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 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.

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.