Introducción a la difusión en el tratamiento de imágenes

La idea que motiva el estudio de la difusión anisótropa en el tratamiento de imágenes es la búsqueda de métodos de suavizamiento de imágenes (“filtros”) que atenúen el ruido a la vez que respeten la información de bordes (“señal”) de la imagen

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates

A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves

We develop a novel remote sensing technique for the observation of waves on the ocean surface. Our method infers the 3-D waveform and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are given by minimizers of a composite energy functional that combines a photometric matching term along with regularization terms involving the smoothness of the unknowns. The desired ocean surface shape and radiance are the solution of a system of coupled partial differential equations derived from the optimality conditions of the energy functional. The proposed method is naturally extended to study the spatiotemporal dynamics of ocean waves and applied to three sets of stereo video data. Statistical and spectral analysis are carried out. Our results provide evidence that the observed omnidirectional wavenumber spectrum S(k) decays as k-2.5 is in agreement with Zakharov's theory (1999). Furthermore, the 3-D spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents

Directional Geodesic Active Contours

We present a non-conformal metric that generalizes the geodesic active contours approach for image segmentation. The new metric is obtained by adding to the Euclidean metric an additional term that penalizes the misalignment of the curve with the image gradient and multiplying the resulting metric by a conformal factor that depends on the edge intensity. In this way, a closer fitting to the edge direction results. The provided experimental results address the computation of the geodesics of the new metric by applying a gradient descent to externally provided curves. The good performance of the proposed techniques is demonstrated in comparison with other active contours methods

Offshore Measurements of Ocean Waves using Stereo Vision Systems

In recent years, remote sensing imaging systems for the measurement of oceanic sea states have attracted renovated attention. Imaging technology is economical, non-invasive and enables a better understanding of the space-time dynamics of ocean waves over an area rather than at selected point locations of previous monitoring methods (buoys, wave gauges, etc.). We present recent progress in space-time measurement of ocean waves using stereo vision systems on offshore platforms, which focus on sea states with wavelengths in the range of 0.01 m to 10 m. Classical epipolar techniques and modern variational methods are reviewed to reconstruct the sea surface from the stereo pairs sequentially in time. The statistical and spectral properties of the resulting observed waves are analyzed. Current improvements of the variational methods are discussed as future lines of research

Sistema de Autocalibración de Cámaras y Reconstrucción 3D

El presente proyecto está englobado dentro del campo de la visión artificial, la cual pretende emular el comportamiento de la visión humana utilizando una cámara como sensor y un ordenador como procesador. Suponemos que se dispone de un conjunto de imágenes digitales o una secuencia de vídeo que re�fleja una escena estática. El objetivo del proyecto es fascinante: sólo con la información contenida en las imágenes, obtener un modelo en tres dimensiones de la escena y las características de la cámara con que fueron adquiridas las imágenes. Suponemos que se desconoce la posición espacial de la cámara respecto de la escena (parámetros extrínsecos), así como los parámetros intrínsecos de la misma. Los dos elementos principales del título del proyecto ya han sido presentados: el término autocalibración significa obtener los parámetros que definen la cámara (distancia focal, punto principal, posición del espacio, etc.) sin ningún conocimiento a priori de la escena adquirida, mientras que el término reconstrucción 3D significa obtener un modelo tridimensional de la escena bajo estudio: forma y localización de los objetos que están delante de la cámara. Las herramientas necesarias para lograr el citado objetivo son: el tratamiento digital de imágenes, la geometría proyectiva y las técnicas de optimización. El tratamiento digital de imágenes permite extraer la información adecuada de las proyecciones de la escena, características tales como puntos y/o rectas. Esto reduce el problema a uno puramente geométrico. La geometría proyectiva permite crear modelos sencillos que describen el sistema de formación de la imagen en la cámara y plantear diversos algoritmos para invertir dicha operación. Las técnicas de optimización consiguen que dichos algoritmos sean útiles desde el punto de vista numérico y práctico. No es objeto del proyecto la extracción de características de las imágenes digitales de partida, ni su correspondencia entre imágenes, ni la representación tridimensional de la escena reconstruida mediante mallado y pegado de texturas. El proyecto se centra en abordar las etapas intermedias entre estos extremos. Este proyecto es innovador en la teoría de autocalibración de cámaras y reconstrucción 3D. El ejemplo del capítulo 8 es muy ilustrativo y se recomienda su consulta en caso de que el lector se sienta abrumado por los capítulos intermedios. Así no se pierde de vista el objetivo final

Applications of image-based, multi-view stereo reconstruction methods = (Aplicaciones de los métodos de reconstrucción estéreo multivista)

These slides present several 3-D reconstruction methods to obtain the geometric structure of a scene that is viewed by multiple cameras. We focus on the combination of the geometric modeling in the image formation process with the use of standard optimization tools to estimate the characteristic parameters that describe the geometry of the 3-D scene. In particular, linear, non-linear and robust methods to estimate the monocular and epipolar geometry are introduced as cornerstones to generate 3-D reconstructions with multiple cameras. Some examples of systems that use this constructive strategy are Bundler, PhotoSynth, VideoSurfing, etc., which are able to obtain 3-D reconstructions with several hundreds or thousands of cameras. En esta presentación se tratan varios métodos de reconstrucción 3-D para la obtención de la estructura geométrica de una escena que es visualizada por varias cámaras. Se enfatiza la combinación de modelado geométrico del proceso de formación de la imagen con el uso de herramientas estándar de optimización para estimar los parámetros característicos que describen la geometría de la escena 3-D. En concreto, se presentan métodos de estimación lineales, no lineales y robustos de las geometrías monocular y epipolar como punto de partida para generar reconstrucciones con tres o más cámaras. Algunos ejemplos de sistemas que utilizan este enfoque constructivo son Bundler, PhotoSynth, VideoSurfing, etc., los cuales, en la práctica pueden llegar a reconstruir una escena con varios cientos o miles de cámaras

In-loop Feature Tracking for Structure and Motion with Out-of-core Optimization

In this paper, a novel and approach for obtaining 3D models from video sequences captured with hand-held cameras is addressed. We define a pipeline that robustly deals with different types of sequences and acquiring devices. Our system follows a divide and conquer approach: after a frame decimation that pre-conditions the input sequence, the video is split into short-length clips. This allows to parallelize the reconstruction step which translates into a reduction in the amount of computational resources required. The short length of the clips allows an intensive search for the best solution at each step of reconstruction which robustifies the system. The process of feature tracking is embedded within the reconstruction loop for each clip as opposed to other approaches. A final registration step, merges all the processed clips to the same coordinate fram

Weak Statistical Constraints for Variational Stereo Imaging of Oceanic Waves

We develop an observational technique for the stereoscopic reconstruction of the wave form of oceanic sea states via a variational stereo method. In the context of active surfaces, the shape and radiance of the wave surface are obtained as minimizers of an energy functional that combines image observations and smoothness priors. To obey the quasi Gaussianity of oceanic waves observed in nature, a given statistical wave law is enforced in the stereo variational framework as a weak constraint. Multigrid methods are then used to solve the partial differential equations derived from the optimality conditions of the augmented energy functional. An application of the developed method to two sets of experimental stereo data is finally presented

Optimal polygonal L1 linearization and fast interpolation of nonlinear systems

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using polygonal (continuous piecewise linear) models under the L1 norm. A thorough error analysis is developed to guide an optimal design of two kinds of polygonal approximations in the asymptotic case of a large budget of evaluation subintervals N. The method allows the user to obtain the level of linearization (N) for a target approximation error and vice versa. It is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), allowing real-time performance of computationally demanding applications. The quality and efficiency of the technique has been measured in detail on two nonlinear functions that are widely used in many areas of scientific computing and are expensive to evaluate