253 research outputs found
Signal and image restoration using shock filters and anisotropic diffusion
No full textThe authors define a new class of filters for noise elimination and edge enhancement by using shock filters and anisotropic diffusion. Some nonlinear partial differential equations used as models for these filters are studied. The authors develop recursive and unconditional stable schemes which drastically reduce the computational effort of the algorithms. A new fast recursive approach to linear Gaussian filters is also shown by using the heat equation.605590SCI
Classification of complex Wishart matrices with a diffusion-reaction system guided by stochastic distances
No full text0,782,441Q1Q1SCI
A formal introduction to zero-knowledge proofs
No full textTreballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Bruno Mazorra i Luis Victor DieulefaitThe idea of zero-knowledge proof was first introduced by Goldwasser, Micali and Rackoff [GMR89] and has found its way to many real-world applications. The growing need for privacy in information exchange (e.g. transactions, digital signatures, commitment schemes, ...) lead to the development of proofs that yield nothing more than their validity.
We introduce the building blocks for zero-knowledge proofs through mathematical rigour, allowing the reader to gain a solid foundation to research further related topics. We explore some necessary notions of cryptography and probability, as well as computation theory by utilizing Turing machines as an automation abstraction. We delve into the theory of decision problems and the consequent classification through complexity classes, specially and . We use the concepts of repetition and interaction to prove that the decision error for languages in and can be decreased exponentially and explore the example of Graph Non-Isomorphism. We introduce the idea of zero-knowledge interactive proof systems and define some variations of its definition. We explore the example of Graph Isomorphism and conclude showing that the sequential repetition of zero-knowledge interactive proofs is indeed a zero-knowledge interactive proof
A formal introduction to zero-knowledge proofs
No full textTreballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Bruno Mazorra i Luis Victor DieulefaitThe idea of zero-knowledge proof was first introduced by Goldwasser, Micali and Rackoff [GMR89] and has found its way to many real-world applications. The growing need for privacy in information exchange (e.g. transactions, digital signatures, commitment schemes, ...) lead to the development of proofs that yield nothing more than their validity.
We introduce the building blocks for zero-knowledge proofs through mathematical rigour, allowing the reader to gain a solid foundation to research further related topics. We explore some necessary notions of cryptography and probability, as well as computation theory by utilizing Turing machines as an automation abstraction. We delve into the theory of decision problems and the consequent classification through complexity classes, specially and . We use the concepts of repetition and interaction to prove that the decision error for languages in and can be decreased exponentially and explore the example of Graph Non-Isomorphism. We introduce the idea of zero-knowledge interactive proof systems and define some variations of its definition. We explore the example of Graph Isomorphism and conclude showing that the sequential repetition of zero-knowledge interactive proofs is indeed a zero-knowledge interactive proof
Normalization and feature extraction on ear images
No full textEar image analysis is an emerging biometrie application. A method for normalizing ear images and extracting from them a set of measurable features (feature vector) that can be used to identify its owner is proposed. The identification would be made based on the comparison between the feature vector of the input image and all feature vectors of the images in the database we work with. The feature vector is based on the ear contours. One important goal of this paper is to identify the most significant areas in the ear contour for human being identification purpose. Another important contribution of the paper is the combination of active contours techniques and ovoid model ear fitting (used to normalize ear features) and a high accurate invariant approach of internal and external ear contours. Ear geometry is characterized using a set of distances to external and internal contours points. This set of distances, along with six ovoid parameters is considered as the feature vector of the image. To test the method a new ear images database has been created. The proposed method identifies front-parallel views pretty good, even when varying the distance of the individual to the camera or the camera lens.1049
Fitting ear contour using an ovoid model
No full textEar analysis is an emergent biometric application. The main advantages are the no requirement for subject contact and acquisition without demand. To recognize a subject's ear, we aim to extract a characteristic vector from a human ear image that may subsequently be used to identify or confirm the identity of the owner. Towards this end, a new technique, combining geodesic active contours and a new ovoid model, has been developed, which can be used to compare ears in an independent way of the ear location and size.14814
Classification of PolSAR imagery by solving a diffusion-reaction system
No full textPolSAR (Polarimetric Syntethic Aperture Radar) imagery classification plays an essential role in monitoring remote sensing data. Such classification is a difficult task due to the speckle noise which appears in these kind of data. Therefore, there is a need to design new efficient methods to classify PolSAR images. In this work, a new approach to classify PolSAR data is proposed. The method relies on simultaneously filtering and classifying pixels within the image through embedding the problem into a diffusion-reaction partial differential equation system. The diffusion term smooths the patches within the image, and the reaction term tends to move the pixel PolSAR values towards the closest (in some sense) representative class. In particular, the method inherits the benefits of speckle filtering reduction by diffusion-like methods. An iterative schema is stated and, by properly selecting the algorithm control parameters, the user may force the classification to evolve according to her/his requirements to account for other image post-processing tasks (i.e. quantitative analysis to monitor deforestation, drought or urban areas growing). Results on real PolSAR data show the performance of the method, which is evaluated both visually and by means of the confusion matrix, showing an average classification rate 87.56 %807
Image restoration scale space
No full textWe present a study of some image restoration techniques based on Partial Differential Equations (PDE). We study separately the denoising problem and the restoration of discontinuities. We analize the capabilities of the differential operators to restore images. In particular, we analyze a number of models present in the literature, and we present comparative results. Finally, we present a model based in the combination of the anisotropic diffusion of Alvarez, Lions and Morel and the shock filters of Osher and Rudin.494
Puente Luis Ignacio Andrade
No full textPersonas, automóviles y camiones pasan por el puente Luis Ignacio Andrade. Se ve también la estructura en metal, que soporta un letrero que dice ‘Feliz viaje’. Al finalizar el puente se ven algunas casas y al fondo la montaña. En la parte inferior derecha está una mujer recostada sobre la estructura metálica.
El puente Luis Ignacio Andrade, erigido para conectar a Honda —y a Bogotá— con buena parte del país, fue donado por el gobierno de Estados Unidos y construido durante el gobierno de Laureano Gómez, aunque las gestiones se hicieron durante el gobierno de Mariano Ospina Pérez. La obra, hecha por la firma de ingenieros Cayo Antonio Mazorra y E. Santos Potess, comenzó en 1950 y terminó en 1952. Luis Ignacio Andrade era el ministro de Obras Públicas de la época y fue uno de los principales gestores de su construcción.Arquitectura moderna; Paisaje arquitectónico ciudade
Morphological Thick Line Center Detection
No full textThick line center and width estimation are important problems in computer vision. In this paper, we analyze this issue in real situations where we have to deal with some additional difficulties, such as the thick line distortion produced by interlaced broadcast video cameras or large shaded areas in the scene. We propose a technique to properly extract the thick lines and their centers using mathematical morphological operators. In order to illustrate the performance of the method, we present some numerical experiments in real images.807
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