por imagem, contra 49% em 19,58s do GrabCut. Não obstante o foco em segmentação de moedas antigas, este método pode ser usado noutros contextos que incluam objetos planos de cor uniforme. Na segunda parte, o estado da arte de Machine Learning é testado e comparado em busca da abordagem mais promissora para classificar estas moedas. Os melhores resultados são alcançados usando descritores dense SIFT, organizados em Bags of Visual Words e usando Support Vector Machine ou Naive Bayes como estratégias de machine learning