A variational approach to 3D geometry reconstruction from two or multiple views

[EN] In the last years we have developed some methods for 3D reconstruction. First we began with the problem of reconstructing a 3D scene from a stereoscopic pair of images. We developed some methods based on energy functionals which produce dense disparity maps by preserving discontinuities from image boundaries. Then we passed to the problem of reconstructing a 3D scene from multiple views (more than 2). The method for multiple view reconstruction relies on the method for stereoscopic reconstruction. For every pair of consecutive images we estimate a disparity map and then we apply a robust method that searches for good correspondences through the sequence of images. Recently we have proposed several methods for 3D surface regularization. This is a postprocessing step necessary for smoothing the final surface, which could be afected by noise or mismatch correspondences. These regularization methods are interesting because they use the information from the reconstructing process and not only from the 3D surface. We have tackled all these problems from an energy minimization approach. We investigate the associated Euler-Lagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method.

3D reconstruction from a vascular tree model

[EN] In this paper, we present a vascular tree model made with synthetic materials and which allows us to obtain images to make a 3D reconstruction.We have used PVC tubes of several diameters and lengths that will let us evaluate the accuracy of our 3D reconstruction. In order to calibrate the camera we have used a corner detector. Also we have used Optical Flow techniques to follow the points through the images going and going back. We describe two general techniques to extract a sequence of corresponding points from multiple views of an object. The resulting sequence of points will be used later to reconstruct a set of 3D points representing the object surfaces on the scene. We have made the 3D reconstruction choosing by chance a couple of images and we have calculated the projection error. After several repetitions, we have found the best 3D location for the point.

Model of vessels for the 3D reconstruction

[EN] In this paper, we present a vascular tree model made with synthetic materials and which allows us to obtain images to make a 3D reconstruction. In order to create this model, we have used PVC tubes of several diameters and lengths that will let us evaluate the accuracy of our 3D reconstruction. We have made the 3D reconstruction from a series of images that we have from our model and after we have calibrated the camera. In order to calibrate it we have used a corner detector. Also we have used Optical Flow techniques to follow the points through the images going and going back. Once we have the set of images where we have located a point, we have made the 3D reconstruction choosing by chance a couple of images and we have calculated the projection error. After several repetitions, we have found the best 3D location for the point.

A variational approach to 3D cylindrical geometry reconstruction from multiple views

[EN] In this paper we present a variational technique for the reconstruction of 3D cylindrical surfaces. Roughly speaking by a cylindrical surface we mean a surface that can be parameterized using the projection on a cylinder in terms of two coordinates, representing the displacement and angle in a cylindrical coordinate system respectively. The starting point for our method is a set of different views of a cylindrical surface, as well as a precomputed disparity map estimation between pair of images. The proposed variational technique is based on an energy minimization where we balance on the one hand the regularity of the cylindrical function given by the distance of the surface points to cylinder axis, and on the other hand, the distance between the projection of the surface points on the images and the expected location following the precomputed disparity map estimation between pair of images. One interesting advantage of this approach is that we regularize the 3D surface by means of a bi-dimensio al minimization problem. We show some experimental results for large stereo sequences.

Performance Optimization of a Floating Breakwater Model Using SPH Method, with a Practical Application

Máster en Oceanografía

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

Regularization of 3D cylindrical surfaces

[EN] In this paper we present a method for the regularization of 3D cylindrical surfaces. By a cylindrical surface we mean a 3D surface that can be expressed as an application S(l; µ) ! R3 , where (l; µ) represents a cylindrical parametrization of the 3D surface. We built an initial cylindrical parametrization of the surface. We propose a new method to regularize such cylindrical surface. This method takes into account the information supplied by the disparity maps computed between pair of images to constraint the regularization of the set of 3D points. We propose a model based on an energy which is composed of two terms: an attachment term that minimizes the difference between the image coordinates and the disparity maps and a second term that enables a regularization by means of anisotropic diffusion. One interesting advantage of this approach is that we regularize the 3D surface by using a bi-dimensional minimization problem.

Regularizing a set of unstructured 3D points from a sequence of stereo images

[EN] In this paper we present a method for the regularization of a set of unstructured 3D points obtained from a sequence of stereo images. This method takes into account the information supplied by the disparity maps computed between pairs of images to constraint the regularization of the set of 3D points. We propose a model based on an energy which is composed of two terms: an attachment term that minimizes the distance from 3D points to the projective lines of camera points, and a second term that allows for the regularization of the set of 3D points by preserving discontinuities presented on the disparity maps. We embed this energy in a 2D finite element method. After minimizing, this method results in a large system of equations that can be optimized for fast computations. We derive an efficient implicit numerical scheme which reduces the number of calculations and memory allocations.

Diseño y desarrollo de un videojuego en 3D basado en la defensa de una plataforma, haciendo énfasis en el estudio de controles para pantalla táctil de los dispositivos móviles

[ES] El siguiente trabajo de fin de grado consiste en el análisis, desarrollo e implementación de una pequeña parte de un  videojuego, que tiene como título Darkest Nights, que se basa en la defensa de una plataforma, haciendo uso del motor gráfico Unity 3D. Con este trabajo se pretenden analizar los distintos componentes que influyen en el proceso de desarrollo e implementación del mismo, haciendo uso de distintas herramientas como, el canvas gamificado o una ficha de concepto que nos permitan definir y establecer un conjunto de características que nos servirán como punto de partida, desde el cual podremos identificar desde una temprana fase las partes más importantes y que requerirán más atención del videojuego. Dentro de este proyecto también se pretende realizar la implementación de distintos tipos de controles de un jugador en un entorno 3D, el jugador debe realizar distintas acciones como moverse, esquivar y atacar a sus enemigos para defender con éxito una plataforma. Estos controles se implementaran con la finalidad de analizar y evaluar su viabilidad en las pantallas táctiles de los dispositivos móviles. En concreto se realiza la implementación y explicación de 4 tipos distintos de controles donde se comentan sus  ventajas, desventajas y las sensaciones que causaban en los jugadores, llevándonos a sacar conclusiones que nos permitían mejorar las siguientes implementaciones.  Además se explica con detalle la generación de personajes y enemigos en 3D con sus respectivas animaciones, explicando los distintos componentes necesarios para su implementación, al igual que la lógica básica necesaria para que sigan un determinado comportamiento.

Dynamic analysis of piled foundations in stratified soils by a BEM-FEM model

[EN] 3D BEM-FEM coupling model is used to study the dynamic behavior of piled foundations in elastic layered soils in presenceof a rigid bedrock. Piles are modelled by FEM as beams according to the Bernoulli hpothesis, and every layer of the soil is modelled by BEM as a cointinuum, semi-infinite, isotropic, homogeneous, linear, viscoelastic medium.