Tesis y Trabajos de Investigación PUCP
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Ítem Texto completo enlazado Novel Edge-Preserving Filtering Model Based on the Quadratic Envelope of the l0 Gradient Regularization(Pontificia Universidad Católica del Perú, 2023-01-26) Vásquez Ortiz, Eduar Aníbal; Rodríguez Valderrama, Paul AntonioIn image processing, the l0 gradient regularization (l0-grad) is an inverse problem which penalizes the l0 norm of the reconstructed image’s gradient. Current state-of-the art algorithms for solving this problem are based on the alternating direction method of multipliers (ADMM). l0-grad however, reconstructs images poorly in cases where the noise level is large, giving images with plain regions and abrupt changes between them, that look very distorted. This happens because it prioritizes keeping the main edges but risks losing important details when the images are too noisy. Furthermore, since kÑuk0 is a non-continuous and non-convex regularizer, l0-grad can not be directly solved by methods like the accelerated proximal gradient (APG). This thesis presents a novel edge-preserving filtering model (Ql0-grad) that uses a relaxed form of the quadratic envelope of the l0 norm of the gradient. This enables us to control the level of details that can be lost during denoising and deblurring. The Ql0-grad model can be seen as a mixture of the Total Variation and l0-grad models. The results for the denoising and deblurring problems show that our model sharpens major edges while strongly attenuating textures. When it was compared to the l0-grad model, it reconstructed images with flat, texture-free regions that had smooth changes between them, even for scenarios where the input image was corrupted with a large amount of noise. Furthermore the averages of the differences between the obtained metrics with Ql0- grad and l0-grad were +0.96 dB SNR (signal to noise ratio), +0.96 dB PSNR (peak signal to noise ratio) and +0.03 SSIM (structural similarity index measure). An early version of the model was presented in the paper Fast gradient-based algorithm for a quadratic envelope relaxation of the l0 gradient regularization which was published in the international and indexed conference proceedings of the XXIII Symposium on Image, Signal Processing and Artificial Vision.Ítem Texto completo enlazado Análisis del algoritmo FISTA orientado a mejorar la velocidad de convergencia(Pontificia Universidad Católica del Perú, 2022-03-08) Rámirez Orihuela, Gabriel; Rodríguez Valderrama, Paul AntonioLos problemas lineales inversos existen en numerosas ramas de la ciencia e ingeniería, lo cual genera la necesidad de definir algoritmos de solución e cientes, que requieran poco costo computacional y converjan en el menor número de iteraciones. Se desea recuperar información original a la cual no se tiene acceso lo más similarmente posible y con dimensiones reducidas, produciendo así una disminución en el uso de recursos computacionales y por ende en el tiempo de ejecución. Esto es de particular importancia debido a que el tamaño de las señales se encuentra en constante aumento y su manipulación puede resultar muy costosa. Se estudia el algoritmo de optimización de primer orden FISTA (Fast Iterative Shrinkage-Thresholding Algorithm), el cual es utilizado en problemas inversos cuya solución se resume a la minimización de funciones convexas empleando información de la gradiente y de iteraciones previas. En este contexto, se analizan métodos que buscan la optimización del algoritmo por medio de tamaños de paso adaptativos para delimitar el paso de la gradiente y una mejor solución inicial mediante la reducción de dimensiones a través de las técnicas conocidas como Screening y Warm Start, produciendo así datos más sparse. Además, se comprueba la e cacia de los métodos desarrollados por medio de un algoritmo generalizado, en el cual son evaluados datos aleatorios generados sintéticamente e imágenes, con el n de obtener la mejor tasa de convergencia.Ítem Texto completo enlazado Efficient algorithms for convolutional dictionary learning via accelerated proximal gradient(Pontificia Universidad Católica del Perú, 2019-04-05) Silva Obregón, Gustavo Manuel; Rodríguez Valderrama, Paul AntonioConvolutional sparse representations and convolutional dictionary learning are mathematical models that consist in representing a whole signal or image as a sum of convolutions between dictionary filters and coefficient maps. Unlike the patch-based counterparts, these convolutional forms are receiving an increase attention in multiple image processing tasks, since they do not present the usual patchwise drawbacks such as redundancy, multi-evaluations and non-translational invariant. Particularly, the convolutional dictionary learning (CDL) problem is addressed as an alternating minimization between coefficient update and dictionary update stages. A wide number of different algorithms based on FISTA (Fast Iterative Shrinkage-Thresholding Algorithm), ADMM (Alternating Direction Method of Multipliers) and ADMM consensus frameworks have been proposed to efficiently solve the most expensive steps of the CDL problem in the frequency domain. However, the use of the existing methods on large sets of images is computationally restricted by the dictionary update stage. The present thesis report is strategically organized in three parts. On the first part, we introduce the general topic of the CDL problem and the state-of-the-art methods used to deal with each stage. On the second part, we propose our first computationally efficient method to solve the entire CDL problem using the Accelerated Proximal Gradient (APG) framework in both updates. Additionally, a novel update model reminiscent of the Block Gauss-Seidel (BGS) method is incorporated to reduce the number of estimated components during the coefficient update. On the final part, we propose another alternative method to address the dictionary update stage based on APG consensus approach. This last method considers particular strategies of theADMMconsensus and our first APG framework to develop a less complex solution decoupled across the training images. In general, due to the lower number of operations, our first approach is a better serial option while our last approach has as advantage its independent and highly parallelizable structure. Finally, in our first set of experimental results, which is composed of serial implementations, we show that our first APG approach provides significant speedup with respect to the standard methods by a factor of 1:6 5:3. A complementary improvement by a factor of 2 is achieved by using the reminiscent BGS model. On the other hand, we also report that the second APG approach is the fastest method compared to the state-of-the-art consensus algorithm implemented in serial and parallel. Both proposed methods maintain comparable performance as the other ones in terms of reconstruction metrics, such as PSNR, SSIM and sparsity, in denoising and inpainting tasks.Ítem Texto completo enlazado Object detection in videos using principal component pursuit and convolutional neural networks(Pontificia Universidad Católica del Perú, 2018-05-03) Tejada Gamero, Enrique David; Rodríguez Valderrama, Paul AntonioObject recognition in videos is one of the main challenges in computer vision. Several methods have been proposed to achieve this task, such as background subtraction, temporal differencing, optical flow, particle filtering among others. Since the introduction of Convolutonal Neural Networks (CNN) for object detection in the Imagenet Large Scale Visual Recognition Competition (ILSVRC), its use for image detection and classification has increased, becoming the state-of-the-art for such task, being Faster R-CNN the preferred model in the latest ILSVRC challenges. Moreover, the Faster R-CNN model, with minimum modifications, has been succesfully used to detect and classify objects (either static or dynamic) in video sequences; in such setup, the frames of the video are input “as is” i.e. without any pre-processing. In this thesis work we propose to use Robust PCA (RPCA, a.k.a. Principal Component Pursuit, PCP), as a video background modeling pre-processing step, before using the Faster R-CNN model, in order to improve the overall performance of detection and classification of, specifically, the moving objects. We hypothesize that such pre-processing step, which segments the moving objects from the background, would reduce the amount of regions to be analyzed in a given frame and thus (i) improve the classification time and (ii) reduce the error in classification for the dynamic objects present in the video. In particular, we use a fully incremental RPCA / PCP algorithm that is suitable for real-time or on-line processing. Furthermore, we present extensive computational results that were carried out in three different platforms: A high-end server with a Tesla K40m GPU, a desktop with a Tesla K10m GPU and the embedded system Jetson TK1. Our classification results attain competitive or superior performance in terms of Fmeasure, achieving an improvement ranging from 3.7% to 97.2%, with a mean improvement of 22% when the sparse image was used to detect and classify the object with the neural network, while at the same time, reducing the classification time in all architectures by a factor raging between 2% and 25%.Ítem Texto completo enlazado Implementación del detector de esquinas de Harris en la plataforma Jetson TK1(Pontificia Universidad Católica del Perú, 2017-06-27) Chahuara Silva, Hector Francisco; Rodríguez Valderrama, Paul AntonioLas esquinas son puntos invariantes, estructurales y con alto contenido de información en una imagen. Estas son usadas en aplicaciones importantes de Procesamiento de imágenes o video entre las cuales destacan Navegación de UAVs (Unmanned Aerial Vehicles) [1] o Detección de objetos [2] que son importantes en distintas áreas y tienen requerimientos de tiempo real. Entre las soluciones para detección de esquinas propuestas destaca el detector de esquinas de Harris [3], el cual demuestra ser robusto y eficiente. El uso de plataformas que permiten realizar procesamiento paralelo permiten implementar métodos de alto costo computacional con un bajo tiempo de procesamiento. Entre ellas destacan los GPU (Graphic Processor Unit) que generalmente tienen un alto consumo energético, lo cual es inconveniente en aplicaciones dirigidas a dispositivos móviles como celulares, robots, drones, entre otros. Por ello, plataformas basadas en mobile CPU que tienen bajo consumo energético son opciones a tomar en cuenta. En la presente tesis se propone el diseño e implementación del Detector de esquinas de Harris en la plataforma Jetson TK1 de Nvidia [4] la cual se distingue por su bajo consumo energético y alto rendimiento. El método será implementado en MATLAB, ANSI-C y CUDA. Los resultados muestran que la implementación en CUDA presentada es hasta 32.08 veces aproximadamente más rápida que la implementación en ANSI-C y permite procesar imágenes de resolución full HD (1920 x 1080) en tiempo real. Además, es comparable a implementaciones en software en plataformas con mayores recursos e implementaciones en hardware usando FPGAs (Field Programmable Gate Array). La estructura del presente documento es la siguiente: En el primer capítulo se presenta el estado del arte sobre detección de esquinas y el Detector de esquinas de Harris. En el segundo capítulo se presenta la plataforma Jetson TK1. El diseño del algoritmo paralelo se detalla en el tercer capítulo. Por último, se presenta la implementación y sus resultados en el cuarto capítulo, seguido de las conclusiones y recomendaciones.