Consideraciones acerca de la viabilidad de un sensor plenóptico en dispositivos de consumo

Doctorado en Ingeniería IndustrialPassive distance measurement of the objects in an image gives place to interesting applications that have the potential to revolutionize the field of photography. In this thesis a prototype of plenoptic camera for mobile devices was created and studied. This technique has two main disadvantages: the need for modifying the camera module and the loss of resolution. Because of this, the prototype was discarded in order to utilize another technique: depth from focus. In this technique the capture method consists in taking several images while varying the focus distance. The set of images is called focal-stack. Different focus operators are studied, which give a measure of defocus per pixel and plane of the focal-stack. The curvelet based focus operator is chosen as the most adequate. It is computationally more intensive than other operators but it is capable of decomposing natural images using few coefficients. In order to make viable its usage in mobile devices a new curvelet transform based on the discrete Radon transform is built. The discrete Radon transform has logarithmic complexity, does not use the Fourier transform and uses only integer sums. Lastly, different versions of the Radon transform are analyzed with the goal of achieving an even faster transform. These transforms are implemented to be executed on mobile devices. Additionally, an application of the Radon transform is presented. It consists in the detection of bar-codes that have any orientation in an image.La medida pasiva de distancia a los objetos en una imagen da lugar a interesantes aplicaciones con capacidad para revolucionar la fotografía. En esta tesis se creó y estudió un prototipo de cámara plenóptica para dispositivos móviles. Esta técnica presenta dos inconvenientes: la necesidad de modificar el módulo de cámara y la pérdida de resolución. Por ello, el prototipo fue descartado para utilizar otra técnica: la profundidad a partir del desenfoque. En esta técnica el método de captura consiste en tomar varias imagenes variando la distancia de enfoque. El conjunto de imágenes se denomina focal-stack. Se estudian distintos operadores de desenfoque, que dan una medida de desenfoque por pixel y por plano del focal-stack. Siendo elegido como óptimo el operador de desenfoque curvelet, que es computacionalmente más intensivo que otros operadores pero es capaz de descomponer imagenes naturales utilizando muy pocos coeficientes. Para hacer posible su uso en dispositivos móviles se construye una nueva transformada curvelet basada en la transformada discreta de Radon. La transformada discreta de Radon tiene complejidad linearítmica, no utiliza la transformada de Fourier y usa sólo sumas de enteros. Por último, se analizan distintas versiones de la transformada de Radon con el objetivo de conseguir una transformada aún más rápida y se implementan para ser ejecutadas en dispositivos móviles. Además se presenta una aplicación de la transformada de Radon consistente en la detección de códigos de barras con cualquier orientación en una imagen

A fast but ill-conditioned formal inverse to Radon transforms in 2D and 3D

We present a formal inversion of the multiscale discrete Radon trasform, valid both for 2D and 3D. With the transformed data from just one of the four quadrants of the direct 2D Radon transform, or one of the twelve dodecants, in case of 3D Radon transform, we can invert exactly and directly, with no iterations, the whole domain. The computational complexity of the proposed algorithms will be O(N log N). With N the total size of the problem, either square or cubic. But this inverse transforms are extremely ill conditioned, so the presence of noise in the transformed domain turns them useless. Still we present both algorithms, and characterize its weakness against noise

Weighted nonnegative tensor factorization for atmospheric tomography reconstruction

Context. Increasing the area on the sky over which atmospheric turbulences can be corrected is a matter of wide interest in astrophysics, especially when a new generation of extremely large telescopes (ELT) is to come in the near future. Aims. In this study we tested if a method for visual representation in three-dimensional displays, the weighted nonnegative tensor factorization (WNTF), is able to improve the quality of the atmospheric tomography (AT) reconstruction as compared to a more standardized method like a randomized Kaczmarz algorithm. Methods. A total of 1000 different atmospheres were simulated and recovered by both methods. Recovering was computed for two and three layers and for four different constellations of laser guiding stars (LGS). The goodness of both methods was tested by means of the radial average of the Strehl ratio across the field of view of a telescope of 8m diameter with a sky coverage of 97.8 arcsec. Results. The proposed method significantly outperformed the Kaczmarz in all tested cases (p ≤ 0.05). In WNTF, three-layers configuration provided better outcomes, but there was no clear relation between different LGS constellations and the quality of Strehl ratio maps. Conclusions. The WNTF method is a novel technique in astronomy and its use to recover atmospheric turbulence profiles was proposed and tested. It showed better quality of reconstruction than a conventional Kaczmarz algorithm independently of the number and height of recovered atmospheric layers and of the constellation of laser guide star used. The WNTF method was shown to be a useful tool in highly ill-posed AT problems, where the difficulty of classical algorithms produce high Strehl value maps